bulent eris model development for planning and forecasting in diagnostic and treatment systems...

8/8/2019 Bulent Eris Model Development for Planning and Forecasting in Diagnostic and Treatment Systems 9022004

http://slidepdf.com/reader/full/bulent-eris-model-development-for-planning-and-forecasting-in-diagnostic-and 1/182

T.C.MARMARA UNIVERSITY

INSTITUTE FOR GRADUATE STUDIES INPURE AND APPLIED SCIENCES

MODEL DEVELOPMENT FOR PLANNING ANDFORECASTING IN DIAGNOSTIC AND TREATMENT

SYSTEMS

Salih Bülent ER ŞMSc.(Management Engineering)

THESISFOR THE DEGREE OF DOCTOR OF PHILOSOPHY

ININDUSTRIAL ENGINEERING

SUPERVISOR

Prof.Dr. Erkan TÜRE

STANBUL 2004



T.C.MARMARA UNIVERSITY

INSTITUTE FOR GRADUATE STUDIES INPURE AND APPLIED SCIENCES

MODEL DEVELOPMENT FOR PLANNING ANDFORECASTING IN DIAGNOSTIC AND TREATMENT

SYSTEMS

Salih Bülent ER ŞMSc.(1412009 19920009)

THESISFOR THE DEGREE OF DOCTOR OF PHILOSOPHY

ININDUSTRIAL ENGINEERING

SUPERVISOR

Prof.Dr. Erkan TÜRE

STANBUL 2004



ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my thesis advisor, Prof. Dr. ErkanTüre, for his supervision, guidance, continued support and motivation throughout this study.

I wish to extend my thanks and Prof Dr. Sevil Ünal, Prof Dr. Sami Ercan, Prof. Dr.

Taylan Ula and Asst. Prof. Dr Güldal Büyükdamgacı for serving on my thesis committee and

for their valuable advices and comments.

Special appreciation is due to my General Manager Asst. Prof. Dr. Giray Velioğlu,

and Asst. General Manager Umur Çullu and my colleagues Burak Sayın, Deniz Sümengen,Esra Güler, Ulas Öncül, Ercan Tekin, Utku Birdal and Ali Özmen for their valuable technical

advice.

Finally, I would like to thank to my wife Nalan and son Onat for their patience,

encouragement and support

Eylül, 2003 Salih Bülent Eriş



TABLE OF CONTENTS

ACKNOWLEDGEMENTS.................................................I

TABLE OF CONTENTS....................................................II

ÖZET ..........................................................................................V

ABSTRACT .....................................................................................VI

ORIGINALITY CLAIM..................................................VII

LIST OF SYMBOLS............................................................. X

ABBREVATIONS..................................................................XI

LIST OF FIGURES............................................................XII

LIST OF TABLES..............................................................XIV

PART.I. INTRODUCTION AND OBJECTIVES ......................1

PART.II. GENERAL BACKGROUND ........................................4

II.1 PRIVATE HEALTH INSURANCE IN THE WORLD .......................4

II.2 TURKEY PRIVATE HEALTH INSURANCE BACKGROUND.......7

II.3 HEALTH RISK MODELS IN LITERATURE..................................11

II.3.1 Demographic Models .......................................................12

II.3.2 Prior Year Expenditures ...................................................14II.3.3 Diagnosis-Based Risk Adjustment....................................15

II.3.4 Information Derived from Prescription Drugs...................17

II.3.5 Self-Reported Health Information.....................................17

II.3.6 Mortality..........................................................................18



II.3.7 Other Models ...................................................................18

II.4 PRIVATE HEALTH INSURANCE PRICING .................................18

II.4.1 Practice of Pricing in the World........................................18

II.4.2 Theory of Health Insurance Pricing ..................................23

PART.III. ANALYSIS OF THE DATA........................................26

III.1 DIAGNOSIS AND TREATMENT SERVICES CATEGORIES.......27

III.1.1 Out- patient Treatment (without hospitalization) ............27

III.1.2 In-patient Treatment.............. ..........................................28

III.2 ESTIMATION OF PARAMETERS .................................................29

III.2.1 Prior year stats ................................................................30

III.2.2 Group size.......................................................................33

III.2.3 Parameters .............................................. ........................37

III.3 MOMENTS OF USAGE ..................................................................43

III.3.1 Comparison of the Data from Other Sources ...................50

PART.IV. THE MODEL................................................................52

IV.1 ALTERNATIVE MODELS..............................................................52

IV.1.1 Moments Based Approach ..............................................52

IV.1.2 Recursive Algorithm.......................................................55

IV.1.3 Inversion -Methods Fast Fourier- ....................................55

IV.2 SIMULATION MODEL STRUCTURE...........................................57

IV.2.1 Individual Expenses Module...........................................58IV.2.1.1 Pc, n, X 61 IV.2.1.2 Age and Gender 61 IV.2.1.3 Distribution Assumptions 61 IV.2.1.4 Limits and Deductibles 63 IV.2.1.5 Dependency 66 IV.2.1.6 Short Term Monthly Analysis 68

IV.2.2 Experience - Credibility Module .....................................75IV.2.2.1 Experience Rating with monthly and Quarter Yearly Periods 80

IV.2.3 Individual to Group Module............................................81

IV.2.4 Characteristics of the Model Output and Sensitivity........83IV.2.4.1 The Effect of Dependency 84 IV.2.4.2 The Effect of Group Size and Uncertainty on Individual to Group Module 87 IV.2.4.3 Sensitivity 90

PART.V. IMPLEMENTATION AND MODELVALIDATION ..........................................................95



V.1 IMPLEMENTATION.......................................................................95

V.1.1 Characteristic of the Sample Data ....................................95V.1.1.1 Age and Gender Profiles 95 V.1.1.2 Profile of Group 1 97 V.1.1.3 Profile of Group 2 97 V.1.1.4 Profile of Group 3 97

V.1.2 Scenarios .........................................................................97V.1.2.1 Output Analysis 99

PART.VI. CONCLUSION ...........................................................139

REFERENCES..............................................................................143

APPENDIX 1..........................................................................146

Definiton of the Actuary.............................................................146

Extreme Cases............................................................................148

APPENDIX 2..........................................................................150

APPENDIX 3..........................................................................157

CURRICULUM VITAE...............................................................161



ÖZET

TEŞH S VE TEDAV S STEMLER NDE PLANLAMA AMAÇLITAHM NE YÖNELK MODEL GEL ŞT R LMES

Bu çalışmanın amacı ülkemizdeki gerek özel sağlık sigortalarında gerekse sağlık

sandıklarındaki grupların kullanılmak üzere gelecekteki sağlık hizmetlerinden faydalanma

adetleri-miktarları ve maliyetlerini kısa ve orta vadede tahminde kullanılacak dinamik bir

model geliştirilmesidir. Bu çalışma simülasyon modelinin kurulması, duyarlılık analizi ve

7436 kişilik örnekli pilot uygulamalarla sınanmasıyla amaca ulaşmıştır. Güvenilir sonuçlara

ulaşabilmek amacıyla eldeki gerçek verilerden faydalanılarak çeşitli değişkenler

kullanılmıştır.

Geleneksel modellerde sadece grup büyüklüğüne dayanarak limit ve muafiyetinetkilerini göz ardı ettiğinden karşılaşılan risk ve dolayısıyla maliyetlerle ilgili yeterince bilgi

sağlamamaktadır. Bu çalışmada üç modül kullanılmıştır. Bireysel Harcamalar Modülü’nde

değişik yaş cinsiyet dağılımlarından oluşan gruplarda, değişik limit ve muafiyet sonucu ortaya

çıkacak maliyet tahminleri yapılmıştır. Bireysel’den Gruba Modülünde gerçek yaşamda

incelenmesi zor olan değişkenler arası bağımlılığın etkisi, tahmin üzerinde istatistiksel

dalgalanma ve bunların dışındaki, parametre hataları veya verinin uygunluğu gibi

belirsizliklerin etkilerinin nasıl incelenebileceği gösterilmiştir. Grubun önceki harcamalarının

değerlendirilmesi Deneyim-Kredibilite Modülü’nde kullanılmıştır.

Bu çalışmada ayrıca Türkiye’deki Sağlık hizmetleri konusunda ekonomi, ekonometri,

aktüerya ve yöneylem araştırması/endüstri mühendisliği konularında çok az sayıda araştırma

olduğundan tahmin konusundaki araştırmalara geniş olarak yer verilmiştir.

Eylül, 2003 Salih Bülent Eriş



ABSTRACT

MODEL DEVELOPMENT FOR PLANNING AND FORECASTING INDIAGNOSTIC AND TREATMENT SYSTEMS

In this study we intended to build a dynamic forecasting model for future health care

service costs and utilizations of the groups in the short and mid term ranges in private health

insurance and health funds. This study covers its scope by developing and testing validity of a

simulation model together with the sensitivity analysis and pilot applications on a sample of

7436 people. Real data have been used to describe a model with a number of variables so that

reliable forecasts can be made.

Traditional models that rely on just group size and ignore the effect of limit and

deductibles do not furnish adequate information on the potential risk and therefore the cost

involved. Three different modules have been used. In Individual Expenses Module cost

forecasts for the groups with different age and gender distributions where different limits and

deductibles are done. Factors which can not be tested in real life like interrelational

dependency between variables, statistical fluctuations due to group size, uncertainty due to

credibility and suitability of the data are examined in Individual to Group Module. Group

prior statistics are used in the Experience Rating – Credibility Module.

As there are very few academic or non-academic research studies on economics,econometrics, actuarial or operations research/industrial engineering fields concerning health

care services in Turkey we provided a wide range of literature for forecasting research on

health systems on different disciplines.

September, 2003 Salih Bülent Eriş



ORIGINALITY CLAIM

MODEL DEVELOPMENT FOR PLANNING AND FORECASTING INDIAGNOSTIC AND TREATMENT SYSTEMS

Health is a dynamic and relative concept both on individual and national base. The

objective of health care systems, their structures, functions, their effectiveness largely differ at

local, regional and national levels. Relations between the elements of the health care systems

and the interaction of these elements with the other elements like cultural behaviors of the

people in the society, environmental conditions etc have complex and dynamic

characteristics.

Strategic health care decision problems including medical, behavioral, socio-economic,

managerial and technical variables can be solved only by integrated and inter disciplinaryapproach. Quantitative techniques and methods have been applied with success for more than

30 years now in finding solutions to the health care decision problems of developed countries.

In Turkey, there is a multi provider health care system which is managed by the

Ministry of Health, social security organizations, armed forces, universities and private

organizations. This system has many problems like over utilization of health care services

leading to the huge health care expenses and budget deficits. Until now the government or the

other parties involved have offered solutions and approaches regarding the political medical,financial and organizational factors. But the approach of mathematical modeling and

prediction techniques that can be employed in health care systems to control the expenditures

and service utilization has been largely ignored .



The condition stated above is also valid for the insurance sector. When Turkish and big

European Health Insurance markets are observed, it is seen that there is enormous need for

development of forecasting models. It is nearly impossible to find neither detailed academic

studies nor application examples on decision-making and health insurance claims prediction

models. Models should be adaptive and should be suitable for all kinds of health insurance

products. Most of the common approaches in the market are far from supplying flexible

solutions for different health insurance products including various specifications. Simple

common assumptions, pricing and prediction approaches are believed to insufficient and so

they are criticized in this study

The problem in model building in health systems comes from the lack of data and the

uncertainty concerning the model structure, parameters and interrelations between variables.

The complexity (compound and mixed statistical nature of the health utilizations and costs)

makes it harder in addition to issues stated above.

The originality of this study is that it is the first example of a health care expenses

prediction simulation model in group health insurances in Turkish health insurance sector.

The model is purely constructed from the scratch using the actuarial, mathematical and

statistical techniques. The originality also lies in the real insurance claims data which was

derived from the health insurance expenses (claims) made by the insured population building

up the portfolio of a certain insurance company. In this context the data is unique andcontrollable since it is obtained through real observations and a well running IT system.

While building up the model, the stochastic nature of the process is examined and the

distribution characteristics of costs and utilizations in monthly and annual intervals are shown

depending on the real data.

The model has 3 different modules as follows;

A- Individual Expense Module: This module reduces the group medical expensesbehavior to individual and creates a representative individual expense form on an expense

type basis. The module variables are set as; probability of claiming (Pc), number of claims(n),

claim size(X) for demographical classes. Setting these variables is a new approach that allows

the usage of positively skewed or long tailed non-zero distributions, which are allocated to

severity and frequency of variables.



B-Experience and Credibility Module: This module combines the observed results of

the examined groups’ statistics with the standard portfolio values to improve the estimation.

This is done for the distributional characteristics of each utilization type (physician visit

prescribed drugs, etc) for each variable of the model (Pc, n and X). This is also another new

proposal to the actuarial study ground where the actuarial health studies are rarely

sophisticated.

C-Individual to Group Module: Taking into account the group size and the uncertainty

from other factors (trend, credibility and suitability of the data), this module examines the

possible variations on the empirical distribution output from the A and B modules to quantify

the stochastic nature. This prediction of uncertainty approach is also new to Turkish health

insurance sector.

The model presented in this study is a potentially useful tool for either private insurance

companies (which have approximately 700,000 insured) or health aid funds (which have more

than 270,000 members) in Turkey. The companies or health aid funds can determine the

distribution characteristics of health care needs for populations that are formed of people in

different age and gender groups. The suggested methods could also be used for social security

or governmental planning purposes when the data is based on a short-term period.

September, 2003 Prof.Dr. Erkan TÜRE Salih Bülent Eriş



LIST OF SYMBOLS

n :Claim Count(utilization of the observed health care service)

Pc :Probability of claimingX :Cost of the utilized health care service

αααα , λλλλ :Parameters of Gamma and Pareto distributions

σσσσ :Population STD

1 X φ :The characteristic functions of the input distributions

ω :The correlation matrix for two different benefits

γ γγ γ : Skewness

Z : Credibility



ABBREVATIONS

MSA : Medical Saving Accounts

MCO : Managed Care Organization

LER : Loss Elimination RatioLEV : Limited Expected Value

ACG : Ambulatory Care Group

DCG : Diagnostic Cost Group

DPS : Disability Payment System

HCC : Hierarchical Condition Categories.

ICD : International Classification of Diseases

CDS : Chronic Disease Score

NHE : National Health ExpenditureCPI : Consumer Price Increases

NCD: : No Claim Discount

RF: Rating Factors

PMPM: Per Member Per Month



LIST OF FIGURES

Figure II.1 Health Spending for Gender, Age Sample Netherlands........................................13

Figure II.2 Health Spending for Gender, Age Sample USA Privately Insureds......................13

Figure II.3 Health Spending for Gender, Age Sample USA Medicaid Eligibles ....................13Figure II.4 Distribution of population costs to the members for year one and two .................14

Figure II.5 Group and Individual Rating Structures ..............................................................19

Figure II.6 Distribution of Relative Costs Between Groups...................................................22

Figure III.1 Ratio of Users to the Population.........................................................................37

Figure III.2 Ratio of Physician Users in Age and Gender Band Population ...........................38

Figure III.3 Average Number of Visits for Different Age and Gender Bands ........................38

Figure III.4 Distribution of Number of Visits for Different Age and Gender Bands ..............39

Figure III.5 Average Cost Per Usage ....................................................................................39Figure III.6 Distribution of Visit Costs for Different Age and Gender Bands ........................40

Figure III.7 Gender and age effect on sample data ................................................................42

Figure IV.1 Output for Prescribed Drugs of a Group.............................................................56

Figure IV.2 Second Fourier Example....................................................................................57

Figure IV.3 Creation of the Input Parameters for Individual to Group Module + Experience-

Credibility Module........................................................................................................59

Figure IV.4 Iteration of the Individual Expense Module(fed with credibility if any) .............60

Figure IV.5 Hospital Claim Cost X graph produced with gamma and real data.....................62

Figure IV.6 Number of Physician Visits n graph produced with gamma and real data...........62

Figure IV.7 Limit and Deductible Application Process ................................. ........................64

Figure IV.8 Limit and Deductible Affect On Diagnostic Annual Costs.................................65

Figure IV.9 When various scenarios Applied Total Costs on Individual Basis ......................66

Figure IV.10 Development of Distributions..........................................................................69



Figure IV.11 Distribution of "n" in March and August..........................................................70

Figure IV.12 Flow Process for the Individual to Group Module............................................83

Figure IV.13 Std B coefficients for Total Costs Incurred ......................................................91

Figure IV.14 Std B coefficients for Total Costs After the Limits and Deductibles.................93

Figure V.1Graph of Group 1 Total Costs ............................................................................101

Figure V.2 Graph of Group 1 After First Scenario .............................................................104

Figure V.3 Graph of Group 1 After Second Scenario.........................................................108

Figure V.4 Graph of Group 2 Total Costs ...........................................................................110


Figure V.6 Graph of Group 2 After Second Scenario.........................................................117

Figure V.7 Graph of Group 3 Total Costs ...........................................................................119


Figure V.9 Graph of Group 3 After Second Scenario..........................................................126

Figure V.10 Physician Visit Comparison ............................................................................130

Figure V.11 Prescribed Drug Comparison ..........................................................................132

Figure V.12 Diagnostic procedure comparison ...................................................................134

Figure V.13 Minor treatment comparison ...........................................................................136

Figure V.14 Hospital benefit comparison............................................................................138



LIST OF TABLES

Table II-1 Types of VHI in the EU .........................................................................................5

Table II-2 VHI coverage in the EU in 1998 ................................ ............................................5

Table II-3 VHI expenditure as a percentage of total expenditure on health in the EU, 1980-

1998 ...............................................................................................................................6Table III-1 Out Patient Benefits............................................................................................27

Table III-2 In patient Benefits...............................................................................................28

Table III-3 Descriptive Stats for 2 year sample data in total expenditures .............................30

Table III-4 Regression for 2 year total expenditures..............................................................30

Table III-5 ANOVA for Regression for 2 year total expenditures ................. ........................31

Table III-6 Coefficients of Regression for 2 year total expenditures......................................31

Table III-7 Line Fit Plot For 2 Year Expenditures.................................................................31

Table III-8 Descriptive Stats for 2 year total number of utilizations ......................................32Table III-9 Regression Statistics for 2 year total number of utilizations ................................32

Table III-10 ANOVA for Regression Statistics for 2 year total number of utilizations ..........32

Table III-11 Coefficients for Regression Statistics for 2 year total number of utilizations .....32

Table III-12 Line Fit Plot For 2 Year Utilizations .................................................................33

Table III-13 Descriptive stats of the groups formed of males born between 1960 -1970........34

Table III-14 Different Group Size Characteristics.................................................................35

Table III-15 Single Factor ANOVA......................................................................................35

Table III-16 ANOVA table for different group sizes.............................................................36

Table III-17 Correlation of Average Physician Visits vs Group Size.....................................37

Table III-18 Comparison of Average Expenditures Between the Age Gender Classification.41

Table III-19 Correlation between the Average Figures..........................................................42

Table III-20Moments of Physician(Dr) Visits.......................................................................44

Table III-21 Moments of Prescribed Drugs...........................................................................45



Table III-22 Moments of Diagnostics ...................................................................................46

Table III-23 Moments of Minor Treatment ................................. ..........................................47

Table III-24 Moments of Hospitalization..............................................................................48

Table III-25 Gamma Parameters for Pc, n and X variables for Physician Visits,...................49

Table III-26 Gamma Parameters for Pc, n and X variables for Prescribed Drugs,..................49

Table III-27 Gamma Parameters for Pc, n and X variables for Diagnostics...........................49

Table III-28 Gamma Parameters for Pc, n and X variables for Minor Treatment,..................49

Table III-29 Annual Number Physician Contacts..................................................................50

Table III-30 Annual Number Hospitalizations .............................................. ........................51

Table III-31 Physician contacts with different level of income..............................................51

Table IV-1 Spearman Rank Correlations For Ratio of User Input Data(Pc)...........................67

Table IV-2 Spearman Rank Correlations For Number of Usage Input Data(n) ......................68

Table IV-3 Descriptive Statistics of Monthly Figures ...........................................................71

Table IV-4 Mann-Whitney U test (two-tailed test) for Monthly Incurred Costs.....................72

Table IV-5 Kolmogorov-Smirnov(two-tailed test) test for Monthly Incurred Costs...............72

Table IV-6 Mann-Whitney's U (two-tailed test) test for Monthly Number of Utilizations .....72

Table IV-7 Empirical Distribution for Number of Utilizations for Out Patient Benefits ........73

Table IV-8 Empirical Distribution for Number of Utilizations for In-Patient Benefits...........74

Table IV-9 Credibility ratings for groups with at least 3 year’s claims history ......................76

Table IV-10 Summary Statistic of the Total Costs Incurred(Independent of the limits) .........84

Table IV-11 Distribution of the Total Costs Incurred(Independent of the limits)...................85Table IV-12 Distribution of the Limit and Deductible Applied Costs With Scenario 2..........86

Table IV-13 Summary Statistics of the Limit and Deductible Applied Costs With Scenario 2

.....................................................................................................................................86

Table IV-14 Statistical Summary for Group Members..........................................................88

Table IV-15 Distribution Output for Group Members...........................................................89

Table IV-1612 Std B coefficients for Total Costs Incurred....................................................92

Table IV-17Std B coefficients for Total Costs After the Limits and Deductibles...................94

Table V-1 Age an Gender characteristics of the Sample Data ...............................................96Table V-2 Dr scenarios.........................................................................................................97

Table V-3 Prescription Scenarios..........................................................................................98

Table V-4 Diagnostic Scenarios............................................................................................98

Table V-5 Minor Treatment Scenarios..................................................................................98

Table V-6 Hospital Scenarios ...............................................................................................98



Table V-7 Distribution of Group 1 Total Costs ...................................................................100

Table V-8 Descriptive Stats of Group 1 Total Costs............................................................101

Table V-9 Mann-Whitney test for Gr1 Total Costs ............................................................102

Table V-10 Kolmogorov-Smirnov test for Gr1 Total Costs.................................................102

Table V-11 Distribution of Group 1 After First Scenario ...................................................103

Table V-12 Descriptive Stats of Group 1 After First Scenario...................... ......................104

Table V-13 Mann-Whitney test for Gr. 1 Scen.1.................................................................105

Table V-14 Kolmogorov-Smirnov test for Gr.1 and Scen. 1................................................105

Table V-15 Descriptive Stats of Group 1 After Second Scenario ................. ......................106

Table V-16 Distribution of Group 1 After Second Scenario ...............................................107



Table V-19 Distribution of Group 2 Total Costs .................................................................109

Table V-20 Descriptive Stats of Group 2 Total Costs..........................................................110

Table V-21 Mann-Whitney test for Gr2 Total Costs ..........................................................111


Table V-23 Distribution of Group 2 After First Scenario ...................................................112

Table V-24 Descriptive Stats of Group 2 After First Scenario...................... ......................113



Table V-27 Descriptive Stats of Group 2 After Second Scenario ................. ......................115Table V-28 Distribution of Group 1 After Second Scenario ...............................................116



Table V-31 Distribution of Group 3 Total Costs .................................................................118

Table V-32 Descriptive Stats of Group 3 Total Costs..........................................................119

Table V-33 Mann-Whitney test for Gr3 Total Costs ..........................................................120


Table V-35 Distribution of Group 3 After First Scenario ...................................................121Table V-36 Descriptive Stats of Group 3 After First Scenario...................... ......................122



Table V-39 Descriptive Stats of Group 3 After Second Scenario ................. ......................124

Table V-40 Distribution of Group 3 After Second Scenario ...............................................125





Table V-43 F testf or Physician Simulation and real data comparison.................................128

Table V-44 t testf or Physician Simulation and real data comparison ..................................129

Table V-45 F testf or Prescribed Drugs Simulation and real data comparison .....................130

Table V-46 t testf or Prescribed Drugs Simulation and real data comparison ......................131

Table V-47 F testf or Diagnostic Simulation and real data comparison ...............................132

Table V-48 t testf or Diagnostic Simulation and real data comparison ................................133

Table V-49 F testf or Minor Treatment Simulation and real data comparison......................134

Table V-50 t test f or Diagnostic Simulation and real data comparison ...............................135

Table V-51 F testf or Hospital Simulation and real data comparison...................................136

Table V-52 t testf or Hospital Simulation and real data comparison....................................137

Table 0-1 Earthquake predictions from the California Data.................................................148

Table 0-2 Real Earthquake data ................................ ..........................................................148

Table 0-3 High costs incidence rates...................................................................................149



PART.I.

INTRODUCTION AND OBJECTIVES

Turkey is the third most populous country in World Health Organization’s European

Region, and its economy is among the ten largest in Europe. It has a high growth rate and ayoung population. Turkey is also a candidate for membership of the European Union.

However, the population’s health status and the quality of the health care system are far below

the country’s general level of development.

The last few years have seen a rapid expansion of the private health care sector in

Turkey. The expectations of those with high incomes (last decade has created a high-income

group of between six and eight million people) provide incentives for further expansion and

encourage the private sector to play a larger role in the health care system. Furthermore

patients prefer private to public health care, regardless of their income, due to a lack of

confidence in public health services and a belief that private health care is of better quality

It is difficult to make reliable estimates of the extent of out-of-pocket payments in

Turkey, as private spending on health care is not well documented. Official sources like the

World Health Organization’s European health for all database records, The Organization for

Economic Co-operation and Development (OECD), and reports of the Ministry of Health puts

the percentage of out of pocket expenses to be 28% of all health care expenditures which is 10

billion USD in official figures. This constitutes a total expenditure of 3 billion USD with out

of the record expenses. Taking into account differences in the relative purchasing power of

various currencies, Turkey’s GDP per capita (Intl $) is 6,455 where the total health

expenditure per capita (Intl $) is 323. ( in normal USD currency it is approximately GDP is

2000$ and expenditure is 110$) When we compare health care expenditures with other



comparable countries like Hungary (846$, 24.3 % of this is private expenditure), Greece

(1,390$, 44.5 % of this is private expenditure) we can say that private health care

expenditures are very low and will increase in the following years due to the technological

progress, the new expectations of consumers, population aging and the reluctance of

governments to devote an ever-growing proportion of State budget.

Private health insurance always plays a complementary role, which varies in

significance, in the majority of the countries all over the world. In some countries private

insurance even has partially taken the place of public services. Private insurance plays its role

at two different levels: the financing level, where the insurer reimburses the cost of care or

provides compensation, and the care providing level such as in the case of managed care. So

private health insurance covers a very extensive range of services, and also brings into play

many different operators. Its characteristics, and in particular the extent of its integration in

the various parts of the public systems, differ considerably from one country to another.

Considering the Private Health Care Expenditures covered by private health insurance

in Turkey, (257 Trillion TL which is 170 million USD) and covered population to be 700,000

which is 1% of population) if the system grows like in the western countries then the insured

population will grow to 10 million and will be covering privately insured expenses totaling

more than 2 Billion USD comparatively .

In private health insurance, contracts are done as a group or individually. In group

contracts employers or unions are contracting with the private health insurance company. But

for individual contracts, people are paying for their families. Because of the higher risk of

adverse selection for the insurance company, the conditions are much more stricter and

premium is higher for individual contract than group contracts.

To avoid major inequalities or excessive rise in premiums, group insurance contracts

have been favored by the regulation in the countries where private medical insurance is welldeveloped. And as a result of this group contracts are widespread in a number of countries. (In

US %70 of the population is covered under group business)

Only in a few countries health insurance statistics are published in sufficient volume to

be credible and meaningful. It is very hard to find the technical literature on private health



insurance. For example in UK where 11.5% of the population is under private health

insurance, there are no official published statistics as classified in this thesis. Though the

majority of the published actuarial literature is UK origin, first article on health insurance was

written in 1988 and few additional articles were published after that. Due to the lack of

information new articles written in UK still refer to the overseas articles like the ones that are

published in US or Australia.

The objective of this study is to prepare a dynamic forecasting model in private group

health insurance business and health funds. Real data have been used to describe the model

with a large number of variables so that reliable forecasts can be made. Structure of such a

model that aims to reflect a real life situation made up of various distributions with different

characteristics is very complex.

While developing this model, it is aimed to;

· Outline the approaches and adopt some general actuarial concepts to private health

insurance. (Since this is the first example of a health care expenses prediction simulation

model in group health insurances in Turkey.)

· Determine the structure of the model made up of various modules, taking into account

the age and gender differences on utilizations and unit costs, experience of the examined

group previous year statistics, uncertainty due to various factors such as trend, credibility and

suitability of the data.· Test the model due to interrelations and sensitivity of variables.



PART.II.

GENERAL BACKGROUND

II.1 PRIVATE HEALTH INSURANCE IN THE WORLD

In industrial States, health care financing has historically been inspired by three

competing “models”: the first one, implemented by Bismarck in Germany, relied on

professional enrolment through compulsory contributions from employers and employees;

more recently, Beveridge introduced in the after war UK a public health monopoly, ensuring

universal social protection. The last form of organization is a mix-system, which prevails in

the US, where health insurance is not compulsory [23].

The extend and pace of the development of private health insurance in each country has

been very dependant on the original pattern of the national health care organization, even if

most countries tend to have now a rather hybrid health care system (mixing elements from the

three original models). Amongst OECD member countries, strong contrasts can now be

observed in the balance between private and public health insurance. Although, private sector

is mainly supplementary to public coverage, in some countries it can substitute to public

sector to cover even primary care for all or part of the population. Lastly private health

insurance may provide the same level of coverage than the existing public scheme, whilegiving access to private providers.

According to these regulations, if we would like to explain the systems in EU [23],



Table II-1 Types of VHI in the EU

Supplementary

increases choice / access

Faster access

increased choice of provider

own room in hospital

Complementary

services excluded / not fully covered

by the state

Dental care

‘alternative’ treatment

co-payments

Substitutive

the principle means of protection

Spain

Germany

Netherlands

Table II-2 VHI coverage in the EU in 1998

Country % populationsubstitutive

% populationcomplementary / supplementary

Austria (hospital expenses) 13

(hospital cash payments) 21

Belgium 30

Denmark 28

Finland (children) 33 / (adults) 10

France (co-payments) 85

(other types of VHI) 20

Germany 8.9

Greece 10

Ireland 42

Italy 5

Lux (active population) 75

Neth 31

Portugal 10

Spain 6.8 10.8

Sweden 0.5

UK 11.5



Table II-3 VHI expenditure as a percentage of total expenditure on health in the

EU, 1980-1998

Country 1980 1985 1990 1995 1998Austria 7.6 9.8 9.0 7.8 7.1

Belgium 0.8 1.2 1.6 1.9 *2.0

Denmark 0.8 0.8 1.3 1.2 1.5

Finland 1.4 1.8 2.2 2.4 2.7

France - 5.8 11.2 11.7 12.2

Germany 5.9 6.5 7.2 6.7 **6.9

Greece - - 0.9 - -

Ireland - - - - 9.4

Italy 0.2 0.5 0.9 1.3 **1.3

Luxembourg - 1.6 1.4 1.4 **1.6

Netherlands - 11.2 12.1 - 17.7

Portugal - 0.2 0.8 1.4 **1.7

Spain 3.2 3.7 3.7 5.2 **1.5

Sweden - - - - -

UK 1.3 2.5 3.3 3.2 3.5

Health care expenditures can be financed according to three basic models: risk-based

calculation of premium, community rating and funding.

Risk based calculation is the most common way for private insurers to provide health

products. Two different types of policies may be distinguished: individual and group

insurance. These models involve different kind of selectivity and premium calculations.

Individual policies are scarce in OECD countries (except in Italy and in Denmark). For

such policies, individual contract premiums are calculated on risk-based criteria such as age

or age at entry, sometimes gender (Luxembourg, Portugal, Switzerland) and often health

status. Therefore premiums are higher for older and weaker persons. Moreover, private



insurers are allowed in most case to deny the access to high-risked individuals or to impose

waiting period (such as in the US, Luxembourg or Switzerland). This is the case in nearly all

OECD countries except when policies are aimed at protecting specific categories of persons.

Group insurance policies are more common. They are widespread in a number of

countries such as:

The US, with more than 70% of the population covered by this type of scheme,

France, where two thirds of insured are covered by a global contracts through the

employer,

Germany,

The UK, where three quarters of the population have a supplementary health insurance

cover,

Canada,

And recently Portugal, in which 90% of contracts are group insurance policies.

Reasons for this development certainly lie on the particular financial and access

facilities of these policies. Actually, since risks are borne by more people, insured enjoy lower

premiums based on an experience-rated calculation. Insurers may therefore have fewer

incentives to have recourse to risk selection.

II.2 TURKEY PRIVATE HEALTH INSURANCE BACKGROUND

In essence, private health insurance started to develop circa 1990 by offering per event

limited out-patient based policies with a limited surgery, room and board benefits(Health

Insurance is defined to be a separate branch by 1990).

As many multinational companies started investing in Turkey and as a policy they

require Group Health Covers for their employees, private insurance companies have begun to

take part in the health market.

As a result of the lack of confidence to the social security system, the private insurance

companies have developed policies for individuals in addition to policies providing group

health coverage which are being spread out by the help of direct sales teams, and most



policyholders, although being at the same time contributors to the social security system,

more and more they stopped using the services provided by the social security institutions.

Between 1990 and 1993, as a consequence of the insufficient understanding of

principles of health insurance, health insurance policies were mostly out-patient oriented and

were insufficient for in-patient benefits. In 1994, the benefit structure of these policies was

changed to ones in which more comprehensive in-patient benefits were provided.

Between 1993 & 1995, a serious increase in the private health organizations was

observed. With these modern hospitals, there came a professional approach to private health

insurance. For example, Bayındır Hospital which was owned by a group who has also a life

insurance company, produced a Preferred Provider Organization (PPO) product to sell to the

upper and middle class markets in Ankara. This hospital has established contacts with the

health insurers of Istanbul in 1994.

PPO agreements were done with some of the well known hospitals in Istanbul and in

Ankara by Halk Yaşam and Koç-Allianz Hayat which were the first companies to initiate

PPO concept to the market through the end of 1994.

The leading companies in the market aim to expand this system gradually to the whole

country and thus create a private health service system. These products offer unlimitedbenefits with some exclusions and cost containment measures. Even though the policy is

unlimited, when the insured wants to get service from another provider (non-PPO) then, a

maximum limit, deductibles or coinsurance are applied. But for the emergency cases, when

someone could not reach a PPO, this condition is usually not enforced.

Due to the development in the private health insurance industry, Munich-Re, the most

known foreign reinsurance company in Turkish insurance market established Med-Net system

with foreign partners (a Third Party Administration) in 1994, which was a new concept for theinsurance sector. Small companies prefer this system because policy related services such as

underwriting, policy issuing, premium collections and claim settlements are done by Med-

Net. Med-Net offers a wide range of plans which are equipped with different geographical

scopes, limits, co-insurance and deductibles.



In 1994, affordable check-up benefits started to be offered by policies.

In 1993 and 1994, insurance companies began to provide air ambulance services which

are not unfortunately being able to be used efficiently. Air ambulances are employed

according to the distribution of the insureds within big cities. The air ambulance system is

supported by wide spread road ambulance system as well.

Since 1995, many different kinds of products have been introduced to the market, some

of which offer benefit limited products both per prescription, per visit limit and annual limit

per benefit whereas new models with annual maximum limits per person are being developed

as package options. In order to increase market penetration, more attractive policy options are

being developed in the market for the middle class people. As far as product designs are

concerned, the market has been moving from a fee for service model to annual limits and even

to unlimited benefit models. Halk Yaşam and Koç-Allianz Hayat have started a family

physician service including also free laboratory tests and keeping health condition records of

the insureds.

In late 1994 and 1995, guaranteed renewability rights were added to some of the

products of the leading companies in the market and Med-Net.

In 1997, companies which were not satisfied with the service quality and continuousincrease in prices started to quit from the market. Another Third Party Administration

Company named Med-Ex entered the market.

In 2001 Private pension law put the condition for life insurance companies who would

like to serve pension business, segregation of the health business is obliged.

As of 2002, there are approximately 700,000 policyholders in the health branch who are

either individually insured or members of group plans.

As a result of a number of factors including the following, there is an expectation of a

significant growth in health insurance business in Turkey in the coming years:

1. The poor quality of health services offered by the social security system.



2. The introduction of innovative health products which has already built public

confidence.

3. Increase in income levels.

4. Increased awareness.

5. Regulatory changes requiring separate life insurance companies, which

increased management's focus on health and life insurance.

6. Major developments in the financial sector in Turkey, including debt and

equity capital markets which have enabled diverse investment opportunities for individuals

and institutions for life savings (as opposed to bank deposits and real estate being the only

available investment tools pre-1980). Individuals are now more aware of the value added

provided by institutional fund management by investment professionals.

7. Private sector companies becoming more institutionalized as they transform

from family owned businesses into institutionally held corporations and offer better benefits

to their employees. The increased number of multinational companies establishing a presence

or expanding their existing operations in Turkey is resulting in better added benefits to

employees in the form of group health and life programs.

There is also a series of talks and preparations for a health reform, which include

special proposals to maintain the development in the health sector and health insurance

services. This can be outlined as following:

· to unify the 3 major Social Security Institutions ( SSK, BAG-KUR, Emekli Sandigi )

under a Social Security Finance Institution and to separate the concepts of health care

provision and financing;

· to include the non-insured ( almost 35% of the population ) in the new system;

· to expand the service of the Social Security System with the application of a "Green

Card" which provides free health services for people whose monthly income is equal to less

than 1/3 of the minimum wage;

· to separate the financial control of health and pension funds;· to use a modern accounting system throughout the health sector and to use efficient

financial & actuarial methods;

· to provide a modern information system;

· to encourage the establishment of private hospitals with efficient management and

financial systems in order to increase market competition and to decrease the prices;



· to enlarge the extent of support investments in the health sector;

Private health insurance companies are also allowed to participate in the

implementation of this program.

It is observed that 4/5 of the private insureds belongs to the upper income class and the

upper middle class. The rest are mainly members of group health insurance plans which are

offered as a fringe benefit by the employers in the private sector. The development of the

market with increasing number of insureds will reduce the risk of anti-selection which shall

lead to more affordable premiums for middle class people [29].

Private health insurance companies in Turkey compete with each other by their quality

of service, policy premiums and product differentiation. Preventive medicine, family

physician system and family planning are going to be popular benefits in order to make

policies more desirable. It is observed that the market tends to be more in oligopolistic

structure during the recent years because of the vast entrance into the market.

II.3 HEALTH RISK MODELS IN LITERATURE

Health care expenditures are characterized both by large random variation as well as

large predictable variation across individuals. Such differences create the potential for large

efficiency gains due to planning, risk reduction from social or private insurance, and raise

important concerns about fairness across individuals with different expected needs for

services. Although each population not only has unique demographic and socioeconomic

characteristics but also a distinct medical signature [35], it is indispensable to use experiences,

data and techniques of the other models.

Considerable research has been conducted on alternative forecasting models in many

countries, using a wide range of information.

Risk adjustment means the use of information to calculate the expected health

expenditures of individual consumers over a fixed interval of time (e.g., a month, quarter, or

year)



In the United States, actuaries have been slow to accept health-based risk adjustment,

despite its greater accuracy.

According to the demographics only, prior year expenditures, diagnoses, information

derived from prescription drugs, self-reported health and functional health status measures,

mortality, and approaches from the other discipline exist.

While examining these methods it should be noted that it very hard to estimate the

health care spending on individual basis. When the numbers reaches to sufficient size (in risk

adjustment literature it is considered to be more than 5000 members but this number is

defined by the characteristics of the health care system and population) than it becomes

possible to estimate the overall costs of the sample size.

II.3.1 Demographic Models

First data that is used in health estimations are age and sex. When we examine the

worldwide statistics and the Turkish data it is clearly seen that age and sex factors are the

primary factors concerning the health utilization and spending.



Figure II.1 Health Spending for Gender, Age Sample Netherlands

Figure II.2 Health Spending for Gender, Age Sample USA Privately Insureds

Figure II.3 Health Spending for Gender, Age Sample USA Medicaid Eligibles

Age and sex are easy to document and use for risk adjustment, are fair, and generally

accepted by all parties involved. Because the information is independent of medical care, and

not readily gamed, it appears attractive in terms of incentives. Most serious drawback of age



and sex as risk adjusters are simply that they are weak predictors of individual expenditures

[31].

II.3.2 Prior Year Expenditures

Because expenditures in one year are correlated with expenditure the following year -

the correlation coefficient for total health expenditures is on the order of .2 to .3 - a simple

proposal has often been made to regress expenditures in year two on year one expenditures

(together with other demographic variables) and use this model for calculating risk-adjusted

payments. Newhouse et. al. [24], Van de Ven and Van Vliet [32] and Ash et al. [5] have all

estimated such models and typically find that spending an extra dollar on health care in year

one "predicts" spending of $0.20 to $0.30 in year two. The R2 from a regression that includes

age, sex and prior year expenditures, is generally estimated to be in the range of .06 to .10. on

individual basis These measures are a substantial improvement over demographic only

models, and comparable to the predictive power achieved by diagnosis-based models or

models that use self-reported health status measures.

In the study that was done by Ash et al. [5]], by examining MED-STAT Market Scan

Research Database, the largest multi source private sector health care database in the United

States, 2.7 million individuals were selected and year 1997 and 1998 results were examined.Below figures were gathered,

Figure II.4 Distribution of population costs to the members for year one and two

This is the distributions of Year- One and Year- Two Cost by Year- one Cost Group,

which means in year one top (in term of health care costs occurred) 0,5% of the population



had spent %23 of the total population and next year in 1998 this group spent the 8% of the

total health care cost of all. And contrary to this bottom %80 of population had spent %13 of

total costs and next year they spent the %49 of costs. As can be seen top spenders tendency to

pay 2-3 times the average can be recognized easily where the bottom cost %80 has more

volatile nature. This shows us the large random component for the individual figures.

Van de Ven describes that the prior year expenditures or utilization appears to be the

best single predictor(where there is only one predictor in hand) of an individual’s future

health expenditures [31]. But Ash et al.(1998) mentions that prior cost, which was historically

superior to diagnostic information for the purpose of predicting future costs, is no longer

better than the current generation of diagnosis- based risk models for predicting future costs.

In her above-mentioned study diagnostic based methods were slightly superior at identifying

the top group with high costs [5].

II.3.3 Diagnosis-Based Risk Adjustment

Since the early 1980's a considerable amount of research has developed risk adjustment

models that use diagnoses from insurance claims to calculate risk-adjusted payments. In 1997,

the US Congress directed CMS to change the way it paid HMOs that contracted with the

federal government to provide Medicare covered services. [27]

The best-known methods are;

• Ambulatory Care Group (ACG)

• Diagnostic Cost Group (DCG)

• Disability Payment System (DPS)

The starting point for all diagnosis based risk adjustment models is the concept that

certain diagnoses predict of health care expenditures. Each of the three major diagnosis basedmodels begins by identifying a subset of all diagnoses that predict current or subsequent year

resource use. Although the three models differ in how they choose their subset of diagnoses,

each attempts to identify codes that are assigned only for encounters involving a

professionally trained clinician. In particular, diagnoses appearing on laboratory, diagnostic



testing, and medical supplies claims are uniformly not used in classifying individuals for

prediction, on the grounds that they are less reliable than those assigned by clinicians.

ACGs are based on aggregation of all ICD9-CM codes into 32 diagnostic groups using

ambulatory diagnoses only. These diagnostic groups can then be used in a number of

alternative combinations, providing up to 83 mutually exclusive ACGs into which any given

individual may be classified.

DCGs have received the most attention of all classification systems. Early versions of

this system were based on simple hierarchical models of diagnosis grouping, where modeling

was used to identify a large number of clinically homogenous groups, which were then

aggregated into between 9 and 20 Diagnosis Cost Groups. The DPS was developed for US

Medicaid disabled enrollees, and is based on similar principles to the DCG/HCC model. All

diagnoses from clinical encounters are used within a hierarchical system for conditions.

However, the DPS is more additive than the DCG/HCC system in its methods to account for

the number of conditions an individual has within certain body systems. The general disability

of the DPS is unclear, however, as its development and application has focused on people

with disabilities.

Also in USA, where medical infrastructure is said to be the technologically foremost

developed one in the world, the systems that combine diagnoses from patient - clinicianencounters across the spectrum of health care delivery sites with age and sex are now being

used by health care organizations to measure the health risk of populations. However, many

organizations have not implement ed “all encounter” diagnosis models because they require

timely, comprehensive, high- quality data from physician’s offices and other dispersed sites of

care.

In USA many author In patient models (diagnosis based) predict next year’s total costs

reasonably well in Medicare, where nearly 20 percent of the population is hospitalizedannually, of ten for chronic conditions. However, such models are less attractive for privately

insured under 65 populations, where fewer than 5 percent are hospitalized in a year and of ten

for acute conditions. Few previous studies have evaluated inpatient diagnosis models on

younger populations. So-called all encounter models that use both inpatient and out patient

diagnoses to predict cost have been developed for several types of populations: elderly



In Diagnosis based methods the data should be tracked for each member with the

following year costs and the diagnostic codes should be chosen, entered and kept correctly

which is not a very easy situation for Turkish private and social security systems.

II.3.4 Information Derived from Prescription Drugs

A second source of needs measures based on prior utilization is the use of prescription

drugs.

Early work focused on classifying drugs into different therapeutic classes and counting

drug orders in each class. This approach was extended to include clinician judgment of

severity to form weighted disease scores based on outpatient pharmacy utilization and

condition severity to develop the Chronic Disease Score (CDS)

II.3.5 Self-Reported Health Information

Health survey information can be obtained without contact with medical providers, no

prior medical or insurance history is required; reflects individual’s perceptions of their ownneeds and expected utilization, is uniform across health schemes and providers; and other

relevant data, such as socioeconomic measures etc., may also be collected. There are also

disadvantages to self-reported measures of health; surveys are costly to undertake; response

rates may be low and affect the robustness of empirical analysis, requiring large sample sizes;

responses may be correlated with medical risk; reporting may be inaccurate due to errors or

confidentiality issues. Furthermore, provider assistance in conducting surveys may be

required, which may lead to problems in follow up and non-random sampling. Van de Ven

(2000) presents information on the validity of regression models that have sought to explainvariations in health expenditure in terms of health status measures. These studies show that

adding self reported health status measures to demographic variables significantly increases

the predictive power of risk adjustment models. However, self reported health status measures

do not outperform prior diagnosis variables in explaining variations in health expenditure.



II.3.6 Mortality

In individual level analysis mortality has been proposed as a potential explanatory

variable in regressions on expenditure due to the excess costs incurred prior to death.

However, whether mortality is a useful predictor of variations in expenditure at the individual

level is not clear. One argument is that the costs associated with death are largely

unpredictable, and have been found to be 250% above. A more effective means of

reimbursing health schemes for the costs of death may be to control for deaths in the

regression model (through dummy variables for patients who died during the period, and

reimburse schemes retrospectively for those individuals. Van de Ven (2000) have questioned

the political and social acceptability of increasing payment rates to health schemes with

higher mortality rates. Mortality data may also be poorly coded and only partially available in

some contexts, and may raise some concerns about privacy.

II.3.7 Other Models

There is a considerable literature in statistics, econometrics, and health economics that

examines and assesses alternative functional forms for estimating models of health spending.For data source and applications we recommend [2,3,6,7,9,11,13,19,22,28 and 33]

II.4 PRIVATE HEALTH INSURANCE PRICING

II.4.1 Practice of Pricing in the World

Group business is defined as any collection of individuals who combine to make a

single proposal for uniform Insurance cover. Usually the collected individuals will beemployees in the same company and the employer will pay for the premiums either wholly or

in part. Generally the group will be a discrete definable unit of individuals and the insurer will

look for some minimum take-up rate of the terms offered, if the scheme is voluntary, in order

to limit and-selection.



Several kinds of product pricing mechanisms exists in health insurance market starting

from fixed price fully insured plans to experience rated plans with minimal stop loss

insurance protection. The options available to group policy holders increase together with the

increase of the employee within the company. Up to 10 employee groups are invariably

covered by fully insured contracts with no waivers on medical underwriting. Groups of more

than 1000 employees are almost invariably experience rated and all medical underwriting is

relinquished(UK, US) [12, 25,26].

The following chart illustrates the different pricing methods that are used in UK for

different sizes of policy [4]

Size of Policy Pricing methods available

Very large group scheme( > 5000 lives)

Large group scheme( > 500 lives)

Small group scheme( > 100-500 lives)

Very small group scheme

Individual Policyholder

C o s t

P l u s

E x p e r i e n c e

R a

t i n g

M i x o

f B o o

k a n

d

E x p e r i e n c e

R a

t i n g

B o o

k R a

t i n g

Figure II.5 Group and Individual Rating Structures

It should be noted that this chart is dependent on the type of cover offered. The chart is

appropriate for a cover including mainly hospital benefits. The size of scheme at which

Experience rating becomes appropriate would reduce for cover within higher frequency of

claiming (for example cover including primary and dental care) and would increase for cover

with a lower frequency of claiming (for example cover including a very large

excess/deductible).(smaller groups can be experience rated for higher frequency benefits like



for a 100 member group can be experience rated for physician visits while it is hard to give

credibility to the group data for hospital benefits )

The premium quoted by an insurer for new groups will be based on the following

general factors: who will be covered (e.g. employees only, employees plus dependants,

hierarchical status of employees)

• the age profile of the group

• type of product

• the group's past claims experience

• method of payment

• location and occupation might also be considered

If the group has never been covered under Private Health Insurance before, then there

would generally be a calculation based on individual book rates(if so) with an appropriate

discount because it is a group scheme (to allow for the lower anti selection that a group

scheme should bring).

The renewal process will follow the same pattern as outlined above, although the

insurer will have to consider any changes within the group during the previous period of

cover (e.g. increase/decrease of the group membership, change in eligibility criteria, orincrease /Decrease in scale of cover).

• individual policy premiums are generally higher than group premiums as

the risk of anti-selection against the insurer is higher when in individual is

financing has own premium

• Some form of experience rating is usually incorporated in group pricing,

whereas individual business is normally priced on a community rate basisi.e. the premium is assesses pari passu with all other lives in the same risk

cell without reference to individual claims experience

• The larger the group size, the greater the credibility that is placed on the

group's own experience



• No Claim Discounts (NCDs) are sometimes used for individual and group

business in order to make some allowance for individual claims experience

in the premium rates

• Larger groups (more than 50 employees) are often flat rated according to

benefit class, whereas individual business is almost always age rated

• Additional rating factors are considered when pricing group business e.g.

industry, location, size of group, employer's attitude to his employees'

health

• Large groups frequently self-insure up to a point e.g. 125% of expected

claims cost, and purchase administration and stop-loss insurance from the

insurer.

• Benefits and exclusions are generally similar between group and

individual products

• There is other greater scope for customizing benefits for larger groups to

meet their requirements

In US Industry Rating Factors (RFs) were introduced in the late 1950's in an attempt to

appropriately price each group based on its industry. There are a great many "dynamics"

(other than age/sex and geographic area) that drive a group's claims level. The employer's

contribution level, participation rate, the distribution of employees by collar color, and the

annual employee turnover rate, are a few examples of some of the dynamics involved.

“US has the widest library of the written articles in Group Health Insurance Pricing. First group health policy was issued to Montgomery Ward in 1910”[1]



And in the same text distributional models are regarded to be “increasingly

sophisticated”

“but contrary to these developments actuaries continue to use highly simplified models.” [1] .

This practical approaches are some times criticized by some actuaries to be “ancient”

“Over the last 45 years, the advances that have taken place in our world have been mind-boggling to saythe least. However, the sad reality is that the group health insurance industry STILL develops an account's

premiums the same way it did 45 years ago!”[30]

Both in US and UK overall out patient benefits are packaged and most of the models are

based on this benefit structure.

In Turkey excluding few companies (Halk Yaşam was one of them) standard rates are

used to be multiplied with the benefits offered, For example for physician visit benefit limited

by 50$, the premium is calculated by multiplying the limit with fix multiplier (for 20%

coinsurance 1.88 for individual and 3.76 for families. Most of the time deductibles or

different type of limits (like total number of visits etc) are not covered in the models. Most of

the time rule of thump case-by-case evaluations are done. According to group size a discount

is applied like 30% discount for 500 lives covered. (Than the multiplier for physician visits

for 50$ drops to 1.3 for individuals and 2.6 for families. For renewal rates most of the time

100% projection is done according to loss (claims paid)/premium ratio i.e. if the overall claim

/ premium ratio is 150%, for the group of 500 lives with the above limits next year the

physician fee is calculated with 50% increase in premium most of the time regardless of the

new year limits. For example if the group gets the limit as 40$ next year the premium will be

(1.5)(40)(1.88)(0.7) =79$

II.4.2 Theory of Health Insurance Pricing

When we put on limits for number of visits or total costs LEV is used. Well Known

distributions like Gamma and Pareto have exact formulas to calculate these limits and

deductibles.



If we accept the cost of hospitalization to have a Pareto distribution with parameters

alpha and lambda; the limited expected value formula [17]

[ ] ( )

++

+−+

+−

−=

−

x x

x x x X E

λ λ

λ λ α

λ λ α

α λ

α α

111

;1

Equation II-1

And for Gamma;

[ ] ( ) ( )[ ] x x x x X E λ α λ α λ α ;1;1..; Γ −++Γ = Equation (II-2)

This is accepted as the ladder method to see effect of proposed limit or deductible.

Deductible and limits are the amounts which the below and above claims are not paid by the

insured respectively.

The usage of the graph depends on the area of the graph shows the total amount thatwill be paid by the insurer and the insured.



PART.III.

ANALYSIS OF THE DATA

As have seen in preceding chapters, there are various approaches to predict the futurehealth costs/expenditures and utilizations.

“Health care expenditures are characterized both by large random variation as well as

large predictable variation across individuals”. As we have to deal with the data’s available

we should define the data where we have drawn the model structure and available input.

• The first resource is the Halk Yaşam Sigorta Statistics between 1996 and 2000

years covering 140.000 insured lives on the average

• Various world statistics for the missing data and benchmarking

• “Health Service Utilization Survey in Turkey” Ministry of Health, Turkey

When we examine the health expenditures of the population we see that major part of

the total is formed of Outpatient (Physician visits, prescribed drugs, diagnostic procedures and

minor treatment) and Inpatient expenditures where the rest of the expenditures are formed of

Maternity, Dental and Optical costs. We will be examining the outpatient and inpatient costs.

The private insurance data is providing us the major characteristics of the population, but as

this group is a selected group in terms of socio economic characteristics, and requires the

members to be healthy at the start of the first policy year (excluding the newborns and big

group members) we have to examine the above mentioned sources as well. Also as the data is

formed of insufficient for the extremely costly cases like organ transplantation we have to get



benefit from international statistics. Also catastrophe cases like earthquake will be mentioned

in the final part a special estimation for Istanbul with a rule of thump will be provided.

“Health Service Utilization Survey in Turkey” was carried out to provide baseline

information for formulation of National Health System of Turkey has been done with a

30,155 sample size. The information gathered by this survey can be grouped under two part

which are the determination of the characteristics of the consumers, the second is to sort out

the factors influencing utilization.

III.1 DIAGNOSIS AND TREATMENT SERVICES CATEGORIESDifferent kinds of services are obtained from health service providers.

Diagnosis and treatment services will be examined under the below titles:

III.1.1 Out- patient Treatment (without hospitalization)

Table III-1 Out Patient BenefitsBenefit Definition

Medical Visit Physician examinations and

consultations for diagnosis and

treatmentDrug Prescribed or non-prescribed

drug usage

Diagnosis Laboratory, x-ray, MR, etc.

methods

Minor Medical

Treatment

Injections, etc. treatments



III.1.2 In-patient Treatment

Table III-2 In patient BenefitsBenefit Definition

Room/Bed Room/meal/

Accommodation in hospital

Operation Operation theatre charges,

operations and related expenses.

Physicians/drug/diagnosi

s

While hospitalization

Maternity Normal/

Caesarean

Various Dressings, blood supply,

bandages, etc.

These service and cost elements show the areas on which the related community made

medical expenditures within the specified period.



III.2 ESTIMATION OF PARAMETERS

Total utilization numbers and cost for these areas for each of the above-mentioned

classifications are formed of;

Pc: The ratio of people who will use this specific treatment within the defined period (1-

non users ratio) I.e. each year 6 % of the population of a group can be hospitalized where 85%

of the same group can use physicians

n: The frequency of treatment among those who demanded the treatment within the

defined period and the analysis of the related distributions. I.e. people who visits physicians

are experiencing 3.5 visits on the average with a variance of 12.

X: The intensity of demand per treatment (cost/duration/service level) among those whodemanded the treatment within the defined period. I.e. People who are visiting physicians are

paying 30 $ on the average with a variance of 900.

In non life insurance where the casualty branches are very dominant in terms of

actuarial literature, the main variables are derived to be severity and frequency. But

examining the characteristics of the health data, in order to be able to use well known

distributions like Gamma and Pareto we concluded to use three rather than two variables.

These outputs are coming from various distributions, which are affected by various

factors and form these we will be examining the following factors;

• Prior year stats

• Group size

• Age

• Gender

• Socio economic status

Examining the data in hand, we have found similar results that are provided in the

literature survey



III.2.1 Prior year statsExamining the medical expenses between following year medical experiences shows us

the stochastic nature of health expenditures.

In our first sample 1987 insured population is taken and total medical expenditures forall benefits like physician visits, prescribed drugs, diagnostic procedures etc between two

years are compared. USD conversion is used for correlation analysis of the total expenditures

incurred.

This is a very similar result as in literature survey section under “Prior Year Expenditures”

As in the section when we sort the total adjusted costs of the first year and look for the next

year stats than we see that

Table III-3 Descriptive Stats for 2 year sample data in total expenditures

Correlationbetween

years

Averagehealth

expendituresin year 1(USD)

Averagehealth

expendituresin year 2(USD)

top 0.005 0.53 6,134 2,145top 0.01 0.42 5,027 1,757top 0.05 0.42 3,152 1,004

top 0.10 0.31 2,367 875100% 0.25 502 552

When we do regression analysis it is seen that

Table III-4 Regression for 2 year total expendituresRegression Statistics

Multiple R 0.25R Square 0.06

Adjusted R Square 0.06Standard Error 821.35Observations 1987



Table III-12 Line Fit Plot For 2 Year Utilizations

year 1 Line Fit Plot

0102030405060708090

100

0 100 200

year 1

y e a r

2year 2

Predicted year2

III.2.2 Group sizeIn the Turkish insurance market most of the companies are applying discounts for groups with

large number of members like below.Number Of

Lives Under

Insurance

Discountin Unit

Premium25 551 10

101 15176 20

276 25501 30

751 351000 40

As mentioned earlier and that will be provided in the following sections age and gender

categorization has huge impact on the expenditure behavior (not as single person base but a

group of people with the same gender and age band). In order to eliminate the possibility of



groups to have different demographic nature, if we draw out the Males with the birth dates

between 1960 and 1970 than, examining the group size will be healthier.

Now there are 169 group of males (1960-1970) with a minimum group size of 20 and

covering a total number of people 16704 lives. Average number of physician visits are

calculated. When we look a the descriptive stats of the groups

Table III-13 Descriptive stats of the groups formed of males born between 1960

-1970avg

Mean 1.462951303

Standard Error 0.048237183Median 1.447916667Mode 1.4Standard Deviation 0.627083383Sample Variance 0.393233569Kurtosis 0.198298942Skewness 0.196612365Range 3.341294783Minimum 0.054054054Maximum 3.395348837

Sum 247.2387702Count 169

The aim of this research is to show that mean health care cost per person does not vary

depending on the size of the insured group. To achieve this purpose we use the institutional

customers data of Halk Yaşam as our sample. The first step we take is to categorize the

companies. The companies can be divided into three main groups according to two different

approaches. For the first approach the categorization is made according to the number of

claimants and groups are formed as small (having 100 or less claimants) medium (100-500

claimants) and large (500 and over claimants). For the second approach the groups formed

according to number of employees insured and they are small (having 100 or less employees),

medium (having 100 to 500 employees) and large (having 500 and more employees). The

next step after categorization is to apply ANOVA procedure to check whether there is a



significant difference between mean health care costs per person for these groups. As it is

known in order to be able to apply ANOVA the variables we are dealing with must normally

distributed. Since our variable is the mean heath care cost per person for each company,

although mean heath care cost per person(A) has a skewed distribution, central limit theorem

allows us to assume that mean of A is normally distributed. So we have no objection in

applying ANOVA. The mean, variance and standard deviations of each group for the first

approach is given below.

Table III-14 Different Group Size Characteristics1-100 101-500 501+

Mean 58.93391 51.95898 45.29502Variance 2172.165 983.7596 439.9523Standard Deviation 46.60649 31.36494 20.97504

As it can be observed from the above table the means of the groups are close to each

other. However, it is still needed to be assured. At 0,05 level of significance we apply the

ANOVA and output is given below.

H0: Mean claim size per capita is equal for all groups

HA: At least one group has a statistically significantly different Mean claim size per

capita

Table III-15 Single Factor ANOVAANOVA

Source

of

Variation

SS df MS F P-value F crit

BetweenGroups

3553.162 2 1776.581 0.94917 0.387631 3.010442

WithinGroups

1145493 612 1871.721

Total 1149046 614



Since F(calculated)< F(tabulated) we say that we don’t have enough evidence to reject

the null hypothesis at 0,05 level of significance. In other words at 0,95 confidence level we

can say that the mean heath care cost per capita does not vary depending on the size of the

group insured.

For the second approach we can apply the same procedure and test the same hypothesis.

The data summary of the groups constructed according to the number of employees insured is

given below.

(Normality assumption is considered is tested and chi square Goodness of fit values are found

to be satisfactory )

And finally the ANOVA output is

Table III-16 ANOVA table for different group sizes

ANOVASource

of

Variation

SS df MS F P-value F crit

Between

Groups

8799.179 2 4399.59 2.362931 0.094997 3.010349

WithinGroups

1146943 616 1861.92

Total 1155742 618

The decision is parallel to the one we made for the previous case. At 0,95 confidence

level we don’t have enough evidence against equality of the means. Therefore, we can say

that the size of the group do not have a significant effect on the mean health care cost perperson.

As will be seen on the following sections, the group size effect the stochastic nature of

the average annual cost per person and that’s why(it is not easy to explain to small groups) an



additional contingency loading should be added according to distribution characteristics of the

expected overall costs,

Also the correlation between group size and average physician visit utilization is as

below.

Table III-17 Correlation of Average Physician Visits vs Group Sizeavg size

avg 1size -0.14586 1

III.2.3 ParametersDeriving the characteristics of these distributions and dealing with and the analysis of

the related distributions and determination of the parameters of this distribution by the various

point estimation methods.

I.e. if we assume that the demographic characteristics are similar, what percent of the

population uses the physicians?

Figure III.1 Ratio of Users to the Population

But if we differentiate between the age and gender classes;



Figure III.2 Ratio of Physician Users in Age and Gender Band Population

CH is for children, FE is for females and MA is for males. As can be seen the ratio of

usage for the Female on the average is much more than males.

Another measure which is the average number of visit (The frequency of treatment) for theusers

of the physician services (non users are not taken into consideration).

If we show the differentiation according to age and gender;

Figure III.3 Average Number of Visits for Different Age and Gender Bands

If we want the shape of the distributions of these frequencies



Figure III.4 Distribution of Number of Visits for Different Age and Gender

Bands

Again what is the effect of age and gender difference for the cost of each treatment?

The average figures are as follows;

Figure III.5 Average Cost Per Usage

Again the distribution characteristics are;



Figure III.6 Distribution of Visit Costs for Different Age and Gender Bands

When we examine the same group in section “Prior year stats” after classifying the data

according to the age and gender we see the below output,



Table III-18 Comparison of Average Expenditures Between the Age Gender

ClassificationAverage Total Expenditures(Physician+Prescription ...)Gender birth year Year 1 Year 2 CountChildren 1995-1999 454.11 465.52 304

1990-1994 280.25 251.29 1461985-1989 198.97 189.25 681980-1984 302.61 286.55 281975-1979 269.21 134.17 13

Males 1970-1974 374.13 465.16 2641965-1969 448.34 494.92 3161960-1964 424.63 481.09 113

1955-1959 826.46 661.44 381950-1954 387.31 616.47 191945-1949 898.27 690.17 41940-1944 1,844.78 2,098.02 1

Females 1975-1979 548.00 818.45 1171970-1974 723.70 805.14 2651965-1969 784.03 754.61 1671960-1964 621.75 799.29 621955-1959 766.77 643.15 301950-1954 915.34 1,359.18 6

1945-1949 0.00 204.82 1



III.3 MOMENTS OF USAGE

First and second moments of the distributions are two basic estimators of the stochastic

nature of the distributions. As the distributions characteristics are changing with the age andgender, the data is analyzed according to 5 year age bands. While combining the different

weights of age and gender groups it is possible to derive the representative characteristics of

the whole group with the use of first and second moments.



Table III-21 Moments of Prescribed Drugs

Age AVG Pc N AVERAGE

n SECOND

MOMENT X AVERAGE

X SECOND

MOMENT %0-4 0.86 6.67 73.05 18.19 661.39 0.08

5-9 0.73 4.58 34.37 20.69 855.89 0.07

10-14 0.64 2.94 14.17 21.81 951.66 0.0515-19 0.58 2.97 14.44 21.41 917.07 0.03

20-24 0.55 2.82 13.06 23.99 1150.58 0.01

Male

16-20 0.58 2.51 11.41 22.00 975.00 0.0021-25 0.55 3.04 16.70 22.00 975.00 0.04

26-30 0.60 3.26 19.22 22.00 975.00 0.12

31-35 0.63 3.61 23.53 22.00 975.00 0.10

36-40 0.63 3.96 28.33 22.00 975.00 0.07

41-45 0.63 4.44 35.62 22.00 975.00 0.04

46-50 0.63 4.87 42.91 22.00 975.00 0.0351-55 0.67 5.71 59.06 22.00 975.00 0.01

56-60 0.70 6.83 84.34 22.00 975.00 0.0161-65 0.75 7.59 104.17 23.00 1030.02 0.00

66-70 0.75 8.35 126.10 23.00 1030.02 0.00

71-75 0.75 8.35 126.10 23.00 1030.02 0.00

Female

16-20 0.73 2.67 12.89 22.00 975.00 0.01

21-25 0.73 4.26 32.83 22.00 975.00 0.0626-30 0.75 4.39 34.85 22.00 975.00 0.10

31-35 0.75 4.56 37.66 22.00 975.00 0.0736-40 0.76 4.66 39.34 22.00 975.00 0.05

41-45 0.76 4.74 40.63 22.00 975.00 0.03

46-50 0.76 5.72 59.26 22.00 975.00 0.01

51-55 0.76 6.71 81.40 22.00 975.00 0.01

56-60 0.76 6.71 81.40 22.00 975.00 0.00

61-65 0.76 7.63 105.36 23.00 1030.02 0.00

66-70 0.76 8.55 132.41 23.00 1030.02 0.00

71-75 0.76 10.40 195.77 23.00 1030.02 0.00



Table III-22 Moments of Diagnostics

Age AVG Pc

n

AVERAGE

n SECOND

MOMENT X AVERAGE

X SECOND

MOMENT %0-4 0.52 2.7 24.63 35.62 2804.19 0.08

5-9 0.45 2.6 24.63 36.45 2935.61 0.07

10-14 0.35 1.89 14.98 42.05 3908.57 0.05

15-19 0.33 1.89 16.16 52.93 6192.49 0.03

20-24 0.34 2.11 19.95 73.33 11884.73 0.01Male

16-20 0.26 1.84 15.31 44.53 4382.26 0.00

21-25 0.34 2.04 18.66 53.75 6384.00 0.04

26-30 0.36 2.2 21.86 55.76 6871.54 0.12

31-35 0.38 2.35 24.8 62.78 8708.99 0.10

36-40 0.41 2.4 25.83 71.3 11235.6 0.07

41-45 0.43 2.49 27.93 76.73 13011.55 0.04

46-50 0.43 2.78 34.75 86.62 16583.16 0.03

51-55 0.45 3.11 43.65 86.62 16583.16 0.01

56-60 0.46 3.23 47.07 93.83 19455.78 0.01

61-65 0.46 3.35 50.62 101.03 22557.74 0.00

66-70 0.53 3.35 50.62 108.6 26064.13 0.00

71-75 0.7 3.35 50.62 112.53 27983.49 0.00

Female

16-20 0.44 2.2 21.84 53.87 6413.14 0.01

21-25 0.53 2.47 27.38 53.59 6347.97 0.06

26-30 0.53 2.66 31.8 57.23 7238.90 0.10

31-35 0.55 2.75 34.13 60.96 8212.72 0.07

36-40 0.55 2.99 40.33 66.11 9659.99 0.05

41-45 0.54 3.07 42.29 74.14 12149.00 0.03

46-50 0.56 3.4 52.04 78.73 13697.77 0.01

51-55 0.61 3.59 58.07 80.55 14339.27 0.01

56-60 0.55 4.17 78.14 88.06 17139.23 0.00

61-65 0.62 4.17 78.14 90.51 18104.63 0.00

66-70 0.56 4.17 78.14 96.63 20633.86 0.00

71-75 1 4.17 78.14 101.52 22776.26 0.00



Table III-23 Moments of Minor Treatment

Age AVG Pcn

AVERAGEn SECONDMOMENT X AVERAGE

X SECONDMOMENT %

0-4 0.21 2.56 13.10 14.97 1,120 0.085-9 0.14 2.14 9.19 21.25 2,257 0.07

10-14 0.11 1.88 7.09 28.71 4,122 0.05

15-19 0.12 2.11 8.91 36.82 6,778 0.03

20-24 0.10 2.49 12.41 61.68 19,021 0.01Male

16-20 0.10 1.72 5.92 42.59 9,071 0.00

21-25 0.09 1.95 8.83 49.36 12,184 0.04

26-30 0.11 1.95 8.83 51.82 13,426 0.12

31-35 0.13 1.95 8.83 5.82 13,426 0.10

36-40 0.12 1.95 8.83 57.83 16,723 0.07

41-45 0.13 1.95 8.83 62.44 19,495 0.0446-50 0.13 2.01 8.83 77.64 30,141 0.0351-55 0.13 2.01 8.83 83.25 34,652 0.0156-60 0.13 2.21 9.75 89.74 40,270 0.01

61-65 0.13 2.21 9.75 89.74 40,270 0.00

66-70 0.13 2.21 9.75 89.74 40,270 0.00

71-75 0.13 2.21 9.75 89.74 40,270 0.00

Female

16-20 0.11 1.86 6.90 43.43 9,431 0.01

21-25 0.14 2.01 8.10 47.08 11,084 0.0626-30 0.18 2.12 9.01 54.54 14,872 0.10

31-35 0.19 2.12 9.01 56.87 16,173 0.07

36-40 0.17 2.12 9.01 59.50 17,702 0.0541-45 0.17 2.12 9.01 66.40 22,042 0.03

46-50 0.17 2.12 9.01 73.60 27,082 0.01

51-55 0.17 2.51 12.57 113.30 64,188 0.01

56-60 0.17 2.51 12.57 162.18 131,519 0.00

61-65 0.17 2.51 12.57 162.18 131,519 0.0066-70 0.17 2.51 12.57 162.18 131,519 0.00

71-75 0.17 2.51 12.57 162.18 131,519 0.00



Table III-24 Moments of Hospitalization

Age AVG Pc

n

AVERAGE

n SECOND

MOMENT X AVERAGE

X SECOND

MOMENT %0-4 0.09 1.00 1.00 1000.00 3,250,000 0.08

5-9 0.06 1.00 1.00 800.00 2,080,000 0.07

10-14 0.03 1.00 1.00 1100.00 3,932,500 0.05

15-19 0.05 1.00 1.00 1600.00 8,320,000 0.03

20-24 0.05 1.00 1.00 1000.00 3,250,000 0.01Male

16-20 0.05 1.00 1.00 1000.00 2,000,000 0.00

21-25 0.05 1.00 1.00 1000.00 2,000,000 0.04

26-30 0.06 1.00 1.00 1250.00 3,125,000 0.12

31-35 0.06 1.00 1.00 1500.00 4,500,000 0.10

36-40 0.07 1.00 1.00 2000.00 8,000,000 0.07

41-45 0.07 1.00 1.00 2000.00 8,000,000 0.04

46-50 0.07 1.00 1.00 2000.00 8,000,000 0.03

51-55 0.08 1.00 1.00 3000.00 18,000,000 0.01

56-60 0.12 1.00 1.00 4750.00 45,125,000 0.01

61-65 0.13 1.00 1.00 5750.00 66,125,000 0.0066-70 0.16 1.00 1.00 6500.00 84,500,000 0.00

71-75 0.20 1.00 1.00 7250.00 105,125,000 0.00

Female16-20 0.05 1.00 1.00 1000.00 2,000,000 0.01

21-25 0.05 1.00 1.00 1000.00 2,000,000 0.0626-30 0.05 1.00 1.00 1250.00 3,125,000 0.10

31-35 0.06 1.00 1.00 1450.00 4,205,000 0.07

36-40 0.06 1.00 1.00 1550.00 4,805,000 0.0541-45 0.07 1.00 1.00 1900.00 7,220,000 0.03

46-50 0.08 1.00 1.00 2100.00 8,820,000 0.01

51-55 0.09 1.00 1.00 2300.00 10,580,000 0.01

56-60 0.12 1.00 1.00 2300.00 10,580,000 0.0061-65 0.13 1.00 1.00 4500.00 40,500,000 0.00

66-70 0.16 1.00 1.00 6500.00 84,500,000 0.00

71-75 0.20 1.00 1.00 7250.00 105,125,000 0.00

When we weight these moments with population distribution as in the right column,



When we weight these moments with population distribution as in the right column,

Table III-25 Gamma Parameters for Pc, n and X variables for Physician Visits,ALPHA BETA

n NUMBER of CLAIMS 1.51 2.05

X CLAIM SIZE 3.97 9.28

Pc 0.69

Table III-26 Gamma Parameters for Pc, n and X variables for Prescribed Drugs,ALPHA LAMBDA



Pc 0.69

Table III-27 Gamma Parameters for Pc, n and X variables for DiagnosticsALPHA LAMBDA



Pc 0.53

Table III-28 Gamma Parameters for Pc, n and X variables for Minor Treatment,ALPHA LAMBDA



Pc 0.15

ALPHA LAMBDA


X CLAIM SIZE 0.95 1832.26Pc 0.07



III.3.1 Comparison of the Data from Other Sources

When we compare our output with the Turkish and USA statistics, we see that mainindicators are close to the data that is gathered from private insurance for example ;

The National Ambulatory Medical Care Survey (NAMCS) is a national survey designed

to meet the need for objective, reliable information about the provision and use of ambulatory

medical care services in the United States. Also Health, United States, 2000 This report was

compiled by the Centers for Disease Control and Prevention (CDC), National Center for

Health Statistics (NCHS).

And also “Health Service Utilization Survey in Turkey” Ministry of Health, Turkey is a

very big sampled from overall Turkey with different income and educational levels [21]

Table III-29 Annual Number Physician Contacts

Age Group Private Insurance

Data

USA NAMCS data Health Service

Utilization Survey

in Turkey

0-14 M/F 3.11 2.95 1.84

15-44 Male 1.56 1.75 1.54

15-44 Female 2.54 3.25 2.74

45-64 Male 1.83 3.2 3.09

45-64 Female 2.83 4.2 4.48

Note: In private health insurance, maternity visits, optician controls are not included.



Table III-30 Annual Number Hospitalizations

Age GroupPrivate Insurance

Data

Health, United

States, 2000

Health Service

Utilization Survey

in Turkey

0-14 M/F 0.06 0.04 0.013-0.03

15-44 Male 0.06 0.085 (F/M) 0.025

15-44 Female 0.06 0.085(F/M) 0.059

45-64 Male 0.08 0.094-0.145(F/M) 0.061

45-64 Female 0.09 0.094-0.145(F/M) 0.072

In Health Service Utilization Survey in Turkey, to show the effect of various socio-

economic factors.

One of them is the Table V.19, this table conflicts the thesis(although it was mentioned

in the report) that increase in income level will increase the number of physician contacts

Table III-31 Physician contacts with different level of income

Physician contacts at age 15-44 band

Income level 1 1.66Income level 2 1.35

Income level 3 3.51

Income level 4 2.68

Income level 5 2.81



PART.IV.

THE MODEL

IV.1 ALTERNATIVE MODELS

There are various analytical or non analytic approaches to the aggregate distributions

(also called compound distributions). Especially in insurance the actuarial science is dealing

with the analytical solutions of the aggregate distributions.

The main course that we will benefit from actuarial literature are "Aggregate Loss

Models" Where sometimes referred as Compound Distributions.

There are alternative approaches to the problem which are; Moment based Approach(approximation), Recursive Algorithm, Inversion Methods, and simulation are used. No

method is clearly superior to other for all problems. Each method has both advantages and

disadvantages when compared with others.

IV.1.1 Moments Based Approach

In moment-based approach, moments of the aggregate distribution are calculated withthe moments of the compounding distributions. If the model can be based on a very familiar

distributions and the aggregate distribution is calculated to have a reasonable skew ness than

this method is the easiest way to calculate the models.



During the 10 years of experience a moment based model was build for calculating the

group proposals. The reason why a moment based model developed was it is the simplest and

fastest approach for forecasting health insurance quotations trough marketing people

In the model for aggregate distribution and limits various solutions were produced

sizenumber sizenumber annual avgavg 2222 .. σ σ σ += Equation IV-4

Having used the formulas above, related with the group being new or old,

different distributions may be found. These are

groupnumber groupsizegroupannual avgavgavg ___ .= Equation IV-5

If it is a new group, using variances and means of the size claim and number

distributions of the portfolio, a new annual distribution may be found.

portf number portf size portf annual avgavgavg ___ .= Equation IV-6

If we have the prior years experience for the group, , using variances and means of size

claim and number distributions formed with respect to the experience data, a new annual

distribution may be found.

).().( _2

_2

_2

__2

portf size portf number portf size portf number portf annual avgavg σ σ σ += Equation IV-7

If we have the prior years experience for the group,

The mean of size claim distribution via experience and the mean of size claim

distribution of the portfolio combined with a pre-defined coefficient Zi, portf+group sizeclaim average is found.

portf sizeigroupsizegroup portf size avg Z avg Z avg ____ ).1(. −+= Equation IV-8

The variance of size claim distribution via experience and the variance of size claim

distribution of the portfolio combined with a pre-defined coefficient Zq, portf+group size

claim variance is found.

groupsizegroupnumber groupsizegroupnumber groupannual avgavg _2

_2

_2

__2 .. σ σ σ += Equation IV-9

As a result of , setting this data into the formulas given above, variance and mean of

the annual distribution is found.

group portf number group portf sizegroup portf annual avgavgavg ______ .= Equation IV-10



IV.1.2 Recursive Algorithm

This method assumes a discrete claim severity distribution. By choosing a large enough

number of points for the claim severity distribution, one can obtain any desired degree of accuracy. For this reason, it has been called an “exact” method. This method requires far less

computer time than Monte Carlo simulation. Much of the mathematics involved is similar to

that used in the characteristic function in-version method. There are derivation of the

recursive method which does not involve inverting the Laplace transform designed in to work

for (a,b,0) and (a,b,1) parameter distributions pk = ( a + b/k) pk-1 [20]

IV.1.3 Inversion -Methods Fast Fourier-

By using canned routines which are available with many software packages using

vectors in complex number forms Discrete Fourier Transform - Fast Fourier Transform

method; Used both in convoluting and combining various distributions (physician visits and

prescribed drugs etc)

Direct Numerical Inversion; the method inverts the characteristic function of the

aggregate loss distribution using approximations like replacing severity distribution function

by piecewise linear distribution.

Here we define the Fourier application

Fast Fourier Transformation can be used to both combine n fold convolution

and also correlated benefits (physician + prescribed drugs) like simulation contrary to

moments based approach and recursive algorithm,

S x N n X xn

n( ) ( ) ( )*= ×

=

∞

∑0

Equation (IV-11)

))(()( )*1(* x X X x X nn∗= − Equation IV-12



Fourier Estimation

0

0,02

0,04

0,06

0,08

1 4 7 1 0

1 3

1 6

1 9

2 2

2 5

2 8

3 1

Fourier Es timation Real

Figure IV.1 Output for Prescribed Drugs of a Group

In this model an excel plus visual basic applications are used the model is

Two files of FFTsHT.xls and inputfile.xls is used

The input file has the n, X, and annual total variables and the macro creates the total

annual cost distribution by combining n and X distributions

This example was the combination of n and X, while combining two different benefits

again Fourier transformation can be used. In this case the formula will be [34]

( ) ( ) ( ) ( )[ ] ( )[ ]−−+= ∑ ji

j X i X jik X X k X X t t t t t t jik k

p

φ φ ω φ φ φ 111...,..., ,11,..., 11Equation (IV-13)

1 X φ are characteristic functions of the input distributions

ω is the correlation matrix for two different benefits

However the as the mathematics is complex for both explaining the problems in model

development (like below) simulation is preferred for development of the model



Figure IV.2 Second Fourier Example

IV.2 SIMULATION MODEL STRUCTUREModel that is provided here is made up of various parameters and variables, the simplest

technique was chosen. The structure is based on simulation and mathematical statistics, and

actuarial science is used.

@RISK is an Excel add-in software product that provides Excel to perform risk analysis

using Monte Carlo simulation in a spreadsheet based environment. @RISK Version 4.0.5.

Professional Edition of Palisade Corporation (where Best-fit software is also provided) is used

The model is formed of below 3 major modules where each module have different

subdivisions.

A. Individual Expenses Module

B. Experience and Credibility module

C. Group(Individual to Group) Module



IV.2.1 Individual Expenses Module

In this module with limits, deductibles and raw figures health care

expenditures/utilizations of one person for one year and shorter time periods are calculated,

All of these 3 variables are assumed to be have probability distributions and the

characteristics of these distributions are derived by

• Age

• GenderComment [B1]: AlthouStatus of health and Socioeconomic / geographic coare affecting the number aaverage cost of healthexpenditures, for each of tcategories of these differebands

Socio economic and geoconditions



START

INPUT NUMBER OF MEMBERS

ACCORDING TO AGE AND SEXDISTRIBUTION

Calculate the representative First and Second Moments forPc, n ,X

forPhysician, Prescription, Diagnostics,Minor Treatment and Hospitalization

from Age and Sex Bands

Calculate theParameters of the Distributions from the First and SecondMoments forPc (Binomial Dist.)n, X (Gamma Dist.)

forPhysician, Prescription, Diagnostics,Minor Treatment and Hospitalization

IF THE MODEL ISEXPERIENCE RATED

COMBINE THE CALCULATED Pc, nAND X PARAMETERS WITH PRIOR

GROUP DATA

Y

SIMULATIONITERATIONS

N

PERSON TOGROUP MODEL

Figure IV.3 Creation of the Input Parameters for Individual to Group Module +

Experience-Credibility Module



Simualtion Iterations

START

Loop up to Last Iterationand FINISH

Settingn via Gamma Dist.

SettingX's via Gamma Dist.

SettingPc via Binom Dist.

Settingmonth for each X viaEmpiricalDist.

Calculation of totalexpenditure and counts w.r.t.month

Generate Seed forPc, n ,X 's and month' s

forPhysician, Prescription,

Diagnostics,Minor Treatmentand Hospitalization

with the Spearman RankCorrelation forPc and n

Filter n and X's according to limits anddeductibles

Calculation ofAnnual Totals forCosts Incurred

Filtered with Limits and Deductibles

Combine Annual Totals forCosts Incurred

Filtered with Limits and Deductiblesmonthly expenditure and counts

in total sheet

Figure IV.4 Iteration of the Individual Expense Module(fed with credibility if any)



IV.2.1.1 Pc, n, X

These one-year expenditures can be formed of

• Medical Visit

• Drug• Diagnosis

• Minor Medical Treatment

• In-patient Treatment (Hospitalization)

The variables that are used in each category areo Pc (probability of claiming)o n (The frequency of treatment)

o X (Unit cost per treatment (i.e. one physician visit cost , cost of the drugs in oneprescription, one inpatient hospital stay )

IV.2.1.2 Age and Gender

For each 5 benefits there are 3 main category. Children, males and females have in total

29 different categories. Especially most of the health insurance models are calculating the

children in one category but statistics show us that different bands in children have 4 to 5

times different frequency figures and the groups can be very different children demographics

as well as adult demographics.

For different age and gender profiles of groups number of people in that age band are

used as weight factors to get the representative figures.

IV.2.1.3 Distribution Assumptions

For Pc, n and X which means total group of 435 converted to 15 (5 benefits * 3

‘Pc,n,X’). In such kind of a conversion, calculating different types of distributions for each

sub category is impossible. For Pc, Binomial distributions is used as Pc probabilities are not

very low(some times %90) Gamma is used for X and n distribution as it is a very flexibledistribution. After examining the distributions it was seen that Gamma was sufficient for most

of tail lengths(in the individual to group module large medical expenditures are inserted )and

being much more flexible, it was found suitable. For n as its out put is discrete a rounding is

done after the seed is executed and n is produced .



Here are the examples of the different shaped distributions considering the limits

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 6 1 1

1 6

2 1

2 6

3 1

risk GammaOutput

real hospitalclaims

Figure IV.5 Hospital Claim Cost X graph produced with gamma and real data

00.050.1

0.150.2

0.250.3

1 4 7 1 0

1 3

1 6

1 9

# DR Real

# DRGammaRisk

Figure IV.6 Number of Physician Visits n graph produced with gamma and real

data

According to Gamma Beta is Variance / Average and Alpha is Average / Beta

Comment [B2]: 3 no luçalışması

Comment [B3]: 3 noluolan d bank verilerini = daarındırıp çalıştık



IV.2.1.4 Limits and Deductibles

In various social security and private health systems, limits and deductibles are applied.

The effect of these may be very interesting to the aggregate cost or total utilization.

In private insurance systems and some times social security benefits are limited or

applied deductibles.

Briefly Deductible is “Amount of expenses that the insured party must pay before

receiving any benefits from the insurance company” and limit is “the maximum dollar amount

that an insurance company will pay based on annual total or case, illness definition”[14]

Limits are the maximum amounts that the risk career (private or social security fund)

will not compensate above. Deductibles are the minimum amounts that the risk career will not

compensate below.

In the model following types of limits and deductibles can be applied.

• Annual number of case unit (Maximum/out of pocket Number of expenditures

for 1 year applied ton),limit / deductible

• Per case limit /deductible(Cost of each expenditure applied toX)

• Annual USD limit/deductible (Maximum amount of expenditure in USD terms

for 1 year)

Deductibles with the limit category are defined.



Figure IV.7 Limit and Deductible Application Process

Limits and deductibles are drastically affecting the overall characteristics of the costs

and utilizations as well as total and benefit basis. When we compare the limited number of

utilizations and total cost with health care spending without limit and the total cost of the

expenditures after the limits, the shape of the distribution is changing.



0

5 0

1 0 0

1 5 0

2 0 0

Costs Occurred0

0.10.20.30.40.50.6

0.70.8

Costs Occurred 0.554 0.06 0.039 0.035 0.028 0.025 0.026 0.021 0.021 0.019

Annual Limits of 150$ 0.554 0.06 0.039 0.035 0.028 0.025 0.259 0 0 0

Annual Limits of 150$+ AnnualDeductible of 50$ 0.653 0.035 0.028 0.025 0.259 0 0 0 0 0

Annual Limits of 2000$ 0.554 0.06 0.039 0.035 0.028 0.025 0.026 0.021 0.021 0.019

Annual Limits o f 2000$+Annual Deduct ible of 100$

0.716 0.025 0.026 0.021 0.021 0.019 0.015 0.016 0.013 0.012

0 25 50 75 100 125 150 175 200 225

Figure IV.8 Limit and Deductible Affect On Diagnostic Annual Costs

Similar affects occur for the total of the costs from various benefits and deductibles



1 4 7 1 0

1 3

1

6

1 9

CLAIMSINCURRED

00.10.20.30.40.50.60.70.80.9

CLAIMS INCURRED 0.048 0.509 0.211 0.086 0.049 0.036 0.016 0.012 0.007 0.005 0.004 0.004 0.003 0.002 0.003 0 0 9E-04 0 0 0

NUMBER OF CLAIMS0 .048 0 .036 0 .044 0 .063 0 .044 0 .057 0 .068 0 .047 0 .057 0 .043 0 .045 0 .043 0 .049 0 .032 0 .036 0 .029 0 .03 0 .03 0 .019 0 .019 0 .308

HYBRID LIMITED1 0.03 0.627 0.229 0.031 0.02 0.016 0.016 0.017 0.012 0 0 0 0 0 0 0 0 0 0 0 0

HYBRID LIMITED2 0.036 0.842 0.046 0.019 0.019 0.01 0 .027 9E-04 0 0 0 0 0 0 0 0 0 0 0 0 0

HYBRID LIMITED3 0.03 0.45 0.27 0.117 0.047 0.025 0.016 0.015 0.005 0.004 0.004 0.005 0.002 0.002 0.003 0 0 0 0 0 9E-04

HYBRID LIMITED4 0.538 0 .379 0 .047 0.012 0.007 0 .003 0 .002 0 .003 0.004 9E-04 0 0 0 0 0 0 0.003 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Figure IV.9 When various scenarios Applied Total Costs on Individual Basis

IV.2.1.5 Dependency

While producing the seed for the input of these 3 variables Pc and n distributions are

correlated with Spearman Rank Correlation. from the observation it was found that the annual

number of treatment and probability of claiming(Pc) is correlated with each other.

In the model distributions of Pc and n are correlated by @RISK with spearman

correlation where the input Coefficient are entered with matrixes. The rank-order correlationcoefficient was developed by C. Spearman in the early 1900's. It is calculated using rankings

of values, not actual values themselves (as is the linear correlation coefficient). A value's

"rank" is determined by its position within the min-max range of possible values for the

variable. The coefficient is a value between -1 and 1, which represents the desired degree of



correlation between the two variables during sampling. Positive coefficient values indicate a

positive relationship between the two variables — when the value sampled for one is high, the

value sampled for the second will also tend to be high. Negative coefficient values indicate an

inverse relationship between the two variables — when the value sampled for one is high, the

value sampled for the second will tend to be low. @RISK generates rank-correlated pairs of

sampled values in a two-step process. First, a set of randomly distributed "rank scores" are

generated for each variable. If 100 iterations are to be run, for example, 100 scores are

generated for each variable. (Rank scores are simply values of varying magnitude between a

minimum and maximum. @RISK uses Van der Waerden scores based on the inverse function

of the normal distribution). These rank scores are then rearranged to give pairs of scores,

which generate the desired rank correlation coefficient. For each iteration there is a pair of

scores, with one score for each variable.

Using the resources that are presented in the previous chapters as actuarial or other

predicting techniques, we try to take out the risk factors and identify the parameters of the

model affecting the health care demand. When we try to structure the predicting techniques

we have the parameters to be used in the model,

The spearman correlation coefficients for the Probability of claiming as follows;

Table IV-1 Spearman Rank Correlations For Ratio of User Input Data(Pc)

NewMatrixPc (5x5)dr!B8

binom Pc / ALPHA

pres!B8binom Pc /

ALPHA

diagnostic!B8binom Pc /

ALPHA

minortreat!B8binom Pc /

ALPHA

hospital!B8binom Pc /

ALPHAdr!B8

binom Pc / ALPHA1

pres!B8binom Pc / ALPHA

0.616 1

diagnostic!B8binom Pc / ALPHA

0.586 0.466 1

minortreat!B8binom Pc / ALPHA

0.273 0.324 0.286 1

hospital!B8binom Pc / ALPHA

0.596 0.396 0.485 0.423 1



Table IV-2 Spearman Rank Correlations For Number of Usage Input Data(n)

NewMatrixadet(5x5)

dr!B9n

PRODUCER / ALPHA

pres!B9n

PRODUCER / ALPHA

diagnostic!B9

n PRODUCER / ALPHA

minortreat!B9

n PRODUCER / ALPHA

hospital!B9

n PRODUCER / ALPHA

dr!B9n PRODUCER /

ALPHA1

pres!B9n PRODUCER /

ALPHA0.668 1

diagnostic!B9

n PRODUCER / ALPHA 0.57 0.4 1

minortreat!B9n PRODUCER /

ALPHA0.309 0.345 0.239 1

hospital!B9n PRODUCER /

ALPHA0.456 0.396 0.359 0.385 1

Uncertainty approach for the level of dependency problem can also be used if

appropriate software and configuration is handled. There is an example for the application of

Fourier transformation in the Appendix.

IV.2.1.6 Short Term Monthly Analysis

This question arises from the question if we have the stats of one-two month of a

population that we know census (like Turkey pop.) what kind of uncertainties exists and is itpossible to derive an estimation formula which has parameters of limits for expense issues,

deductibles, demographic etc, and other economic input.

This is possibly the most interesting issues complicating because of the shorter time

period creates a bigger randomness in nature. Study. In this part aggregate costs are calculated



Distribution of "n" in Monthly intervals

0

0.05

0.1

0.15

0.2

0.25

0.30.35

0.4

1 2 3 4 5 6 7 8 9 10 11

Real "n" in August Real "n" in March

Figure IV.11 Distribution of "n" in March and August

When we compare the real data for March And August, considering n, following results

occurred



Table IV-3 Descriptive Statistics of Monthly FiguresReal Costs

Occurred inMarch

Real CostsOccurred in

August

CLAIMSINCURRED in All

YearNo. of values used 1951 1951 1951No. of values ignored 0 0 0No. of min. val. 1602 1518 852% of min. val. 82.112 77.806 43.670Minimum 0.000 0.000 0.0001st quartile 0.000 0.000 0.000Median 0.000 0.000 46.2643rd quartile 0.000 0.000 274.225Maximum 1011.270 1875.490 7694.798Range 1011.270 1875.490 7694.798Sum 22097.932 27899.751 468342.505Mean 11.326 14.300 240.053Geometric meanHarmonic meanKurtosis 156.706 293.945 50.291Skewness 11.302 15.618 5.593Kurtosis 157.276 295.008 50.478Skewness 11.320 15.642 5.601CV (standard deviation/mean) 5.047 5.476 2.137Sample variance 3266.456 6128.155 263017.830Estimated variance 3268.131 6131.298 263152.711Sample standard deviation 57.153 78.283 512.853Estimated standard deviation 57.168 78.303 512.984Mean absolute deviation 18.868 22.777 284.704Median absolute deviation 0.000 0.000 46.264Standard-error 1.294 1.773 11.614Lower bound. Mean IC 8.788 10.824 217.276Upper bound. Mean IC 13.865 17.777 262.829

When we examine these results we can say that Coefficient of Variation increase in

monthly statistics(as would be expected)

Comparing the monthly costs occurred between August and March

Note: The calculation of the Mann-Whitney's U takes ties into account



Table IV-4 Mann-Whitney U test (two-tailed test) for Monthly Incurred CostsU 673737.000U (expected value) 715208.000U (variance) 185183031.030

Z (observed value) -3.048Z (critical value) 1.960Two-tailed p-value 0.002Alpha 0.050

The Mann-Whitney's U is normalized and tested against the normal distribution

Decision: At the level of significance alpha=0.050 the decision is to reject the null

hypothesis of absence of difference between samples. In other words, the difference between

samples is significant.

Kolmogorov-Smirnov test / two-tailed test:Table IV-5 Kolmogorov-Smirnov(two-tailed test) test for Monthly Incurred

CostsD 0.063Two-tailed p-value 0.017Alpha 0.050

Decision:

At the level of significance alpha=0.050 the decision is to reject the null hypothesis of

absence of difference between samples. In other words, the difference between samples is

significant.

Also when we do the comparison between number of expenditures

Note: The calculation of the Mann-Whitney's U takes ties into account

Table IV-6 Mann-Whitney's U (two-tailed test) test for Monthly Number of

UtilizationsU 673325.500

U (expected value) 715208.000U (variance) 184916515.611Z (observed value) -3.080Z (critical value) 1.960Two-tailed p-value 0.002Alpha 0.050



For in patient benefits

Table IV-8 Empirical Distribution for Number of Utilizations for In-Patient

Benefitspdf

1 0.08002 0.09003 0.10004 0.08005 0.08006 0.08007 0.08008 0.0700

9 0.080010 0.080011 0.080012 0.1000



All of these Number of cases and total expenditure are presented in each benefit sheet

and also are summed in a summary sheet, which creates one member’s outputMinimum 0

Mean 40.37111

Maximum 11928.55

Std Dev 229.8935

Variance 52851.01

Skewness 25.40516

Kurtosis 1010.965

Mode 0

Left X 0

Left P 5%

Right X 196.7438

Right P 95%Diff. X 196.7438

Diff. P 90%

5th Perc. 0

95th Perc. 196.7438

#Errors 0

Filter Min

Filter Max

#Filtered 0

IV.2.2 Experience - Credibility Module

Although we combine the sub groups according to age and gender and analyze the risk

in uniform sub groups in terms of medical expense and utilizations, we can always improve

our estimations with the experience of that group in the following periods. (we will be dealing

with prospective experience rating techniques as this study is focused on the prediction)

Credibility Theory is one of the most well examined subjects in actuarial profession

within the names of "credibility rating" and "experience rating" dealing with this and has been

published various articles on non-life insurance, disability and life.



Credibility is a procedure by which data external to a particular group or individual are

combined with the experience of the group or individual in order to better estimate te

expected loss(or any other statistical quantity) for each group or quantity.

The external data are typically a rate that has been determined based on historical data

from other, similar policies. The internal data are the experience of the individual or group

itself. Often the calculation is reduced to a very simple form [12].

PrRatedE.premiumportfolio*Z)-(1experiencegroup *Z =+ Equation (IV-14)

Z= credibility factor

Group experience

If the experience size of the group is enough we can base our calculation according to

experience of the group(with the inflationary assumptions etc.) however the question for what

is the group size that the experience should be based on 100% is usually unknown.

In the applications standard tables are used like this.[25, 26]

Table IV-9 Credibility ratings for groups with at least 3 year’s claims history

Number of Peaople Credibility Rates

50 to 99 35-50%

100 to 399 50-70%

400 to 999 70-90%

1000 or more 100%

However we structured the model based on much more sophisticated grounds.

Z is calculated for each benefit (for hospitalization, physician fees, prescribed drugs

etc.) as each of these benefits is defined separately for each group.

• The size of the group

• The limit amount of the benefit (large claims require more experience)

• The incidence rate of the claims



• The number of years experienced

Affects the Z. Z = sqrt of (n / n100%) [18]

n100% is the group size that gives us the full credibility for experience rating

2%100 )

*..*)((

eter RangeParamestimate AVGprior estimateSTDprior confidence NormInv

n = Equation (IV-15)

100%

.

nn

Z concerned groupsize partial =

Equation (IV-16)

concerned groupsize partial nconfidence NormInveter RangeParam

STD AVG

Z .)(×= Equation IV-17

According to this formula for 0,95 confidence and 0,1 accepted deviation, normal

inverse function output is 1.64(=NORMINV(0.95;0;1)) and

(Normal-Inverse / Range Parameter) =(1.65 / 0.1)=16.5

For each variable the Prior year averages and standard deviation will be calculated and

after that according to cases handled the “group size concerned” will be calculated.

We calculate the required number of experience cases for each variable of Pc, n, X to

get 100% credibility in the experience formula (Z to be taken 1 and (1-Z) to be 0).

In Pc as every insured will be a case experience for us for the probability of claiming,

we will be counting the member of the group to give the credibility



Pc AVG STD n100% Physician Visits 0.69 0.46 122

Prescribed Drugs 0.69 0.46 122

Diagnostic Procedures 0.53 0.49 240Minor Treatment 0.15 0.36 1533

Hospital Treatment 0.07 0.26 3595

For n the required number of cases is calculated byn100% but as the all the members are

not spending health care expenditures(Pc is always <1) we have to divide the result of the

n AVG STD Required number of

member (n100% / Pc)

Physician Visits 3.10 2.52 179 / 0.69=260

Prescribed Drugs 4.28 3.88 222/0.69=321

Diagnostic Procedures 3.9 3.92 273/0.53=516

Minor Treatment 1 2.26 271/0.15=1804

Hospital Treatment 1 1 3595

X AVG STD Required number of member (n100% / Pc Xn)

Physician Visits 36.84 18.49 68 / 0.69 X 3.1=32

Prescribed Drugs 21.47 21.47 271 / 0.69 X 4.28=92

Diagnostic Procedures 65.24 72.04 330 / 0.53 X3.9=160

Minor Treatment 57.24 114.48 1082 / 0.15 X

2.06=3502

Hospital Treatment 1740.65 1785.87 285 /0.07 X1 =4068

For each variable there are different credibility weights.



The Trend parameter allows for gradual movements of the inception and termination

rate parameters away from their starting points over time. The shock parameter allows for

sudden jumps in experience, for example due to a change in the legal environment

)}1).(1{(_

1k k k k

Module IndivGroupSize

i

DC B A EmpirDist ++++∑=

Equation IV-19

Individual to Group Formula with Uncertainty from Different Factors

Ak = representing credibility risk (iteration k)

Bk = representing appropriateness risk (iteration k)

Ck = representing trend risk (iteration k)

Dk = representing shock risk (iteration k)

For A, B and C normal distribution issuedParameter Avg StdCredibility 0% 20%Appropriateness 0% 20%Trend 1% 2.50%

Equation IV-20 Normal Distribution Parameters N(µ, σ)

For the Shock risk Generalized Distribution is usedx f(x)

-30 0-29 0.05-1 0.10 99.71 0.1

29 0.0530 0

Equation IV-21 Shock Risk Generalized Distribution Points



Simualtion Iterations for Individual to Group

START

Setting Individual Module OutputX's viaEmprical Dist.

Setting Uncertainty from credibility of thedata via Normal Dist.

Generate Seed for

Pc, n ,X 's and month' sforPhysician, Prescription,

Diagnostics,Minor Treatmentand Hospitalization

with the Spearman RankCorrelation forPc and n

Calculation ofAnnual Totals

Setting Uncertainty from suitability of thedata via Normal Dist.

Setting Uncertainty from allowance forshocks via Generalized Dist.

Setting Uncertainty from trends viaNormal Dist.

Figure IV.12 Flow Process for the Individual to Group Module

IV.2.4 Characteristics of the Model Output and SensitivityIn this section with the help of the model we examined the characteristics that we

cannot examine in real life like effect of dependency, group size(statistical fluctuation) and

Uncertainty due to factors mentioned in Individual to Group Module. After examining these

an overall sensitivity is done according to the parameters that has on effect on the costs and

limit/deductible is provided.



IV.2.4.1 The Effect of Dependency

Using the individual model and testing the sensitivity of the correlation matrix below

output is gathered.

If we take the Spearman correlations as 0 tha below results are taken

Table IV-10 Summary Statistic of the Total Costs Incurred(Independent of the

limits)

NameWith real

correlation

With allcorrelation input –

0.25

With allcorrelation input

0

With allcorrelation input

1

Minimum 0 0 0 0Mean 337.15 350.98 349.40 335.43Maximum 10,592.66 9,762.28 13,968.36 11,001.53Std Dev 657.61 562.09 620.02 547.87Variance 432,446.40 315,940.80 384,420.90 300,159.30Skewness 5.64 6.99 6.17 7.56Kurtosis 52.52 71.79 67.44 91.66Mode 0 0 0 0Left X 0 21.31772 0 0Left P 5% 5% 5% 5%

Right X 1289.10 905.06 1183.33 951.26Right P 95% 95% 95% 95%Diff. X 1289.10 883.74 1183.33 951.26



Table IV-11 Distribution of the Total Costs Incurred(Independent of the limits)

TOTAL COST0

CORREL'-

0.25CORREL1

CORRELREAL

CORRELGrand

Total0 6.77% 2.77% 34.18% 17.71% 15.36%1-500 75.87% 81.28% 45.81% 62.33% 66.32%501-1000 12.85% 11.75% 12.24% 13.18% 12.51%1001-1500 2.18% 1.69% 3.85% 3.52% 2.81%1501-2000 0.82% 0.65% 1.60% 1.18% 1.06%2001-2500 0.39% 0.49% 0.81% 0.63% 0.58%2501-3000 0.36% 0.32% 0.34% 0.33% 0.34%3001-3500 0.17% 0.29% 0.32% 0.29% 0.27%3501-4000 0.17% 0.20% 0.21% 0.27% 0.21%4001-4500 0.09% 0.20% 0.16% 0.12% 0.14%4501-5000 0.10% 0.06% 0.16% 0.09% 0.10%5001-5500 0.05% 0.11% 0.06% 0.18% 0.10%5501-6000 0.00% 0.01% 0.07% 0.05% 0.03%6001-6500 0.04% 0.04% 0.05% 0.03% 0.04%6501-7000 0.03% 0.04% 0.03% 0.00% 0.03%7001-7500 0.01% 0.02% 0.00% 0.02% 0.01%7501-8000 0.03% 0.03% 0.03% 0.02% 0.03%8001-8500 0.03% 0.01% 0.02% 0.02% 0.02%8501-9000 0.01% 0.03% 0.02% 0.01% 0.02%9001-9500 0.01% 0.00% 0.02% 0.00% 0.01%9501-10000 0.00% 0.01% 0.00% 0.01% 0.01%10001-10500 0.01% 0.00% 0.01% 0.00% 0.01%10501-11000 0.01% 0.00% 0.01% 0.00% 0.01%13501-14000 0.00% 0.00% 0.00% 0.01% 0.00%Grand Total 100.00% 100.00% 100.00% 100.00% 100.00%



IV.2.4.2 The Effect of Group Size and Uncertainty on Individual to Group

Module

By just iterating the model to examine the statistical fluctuation combining the twoprobabilities for 2 different groups where the first one has 50 members and the secondhas 500 the simulation of 10.000 iterations gives us the distribution of total cost perheadas follows;



When we examine these out puts with the uncertainty modifications in Individual to

Group Module section

Table IV-15 Distribution Output for Group Members

50 withuncertainty

500 withuncertainty

50 nouncertainty

500 nouncertainty

500 noshockvariable

0 0.000 0.000 0.000 0.000 0.00025 0.000 0.000 0.000 0.000 0.00050 0.000 0.000 0.000 0.000 0.00075 0.000 0.000 0.000 0.000 0.000

100 0.007 0.000 0.004 0.000 0.000

125 0.039 0.000 0.046 0.000 0.000150 0.081 0.000 0.098 0.000 0.000175 0.107 0.002 0.145 0.017 0.019200 0.119 0.034 0.173 0.257 0.230225 0.114 0.154 0.154 0.484 0.454250 0.113 0.257 0.136 0.211 0.248275 0.093 0.222 0.093 0.031 0.047300 0.074 0.129 0.066 0.001 0.003325 0.058 0.068 0.039 0.000 0.000350 0.044 0.046 0.023 0.000 0.000375 0.036 0.034 0.013 0.000 0.000400 0.024 0.019 0.007 0.000 0.000425 0.017 0.014 0.002 0.000 0.000450 0.011 0.007 0.001 0.000 0.000475 0.009 0.005 0.001 0.000 0.000500 0.008 0.003 0.000 0.000 0.000



0

1000

2000

3000

4000

5000

6000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

50 w ith uncertainty

500 w ith uncertainty

50 no uncertainty

500 no uncertainty

500 no shock variable

Equation IV-22 Average Expenditure Per Member For Groups with Different

Number of Members

IV.2.4.3 Sensitivity

In order to identify the most critical inputs in our model we make the sensitivity

analysis. In below graph These results show the sensitivity of each output variable to its inputvariables. The Sensitivity analysis performed on the output variables and their associated

inputs uses either a multivariate stepwise regression analysis or a rank order correlation

analysis. The input distributions in the model are ranked by their impact on the output. In the

@RISK software, multiple regression tries to fit multiple input data sets to a planar equation

that could produce the output data set. The sensitivity values returned by @RISK are

normalized variations of the regression coefficients. During this stepwise regression technique

is used as it is is preferable for large numbers of inputs since it removes all variables that

provide an insignificant contribution from the model. The second technique used is a rankcorrelation calculation. With this analysis, correlation coefficients are calculated between the

output values and each set of sampled input values. The results of each form of sensitivity

analysis are displayed as a "tornado" type chart, with longer bars at the top representing the

most significant input variables.



Regression Sensitivity for TOTAL COSTINCURRED / After P...

Std b Coefficients

TOTAL COST INCURRED/M11 .031

TOTAL COST INCURRED/N11 .031

TOTAL COST INCURRED/K11 .034

date/N9-.035

TOTAL COST INCURRED/Q11 .039

TOTAL COST INCURRED / LIMI.../D11 .047

date/P9 .061

bınom Pc / ALPHA/B8 .064



n PRODUCER / ALPHA/B9 .099


TOTAL COST INCURRED / LIMI.../D11 .126




-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Figure IV.13 Std B coefficients for Total Costs Incurred



Table IV-1612 Std B coefficients for Total Costs IncurredRank

for totalsheet!B11 Cell Name

B11 / TOTAL

COST INCURRED / After Pc % Regression

#1 hospital!B8 bınom Pc / ALPHA 0.549#2 diagnostic!B9 n PRODUCER / ALPHA 0.213#3 diagnostic!B8 bınom Pc / ALPHA 0.142#4 hospital!D11 TOTAL COST INCURRED / LIMIT 0.126#5 dr!B9 n PRODUCER / ALPHA 0.118#6 pres!B9 n PRODUCER / ALPHA 0.099#7 dr!B8 bınom Pc / ALPHA 0.086#8 minortreat!B8 bınom Pc / ALPHA 0.065#9 pres!B8

bınom Pc / ALPHA0.064

#10 minortreat!P9 date 0.061#11 diagnostic!D11 TOTAL COST INCURRED / LIMIT 0.047#12 diagnostic!Q11 TOTAL COST INCURRED 0.039#13 minortreat!N9 date -0.035#14 diagnostic!K11 TOTAL COST INCURRED 0.034#15 minortreat!N11 TOTAL COST INCURRED 0.031#16 diagnostic!M11 TOTAL COST INCURRED 0.031#17 pres!E11 TOTAL COST INCURRED / DEDUCTIBLE 0.031#18 minortreat!R9 date 0.03

#19 pres!D11 TOTAL COST INCURRED / LIMIT 0.03#20 diagnostic!R11 TOTAL COST INCURRED 0.029#21 dr!V11 TOTAL COST INCURRED -0.029#22 diagnostic!E11 TOTAL COST INCURRED / DEDUCTIBLE 0.026#23 diagnostic!AA11 TOTAL COST INCURRED 0.026#24 dr!Q11 TOTAL COST INCURRED -0.026#25 pres!O11 TOTAL COST INCURRED 0.025#26 diagnostic!H11 TOTAL COST INCURRED / mom2 0.024

R-Squared= 0.5822099



Regression Sensitivity for Cell B16

Std b Coefficients

0123456789

10111213141516

TOTAL COST INCURRED / mom2.../H11 .037date/X9-.04

TOTAL COST INCURRED / DEDU.../E11 .041date/R9 .042TOTAL COST INCURRED/N11 .042TOTAL COST INCURRED/M11 .042

date/N9-.043TOTAL COST INCURRED/K11 .05TOTAL COST INCURRED / LIMI. ../ D11 .052TOTAL COST INCURRED/Q11 .054bınom Pc / ALPHA/B8 .057date/P9 .084TOTAL COST INCURRED / LIMI.../D11 .154bınom Pc / ALPHA/B8 .155n PRODUCER / ALPHA/B9 .285b ınom Pc / ALPHA/B8 .393

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Figure IV.14 Std B coefficients for Total Costs After the Limits and Deductibles



Table IV-17Std B coefficients for Total Costs After the Limits and Deductibles

Rank

for totalsheet!B16 Cell Name

B16 / LEVAFTER HYBRIDLIMITS ANDDEDUCTIBLES / AfterPc % Regression

#1 hospital!B8 bınom Pc / ALPHA 0.393#2 diagnostic!B9 n PRODUCER / ALPHA 0.285#3 diagnostic!B8 bınom Pc / ALPHA 0.155#4 hospital!D11 TOTAL COST INCURRED / LIMIT 0.154#5 minortreat!P9 date 0.084#6 minortreat!B8 bınom Pc / ALPHA 0.057#7 diagnostic!Q11 TOTAL COST INCURRED 0.054#8 diagnostic!D11 TOTAL COST INCURRED / LIMIT 0.052

#9 diagnostic!K11 TOTAL COST INCURRED 0.05#10 minortreat!N9 date -0.043#11 diagnostic!M11 TOTAL COST INCURRED 0.042#12 minortreat!N11 TOTAL COST INCURRED 0.042#13 minortreat!R9 date 0.042#14 diagnostic!E11 TOTAL COST INCURRED / DEDUCTIBLE 0.041#15 diagnostic!X9 date -0.04#16 diagnostic!H11 TOTAL COST INCURRED / mom2 0.037#17 diagnostic!G11 TOTAL COST INCURRED / mom1 0.035#18 diagnostic!J11 TOTAL COST INCURRED 0.034#19 diagnostic!L11 TOTAL COST INCURRED 0.034#20 minortreat!B9 n PRODUCER / ALPHA 0.033#21 dr!N11 TOTAL COST INCURRED 0.033#22 diagnostic!R11 TOTAL COST INCURRED 0.033#23 diagnostic!I11 TOTAL COST INCURRED / var 0.031 R-Squared= 0.3596112



Table V-1 Age an Gender characteristics of the Sample DataGENDER AGE Group 1 Group 2 Group 3

CHILD 0-4 0.09 0.10 0.13CHILD 5-9 0.04 0.05 0.09CHILD 10-14 0.03 0.03 0.04CHILD 15-19 0.01 0.01 0.01CHILD 20-24 0.01 0.01 0.01

0.00MALE 16-20 0.00 0.00 0.00MALE 21-25 0.06 0.05 0.02MALE 26-30 0.15 0.14 0.14MALE 31-35 0.08 0.09 0.14MALE 36-40 0.03 0.03 0.05

MALE 41-45 0.01 0.02 0.02MALE 46-50 0.01 0.01 0.01MALE 51-55 0.00 0.00 0.00MALE 56-60 0.00 0.00 0.00MALE 61-65 0.00 0.00 0.00MALE 66-70 0.00 0.00 0.00MALE 71-75 0.00 0.00 0.00

0.00FEMALE 16-20 0.00 0.00 0.00FEMALE 21-25 0.07 0.07 0.11

FEMALE 26-30 0.13 0.13 0.15FEMALE 31-35 0.08 0.08 0.09FEMALE 36-40 0.03 0.03 0.02FEMALE 41-45 0.01 0.01 0.00FEMALE 46-50 0.00 0.00 0.00FEMALE 51-55 0.00 0.00 0.00FEMALE 56-60 0.00 0.00 0.00FEMALE 61-65 0.00 0.00 0.00FEMALE 66-70 0.00 0.00 0.00FEMALE 71-75 0.00 0.00 0.00



V.1.1.2 Profile of Group 1

This group is formed of total members where the 0.58 of the total is employed by the

employer setting up the plan. There have been maximum 1607 members in the group andcosts are formed of records from 1999. This group is formed of white collar all over Turkey

who are on the mid and upper income class.



employer setting up the plan. There have been maximum 1686 members in the group and

costs are formed of records from 2000. This group is formed of white collar all over Turkey

who are on the mid and upper income class.



employer setting up the plan. There have been maximum 4143 members in the group and

costs are formed of records from 1999. this group is formed of white collar office

workers(from Istanbul) and sales representatives from allover Turkey, and in the second part

white collar and blue collar workers(from Anatolian non Ankara metropolitan)who are on themid and upper income class.

V.1.2 Scenarios

And scenario tested is provided as

Table V-2 Dr scenarios

DR LIMITS (all numbers in USD) SCNR1 SCNR2Number of Physician Visit Limit 4 10000Number of Physician Visit Deductible 0 0Per Physician Visit Limit 35 100Per Physician Visit Deductible 0 50



Table V-3 Prescription ScenariosPRES LIMITS SCNR1 SCNR2Number of Prescription Limit 4 10000Number of Physician Visit Deductible 0 0

Per Prescription Limit 35 100Per Prescription Deductible 0 50

Table V-4 Diagnostic Scenarios

DIAGNOSTIC LIMITS SCNR1 SCNR2Number of Diagnostic Proced. Limit 10000 10000Number of Diagnostic Proced. Deductible 0 0Annual Diagnostic Proced. Expense Total

Limit 150 2000

Annual Diagnostic Proced. Expense TotalDeductible 0 100

Table V-5 Minor Treatment Scenarios

MINORTREAT LIMITS SCNR1 SCNR2Number of Diagnostic Proced. Limit 10000 10000Number of Diagnostic Proced. Deductible 0 0Annual Diagnostic Proced. Expense Total Limit 500 2000Annual Diagnostic Proced. Expense Total Deductible 0 100

Table V-6 Hospital Scenarios

HOSPITAL LIMITS SCNR1 SCNR2Number of Hospitalization Limit 10000 10000Number of Hospitalization Deductible 0 0Annual Hospitalization Expense Total Limit 1500 30000Annual Hospitalization Expense Total

Deductible 0 1000



V.1.2.1 Output Analysis

V.1.2.1.1 Analysis on Benefit On Individual Total Cost

The analysis can only be done on individual basis (it is nearly impossible to find out 15-

20 years of a big group experience)

For the number of iterations 10,000 is chosen as it is above the number suggested by

@RISK. @RISK includes a convergence monitoring capability to help evaluate the stability

of the output distributions during a simulation. As more iterations are run, output distributions

become more "stable" as the statistics describing each distribution change less and less with

additional iterations. It is important to run enough iterations so that the statistics generated on

your outputs are reliable. However, there comes a point when the time spent for additionaliterations is essentially wasted because the statistics generated are not changing significantly.

Different random seed is used foe each simulation. Latin Hypercube is used for

sampling.



Mann-Whitney test

Table V-9 Mann-Whitney test for Gr1 Total CostsU 7,947,339U (expected value) 8,425,000U (variance) 16,279,997,479Z (observed value) -3.74Z (critical value) 3.89Two-tailed p-value 0Alpha 0.000

At the level of significance alpha=1.00E-04 the decision is to not reject the null

hypothesis of absence of difference between samples.

In other words, the difference between samples is not significant.

Table V-10 Kolmogorov-Smirnov test for Gr1 Total CostsD 0.213Two-tailed p-value < 0.0001Alpha 0.000

At the level of significance alpha=1.00E-04 the decision is to reject the null hypothesis

of absence of difference between samples.

In other words, the difference between samples is significant.

For the costs after all limits and deductibles for all benefits in scenarios below data is

gathered



Table V-11 Distribution of Group 1 After First Scenario

Sim real100 0.513 0.470

200 0.256 0.219

300 0.112 0.155400 0.056 0.081500 0.011 0.018600 0.010 0.011

700 0.005 0.005800 0.003 0.004900 0.004 0.004

1000 0.002 0.0021100 0.003 0.0011200 0.001 0.0011300 0.001 0.0021400 0.002 0.0031500 0.002 0.0021600 0.007 0.0041700 0.006 0.0021800 0.004 0.0081900 0.003 0.0062000 0.000 0.001

20000 0.000 0.001



Table V-12 Descriptive Stats of Group 1 After First Scenario

Real dataSimulation

data

Mean 187.89 167.15Standard Error 7.44 2.79Median 115.71 96.01Mode 0.00 0.00Standard Deviation 298.05 278.79Sample Variance 88,835.09 77,721.21Kurtosis 16.54 18.25Skewness 3.80 4.03Range 2,054.37 2,343.43Minimum 0.00 0.00Maximum 2,054.37 2,343.43Sum 301,937.72 1,671,533.99Count 1,607.00 10,000.00

0.000

0.100

0.200

0.300

0.400

0.500

0.600

1 0 0

3 0 0

5 0 0

7 0 0

9 0 0

1 1 0 0

1 3 0 0

1 5 0 0

1 7 0 0

1 9 0 0

2 0 0 0 0

Sim

real

Figure V.2 Graph of Group 1 After First Scenario

When we apply a chi-test

Ho: there are no significant differences between real & simulated freq.

H1: there are significant differences between real & simulated freq.

Statistical test: X2



Level of Significant : α=0.05

Rejection area which is the less than value of α =0.05

Ho: is rejected with 45.07 and critical value as 32.67

For other non parametric tests, we applied Mann-Whitney test / two-tailed test:

and the out put is

Table V-13 Mann-Whitney test for Gr. 1 Scen.1U 8,423,444U (expected value) 8,035,000

U (variance) 15,432,295,358Z (observed value) 3.13

Z (critical value) 3.89Two-tailed p-value 0Alpha 0.000


Decision:




Kolmogorov-Smirnov test / two-tailed test:

Table V-14 Kolmogorov-Smirnov test for Gr.1 and Scen. 1D 0.185Two-tailed p-value < 0.0001Alpha 0.000

Decision:






Table V-15 Descriptive Stats of Group 1 After Second Scenario

Real dataSimulation

data




Table V-16 Distribution of Group 1 After Second Scenario

Sim Real100 0.853 0.843

200 0.040 0.060

300 0.025 0.032400 0.017 0.017500 0.011 0.009600 0.010 0.009

700 0.008 0.004800 0.006 0.004900 0.005 0.002

1000 0.003 0.0011100 0.003 0.0021200 0.002 0.0021300 0.003 0.0011400 0.001 0.0011500 0.002 0.0011600 0.001 0.0011700 0.001 0.0011800 0.001 0.0021900 0.001 0.0012000 0.001 0.001

20000 0.007 0.007



0.000

0.1000.200

0.300

0.4000.500

0.600

0.7000.800

0.900

1 4 7 1 0

1 3

1 6

1 9

Sim

real

Figure V.3 Graph of Group 1 After Second Scenario

When we apply a chi-testHo: there are no significant differences between real & simulated freq.





Ho: is rejected with 40.92 and critical value as 32.67

And for non parametrics

Table V-17 Mann-Whitney test for Gr. 1 Scen.2U 7,166,201.00U (expected value) 8,035,000.00U (variance) 13,187,253,313.25Z (observed value) -7.57Z (critical value) 3.89Two-tailed p-value < 0.0001Alpha 0.000

Decision: At the level of significance alpha=1.00E-04 the decision is to reject the nullhypothesis of absence of difference between samples.








V.1.2.1.1.2 Group 2

For the total costs incurred

Table V-19 Distribution of Group 2 Total Costs

Sim real100 0.441 0.510

200 0.180 0.162

300 0.109 0.089400 0.074 0.064500 0.046 0.038600 0.032 0.029

700 0.021 0.020800 0.017 0.016900 0.010 0.015

1000 0.009 0.0111100 0.008 0.0041200 0.007 0.0021300 0.004 0.0041400 0.006 0.0031500 0.004 0.0031600 0.003 0.0021700 0.003 0.0041800 0.003 0.0021900 0.002 0.0012000 0.003 0.003

20000 0.019 0.018



Table V-20 Descriptive Stats of Group 2 Total Costsreal sim

Mean 315.15 295.89Standard Error 45.69 5.88Median 95.08 126.37Mode 0.00 0.00Standard Deviation 1,875.42 588.07Sample Variance 3,517,206.60 345,822.03Kurtosis 1,261.22 74.78Skewness 33.55 6.67Range 71,833.54 12,523.14

Minimum 0.00 0.00Maximum 71,833.54 12,523.14Sum 531,026.66 2,958,873.56Count 1,685.00 10,000.00

0.000

0.100

0.200

0.3000.400

0.500

0.600

1 0 0

3 0 0

5 0 0

7 0 0

9 0 0

1 1 0 0

1 3 0 0

1 5 0 0

1 7 0 0

1 9 0 0

2 0 0 0 0

Sim

real

Figure V.4 Graph of Group 2 Total Costs









Ho: accepted with 27.33 and critical value as 32.67

Mann-Whitney test

Table V-21 Mann-Whitney test for Gr2 Total CostsU 7,947,465.00U (expected value) 8,425,000.00U (variance) 16,298,830,116.85Z (observed value) -3.74Z (critical value) 3.89Two-tailed p-value 0.00Alpha 0.000




Table V-22 Kolmogorov-Smirnov test for Gr2 Total CostsD 0.143

Two-tailed p-value < 0.0001Alpha 0.000





gathered




Sim real100 0.52 0.49

200 0.25 0.24

300 0.10 0.15400 0.06 0.05500 0.01 0.01600 0.01 0.00

700 0.01 0.01800 0.00 0.01900 0.00 0.00

1000 0.00 0.00

1100 0.00 0.001200 0.00 0.001300 0.00 0.001400 0.00 0.001500 0.00 0.001600 0.01 0.001700 0.01 0.001800 0.00 0.011900 0.00 0.002000 0.00 0.00

20000 0.00 0.00




Real dataSimulation

data


0.00

0.10

0.200.30

0.40

0.50

0.60

1 0 0

3 0 0

5 0 0

7 0 0

9 0 0

1 1 0 0

1 3 0 0

1 5 0 0

1 7 0 0

1 9 0 0

2 0 0 0

0

Sim

real



Ho: there are no significant differences between real & simulated freq.H1: there are significant differences between real & simulated freq.






Ho: is accepted with 28.07 and critical value as 32.67


and the out put is

Table V-25 Mann-Whitney test for Gr. 2 Scen.1U 8,877,201.00U (expected value) 8,425,000.00

U (variance) 16,307,707,507.21Z (observed value) 3.54Z (critical value) 3.89Two-tailed p-value 0.00Alpha 0.00


Decision:






Decision:






Table V-27 Descriptive Stats of Group 2 After Second Scenario

Real dataSimulation

data

Mean 84.83 100.12

Standard Error 21.34 4.06Median 0.00 0.00Mode 0.00 0.00Standard Deviation 876.11 405.93Sample Variance 767,561.70 164,780.07Kurtosis 832.91 189.21Skewness 26.73 10.99Range 29,764.68 11,440.17Minimum 0.00 0.00Maximum 29,764.68 11,440.17Sum 142,938.36 1,001,198.50Count 1,685.00 10,000.00



0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1 4 7 1 0

1 3

1 6

1 9

Sim

real








Ho: is accepted with 19.82 and critical value as 32.67


Table V-29 Mann-Whitney test for Gr. 1 Scen.2U 10,159,916.00U (expected value) 8,419,158.00U (variance) 13,727,428,725.43Z (observed value) 14.86Z (critical value) 3.89Two-tailed p-value < 0.0001Alpha 0.00

Decision: At the level of significance alpha=1.00E-04 the decision is to reject the null









V.1.2.1.1.3 Group 3

For the total costs incurred

Table V-31 Distribution of Group 3 Total Costs

Sim real100 0.433 0.486

200 0.177 0.150

300 0.118 0.091400 0.071 0.073500 0.047 0.048600 0.036 0.036

700 0.024 0.024800 0.016 0.015900 0.012 0.011

1000 0.011 0.0091100 0.008 0.0081200 0.006 0.0061300 0.005 0.0041400 0.004 0.0041500 0.003 0.0041600 0.003 0.0041700 0.003 0.0031800 0.003 0.0021900 0.002 0.0022000 0.002 0.001

20000 0.018 0.018



Table V-32 Descriptive Stats of Group 3 Total Costsreal sim

Mean 275.26 297.26Standard Error 8.89 5.79Median 107.20 130.65Mode 0.00 0.00Standard Deviation 559.27 579.28Sample Variance 312,777.78 335,562.02Kurtosis 54.69 61.42Skewness 5.97 6.30Range 8,146.66 10,693.89Minimum 0.00 0.00

Maximum 8,146.66 10,693.89Sum 1,088,926 2,972,594Count 3956 10000

0.0000.100

0.2000.3000.4000.5000.600

1 0 0

3 0 0

5 0 0

7 0 0

9 0 0

1 1 0 0

1 3 0 0

1 5 0 0

1 7 0 0

1 9 0 0

2 0 0 0 0

Sim

real

Figure V.7 Graph of Group 3 Total Costs





Level of Significant : α=0.05Rejection area which is the less than value of α =0.05




Mann-Whitney test

Table V-33 Mann-Whitney test for Gr3 Total CostsU 17,584,590U (expected value) 19,780,000U (variance) 45,381,441,883Z (observed value) -10.31Z (critical value) 3.89Two-tailed p-value < 0.0001Alpha 0.000




Table V-34 Kolmogorov-Smirnov test for Gr3 Total CostsD 0.231Two-tailed p-value < 0.0001Alpha 0.000





gathered




Sim real100 0.507 0.508

200 0.255 0.208

300 0.117 0.132400 0.058 0.068500 0.011 0.016600 0.009 0.009

700 0.005 0.007800 0.004 0.005900 0.002 0.006

1000 0.003 0.0041100 0.002 0.0041200 0.002 0.0041300 0.002 0.0021400 0.002 0.0031500 0.002 0.0021600 0.007 0.0041700 0.006 0.0051800 0.004 0.0051900 0.002 0.0042000 0.001 0.002

20000 0.001 0.003




Real dataSimulation

data


0.000

0.100

0.200

0.300

0.400

0.500

0.600

1 0 0

3 0 0

5 0 0

7 0 0

9 0 0

1 1 0 0

1 3 0 0

1 5 0 0

1 7 0 0

1 9 0 0

2 0 0 0 0

Sim

real



Ho: there are no significant differences between real & simulated freq.H1: there are significant differences between real & simulated freq.








and the out put is

Table V-37 Mann-Whitney test for Gr. 3 Scen.1U 18,496,837U (expected value) 19,780,000

U (variance) 45,381,209,438Z (observed value) -6.02Z (critical value) 3.89Two-tailed p-value < 0.0001Alpha 0.000


Decision:









Decision:



Table V-39 Descriptive Stats of Group 3 After Second ScenarioReal

dataSimulation

data

Mean 69 100Standard Error 5 4Median 0 0Mode 0 0Standard Deviation 322 401Sample Variance 103,957 160,845Kurtosis 156 135Skewness 11 10Range 6,670 9,484Minimum 0 0Maximum 6,670 9,484Sum 273,037 1,004,984Count 3,956 10,000



Table V-40 Distribution of Group 3 After Second Scenario

Sim Real

100 0.856 0.883200 0.043 0.039

300 0.024 0.023400 0.016 0.014500 0.011 0.008600 0.011 0.008

700 0.007 0.003800 0.004 0.004900 0.004 0.002

1000 0.003 0.0031100 0.003 0.0011200 0.002 0.0011300 0.001 0.0011400 0.002 0.0011500 0.001 0.0001600 0.001 0.0011700 0.002 0.0011800 0.001 0.0011900 0.001 0.001

2000 0.001 0.00120000 0.007 0.006



0.000

0.100

0.200

0.300

0.400

0.500

0.6000.700

0.800

0.900

1.000

1 4 7 1 0

1 3

1 6

1 9

Sim

real










Table V-41 Mann-Whitney test for Gr. 3 Scen.2U 16,194,269.00U (expected value) 19,780,000.00U (variance) 37,703,780,245.16Z (observed value) -18.467Z (critical value) 3.891Two-tailed p-value < 0.0001

Alpha 0.000










V.1.2.1.2 Analysis on Benefit Basis

In this part of the research we will look for an effect of scenerio2 to the mean claim size

per capita. To do this the first step to be taken is to construct a simulation data using the

restrictions determined for scenario2. Then the next step is to check whether the means of the

root populations of these samples are the same or not. Since we don’t know the population

variances we have to use T-test to check whether there exist a significant difference or not. At

this point there arises a problem: how can we estimate the variance of the differences of

sample means. There are two approaches to handle this problem. One is assuming the

population variances equal and using pooled variance as estimator of each population

variance and the other one is assuming population variances are not equal and use a weighted

variance as the variance of sample mean difference. To decide which approach to use we will

apply F test to sample variances. Let us now begin with the doctor expenses. First of all, we

begin with stating the null hypothesis H0: variances of two populations are equal and HA:

variances of two populations are not equal. The F test Output is given below.



Table V-43 F test for Physician Simulation and real data comparison

F-Test Two-Sample for

Variances

dr drsim

Mean 57.34699966 57.39982683Variance 7013.093549 5211.470245Observations 1989 7300df 1988 7299F 1.345703462P(F<=f) one-tail 6.98037E-18F Critical one-tail 1.060018295

Since the Calculated F value is greater than the tabulated one we reject the null

hypothesis, in other words we decide that there is a statistically significant difference between

two population variances. Now our next step is to apply T test with unequal variances

assumption. Here the sampling variation of the mean difference is the sum of variances each

divided by its sample size. The T test output is given below.



Table V-44 t test for Physician Simulation and real data comparison

t-Test: Two-Sample Assuming Unequal

Variances

dr drsim

Mean 57.34699966 57.39982683Variance 7013.093549 5211.470245Observations 1989 7300Hypothesized Mean Difference 0Df 2843t Stat -0.025655623P(T<=t) one-tail 0.48976691t Critical one-tail 1.645389602P(T<=t) two-tail 0.979533821t Critical two-tail 1.960797817

The absolute value of the calculated t value is less than the absolute value of the

tabulated one which means we don’t have any evidence to reject the null hypothesis claiming

the means are equal.

So we can say that at 95% level of confidence there is no evidence against our claim.

The scenario2 does not have an effect on doctor expenses. To visualize this more efficiently

we will now plot the real and simulated data on the same axis and compare them.



0

0.05

0.1

0.15

0.2

0.25

0.0001-20.0001

100.0001-120.0001

200.0001-220.0001

300.0001-320.0001

400.0001-420.0001

560.0001-580.0001

REAL DOCTORSIM DOCTOR

Figure V.10 Physician Visit Comparison

Graphical visualization is consistent with our findings. Two series differ from each

other in terms of dispersion but they seem to have similar means.

Now let us apply the same procedure to the prescription expenses. The F test output will

reveal if there exist any significant difference between variances of real and simulated

data.

Table V-45 F test for Prescribed Drugs Simulation and real data comparison

F-Test Two-Sample forVariances

pres pressim

Mean 36.24227677 36.543792Variance 4833.208537 2705.8660

27

Observations 1989 7300df 1988 7299F 1.786196541P(F<=f) one-tail 1.15318E-65F Critical one-tail 1.060018295



The result is similar to the one we did for doctor expenses. So we will use t test

assuming unequal. variances. The t test will look for any significant difference between

population means.

Table V-46 t test for Prescribed Drugs Simulation and real data comparison

t-Test: Two-Sample AssumingUnequal Variances

pres pressim

Mean 36.24227677 36.543792Variance 4833.208537 2705.866027Observations 1989 7300Hypothesized Mean Difference 0Df 2624t Stat -0.180169369P(T<=t) one-tail 0.428516759t Critical one-tail 1.645435077P(T<=t) two-tail 0.857033517t Critical two-tail 1.960870577

At 0,05 level of significance we cannot reject the equality of the means. So scenario2applied to prescription has no significant effect.

We will use a graphical visualization to check consistency of our results as we did for

doctor expenses



0

0.05

0.1

0.15

0.2

0.25

0 . 0 0

0 1 - 1 0

. 0 0 0 1

5 0 . 0 0

0 1 - 6 0

. 0 0 0 1

1 0 0 .

0 0 0 1

- 1 1 0 .

0 0 0 1

1 5 0 .

0 0 0 1

- 1 6 0 .

0 0 0 1

2 0 0 .

0 0 0 1

- 2 1 0

. 0 0 0 1

2 5 0 .

0 0 0 1

- 2 6 0

. 0 0 0 1

3 0 0 .

0 0 0 1

- 3 1 0 .

0 0 0 1

3 5 0 .

0 0 0 1

- 3 6 0 .

0 0 0 1

4 3 0 .

0 0 0 1

- 4 4 0

. 0 0 0 1

5 8 0 .

0 0 0 1

- 5 9 0 .

0 0 0 1

REAL PRESCRIBEDSIM PRESCRIBED

Figure V.11 Prescribed Drug Comparison

This graph again shows two populations differ only in terms of variability not in terms

of mean.

Now let us pass to application of the procedure to diagnostic expenses.

Starting with F test again we will decide whether to assume variances equal or not.

Table V-47 F test for Diagnostic Simulation and real data comparison

F-Test Two-Sample for

Variances

diag diagsim

Mean 35.82434506 40.65171246Variance 3232.504789 3866.209524Observations 1989 7300df 1988 7299F 1.196041

P(F<=f) one-tail 0.00000045F Critical one-tail 0.942297129

Te calculated F value is greater than the tabulated value so The conclusion is to reject

the equality of the variances.



Table V-48 t test for Diagnostic Simulation and real data comparison

t-Test: Two-Sample Assuming

Unequal Variances

diag diagsim

Mean 35.82434506 40.65171246Variance 3232.504789 3866.209524Observations 1989 7300Hypothesized Mean Difference 0df 3397t Stat -

3.288561699P(T<=t) one-tail 0.000508634t Critical one-tail 1.6453032P(T<=t) two-tail 0.001017267t Critical two-tail 1.960661393

The test come up with an unexpected result we rejected the null hypothesis stating the

equality of means so scenario2 applied to diagnostic expenses has a significant effect on the

mean claim size per capita.The graphical representation of this result is given below.



0

0.05

0.1

0.15

0.2

0.250.3

0.35

0.4

0.45

0 . 0 0

0 1 - 1 0

. 0 0 0 1

5 0 . 0 0

0 1 - 6 0

. 0 0 0 1

1 0 0 .

0 0 0 1

- 1 1 0 .

0 0 0 1

REAL DIAGNOSTICSIM DIAGNOSTIC

Figure V.12 Diagnostic procedure comparison

As it can be seen easily the two series do not resemble each other as we concluded in F

and t tests.

Now we will continue with minor treatment case. Again the first step is F test for

variances.

Table V-49 F test for Minor Treatment Simulation and real data comparison


minor minorsim

Mean 12.15380529 10.06403624Variance 3370.709438 2992.406044Observations 1989 7300df 1988 7299

F 1.126421144P(F<=f) one-tail 0.000373858F Critical one-tail 1.060018295

As the calculated test statistic is greater than the tabulated one and since the F test is a

one tailed(right) test we conclude that the variances of two populations are different.



0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.0001-10.0001

50.0001-60.0001

100.0001-110.0001

150.0001-160.0001

220.0001-230.0001

280.0001-290.0001

330.0001-340.0001

410.0001-420.0001

REAL MINORTREATSIM MINORTREAT

Figure V.13 Minor treatment comparison

A close look to the graph will reveal the same conclusion that we made for the tests.

Finally the last variable we will apply the same scenario is hospital expenses.

We again start with the F test.

Table V-51 F test for Hospital Simulation and real data comparison


hosp hospsim

Mean 53.42372541 43.93490211Variance 75392.37087 54916.13154Observations 1989 7300df 1988 7299F 1.372863833P(F<=f) one-tail 3.56962E-20

F Critical one-tail 1.060018295

F test shows that the variances of two populations are different. So we will again use t

test for unequal variances.



Table V-52 t test for Hospital Simulation and real data comparison

t-Test: Two-Sample AssumingUnequal Variances

hosp hospsim

Mean 53.42372541 43.93490211Variance 75392.37087 54916.13154Observations 1989 7300Hypothesized Mean Difference 0Df 2825t Stat 1.407840093P(T<=t) one-tail 0.079644226t Critical one-tail 1.64539415P(T<=t) two-tail 0.159288452t Critical two-tail 1.960802365

The t test couldn’t find any evidence of different population means so we can take them

equal.

The graphical representation is given below.



0 . 0 0

0 . 0 5

0 . 1 0

0 . 1 5

0 . 2 0

0 . 2 5

0 . 3 0

0 . 3 5

5 0 1

1 , 5 0 1

2 , 5 0 1

3 , 5 0 1

4 , 5 0 1

5 , 5 0 1

7 , 0 0 1

8 , 5 0 1

1 0 , 0 0

1

S im H o s p i ta lR e a l H o s p i ta l

Figure V.14 Hospital benefit comparisonIt is seen that the simulated series is less disperse than the original one and the mean is

more or less the same. Without applying tests we could have made the same conclusion.

To sum up at this section of the study we tried to show that there is no significant effect

of scenario2 to any of the expense variables mentioned above. Except for Diagnostic expenses

we accomplished our goal. The problem in the diagnostic expenses case may be the effect of

the experimented company. For the further stages of the study we will apply the same

procedure to the sampled 8 companies and that will be a more precise and can be generalized

to the whole companies insured.



PART.VI. CONCLUSION

This dissertation has showed that, as in every real life problem health care services are

formed of very complex structure and there are various approaches to model the problem.

We presented the first example of a simulation model to predict group health insurances

health care expenses in Turkey. Some approaches are outlined and some general actuarial

concepts are adopted to private health insurance including fast Fourier transformation,

moments approach.

As well as the published statistics, this study is based on the real data. Experience of

140,000 lives of 4 years has been used to describe the model with a large number of variables

so that reliable forecasts can be made. The module variables are set as; probability of claiming

(Pc), number of claims (n), claim size (X). For every utilization area (physician visits etc) and

for each variable(Pc, X and n), as every age/gender band has its own distribution, age band /

gender sub groups are created. Total number of distributions derived adds-up 435 and then,

moments of these distributions are provided in the thesis. While structuring the simulation

model, the interrelations between these variables are examined and Spearman correlation

matrix of the Pc and n variables are calculated and tested. Further to this characteristics of the

monthly and annual output distributions are analyzed.

The model is structured into three modules; Individual Expenses Module, Experience

and Credibility Module, Individual to Group Module



Individual Expenses Module outputs the distributional characteristics of one person

representing the overall group demographics after limits and deductibles applied using the

correlated input. In the Experience and Credibility Module, prior statistics of the model

variables of probability of claiming, number of claims and claim size for demographical

classes are used. Distributional characteristics of each benefit for each variable of the model

(Pc, n and X) are combined with the respective portfolio distribution characteristics. Structure

of full and partial credibility factor formula for each variable is also a new approach for this

area of health insurance.

Individual to Group Module is the part where the distribution output from the Individual

Expense Module is used and uncertainty due to statistical fluctuations, model and data

uncertainty is examined. It is nearly impossible to regenerate the results of one year with

identical conditions to see the overall risk spread in real life therefore this part of the model is

very useful to picture the stochastic nature of the aggregate costs.

In the Characteristics of the Model Output and Sensitivity section we examined the

characteristics that we cannot examine in real life, like effect of dependency, group size

(statistical fluctuation) and uncertainty due to factors mentioned in Individual to Group

Module. After examining these an overall sensitivity analysis is done to identify the most

critical inputs in the model with the limits and deductibles. The out come showed that the

limits and deductibles are decreasing the significance in the coefficients but do not change therank of significance among other variables. Further to this results show that Probability of

claiming (Pc) of hospitalization is the most critical value on the overall results.

The implementation of the model is illustrated on three sample groups with 7,436 lives

who had 59,080 health claims in total. For two different health insurance schemes (scenarios)

all the claims are filtered and compared with the simulation results with same demographic

out put limits and deductibles. Simulated results for total costs (from all areas of usage like

physician visits, hospital etc) and benefit-based costs are compared with actual costs of thesegroups. Although the output is made up of very complex combination of calculations, the

results are satisfactory.

As the model is structured on excel based simulation environment it is easy to

understand and to follow. Although non-technical people can use the model, great care should



be taken for keeping the model input data up to date. For example the unit costs should be

updated with current figures due to health inflation in USD. Also correcting the distribution

characteristics of the model variables or experience parameters great care should be taken for

the changes in the number of members of the exposed population. (If the number of members

of the exposed population changes in examined period, some elimination should be done for

the new comers.)

The model presented in this study is potentially a useful tool for helping a health

insurance company or private health fund to determine the risk characteristics that can be

faced while pricing and designing a health plan. By introducing the concept of credibility to

the distribution characteristics of the expenditure areas predictive accuracy of the model is

improved.

In addition to private health insurance, the issues that are explained in this study can be

used in areas stated below:

• Hospital groups will need advice on preferred provider arrangements. An

actuary with knowledge of health care demographics could forecast the demand

and likely case mix for a new hospital in a geographic region.

• Third party administrators for large group medical expenses plans and health aid

funds that are substitutive to social security will need advice for product design,

premium rating and reserving requirements. They also need advice on specificand aggregate stop loss insurance to limit their clients' exposure to catastrophic

(extremely big) claims.

• Large employers with insured medical expenses plans will need advice on

benefit plan design and the relative merits of competitive bids from a variety of

medical expenses insurers. The experience rating formulae used by different

insurers are not easily comparable; the lowest quoted premium may not result in

the lowest cost. An actuary can also advise on the likely effect of cost

containment measures designed to mitigate future increases in claim costs.

It will be interesting to see to which extent the private health insurance market in

Turkey will follow health insurance product developments in the U.S.A. These developments

might take the form of self funded medical trusts, ASO (Administrative Services Only)

contracts, HMOs (Health Maintenance Organizations) and PPOs (Preferred Provider



Organizations). Many of these developments might open up opportunities for modeling

involvement, particularly in the areas of risk management.

We believe that further studies are needed in this area. The model is built up for a

private health insurance population and that’s why congenital or chronic cases are less than a

public social insurance portfolio. The composition of such population should be examined

and credibility module should be used if only short-term data is available for these sources

before adopting the model to social security applications.



REFERENCES

[1]. Actuarial Standards Board Measuring Retiree Group Benefit Obligations USA(2001)13-27

[2]. Agency for Health Care Policy and Research Center for Cost and FinancingStudies “Medical Expenditure Panel Survey Household Component: Public Use File”Rockville, MD, USA (1997)

[3]. American Academy of Actuaries “Recommendations for Actuarial Advice GivenWith Respect to Self-Insured Employee Benefit Plans”, Washinton DC, USA,(1985)

[4]. Alexander, D.; Hilary N.; Shah S.:” Private Medical Insurance” Institute of Actuaries, London, UK,(2001)

[5]. Ash, A. S. ;Byrne-Logan, S.:“How well do models work? Predicting health carecosts” , in Proceedings of the Section on Statistics in Epidemiology, AmericanStatistical Association,.(1998)42-49

[6]. Barney, H. L.; Doran, P.; Rosenblatt, A.; Yamanoto, D.: “A Review of PremiumEstimates in the Health Security Act” American Academy of Actuaries, WashintonDC, USA (1994)

[7]. Bluhm, W.; Perkins, P.; Carstens, J.; Knapp, A.: “Actuarial Solvency Issues of Health Plans in the United States”(1994) [8]. Bluhm, W.: ”The Small Group Pricing Simulator

“http://www.milliman.com/minneapolis/tools/small_group_pricing_simulator.aspMilliman-USA Minnesota, USA

[9]. Board of Directors of the CAS: ‘Statement of Principles Regarding Property andCasualty Insurance Ratemaking’,(1988)

[10]. Daykin, C. D.; Pentikainen, T.; Pesonen., M.:“Practical Risk Theory for Actuaries” . Chapman and Hall, Washinton DC, USA,(1996)61

[11]. Dederichs, W.: “Claims Reserves in Health Assurances” Paper Presented to theSociety of Actuaries (of Turkey) II International Seminar on Health Insurance,Istanbul, Turkey,(1992)

[12]. Dullaway, D.: “Experience Rating of Medical Expense Insurance” The ActuaryLondon UK(1992)

[13]. Fleischacker, P.; Discenza, J.; Huey, M.; “Actuarial Issues Related to PrizingHealth plans Under Health Care Reform” American Academy of Actuaries,Washinton DC, USA,(1994)

[14]. Glas, J.: “Application of Deductibles and their effects” Paper Presented to theSociety of Actuaries (of Turkey) II International Seminar on Health Insurance,Istanbul, Turkey,(1992)

Comment [B4]:

Edwin C. Hustead, PeterHendee, Roland E. KingE.Litow, Gerald R. SheaL. Sutton Jr.,George. WaJr ‘Medical Savings AccCost Implications and DeIssues’ ,American AcadeActuaries ,1995(V1SLTSMedical Savings A c c oCost implications and DeIssues.pdf)

Board of Directors of the ‘Statement of Principles RProperty and Casualty InsRatemaking’, 1988(sppcrateStatement of PrinRegarding Property and CInsurance Ratemaking.pdf

Paul R. Fleischacker, JudiDiscenza, Martin S. Huey‘Actuarial Issues Related Prizing Health plans Unde

Care Reform’ American Aof Actuaries,1994(PRICINHEALTH PLANS.pdf veyPRICING HEALTH PLARISK2.pdf)(daha cok grup buyuklugdegil ama grup icindeki ygruplarının oranındanbahsediyor ama yararlı oozellikle Appendix kısmHarold L Barney, Phyllis Alice F Rosenblatt, Dale HYamanoto, A Review of PEstimates in the Health SeAct, 1994(PREMIUMESTIMATES.pdf)(Features that affect Primve Methodology kısmı g‘MEPS HC-003:1996 Pan

Population CharacteristicsUtilization Data’ , 1996(PPopulation CharacteristicsUtilization Data for 1996XXXXX.pdf)

‘Medical Expenditure PanSurvey Household CompoPublic Use File 1’, 1997(mexpenditure population chXXXXX.pdf)

‘Recommendations for AAdvice Given With RespeSelf-Insured Employee BePlans’, 1985(recomandatiactuarial adice given with to self insured employee bplans.pdf)

William F Bluhm, Peter PJanet M Carstens, Alan DActuarial Solvency IssuesHealth Plans in the United1994 (HEALTH PLANSOLVENCY.pdf)(Who takes the Risk veManaging the Risk bolumgenel bilgi verilen bir bokullanılabilir)Julia T Philips, Janet M C



[15]. Grazier, K.L., G’Sell Associates,“Group Medical Insurance Large Claims Database Collection and Analysis” American Academy of Actuaries, Washinton DC,USA, (1997)

[16]. Hauboldt, R.H.: “Cost Implications of Human Organ and Tissue Transplantations,an update: 1999”, Milliman & Robertson, Inc. Seattle, USA,(1999)

[17]. Hogg, R.; Klugman S.:“Loss Distributions” , John Wiley &Sons, New York,USA,(1984) [18]. Hossack, I. B.“Introductory Statistics with Applications in General Insurance”

Cambridge University Press, London, UK,(1983) [19]. Hustead, E.; Hendee, P.; King, R.; Litow, M., Shea, G.; Sutton, H.; Wagoner, G.;

“Medical Savings Accounts Cost Implications and Design Issues” , AmericanAcademy of Actuaries, Washinton DC, USA,(1995)

[20]. Klugman, S.; Panjer,H., Willmot, G.: ”Loss Models” John Wiley and Sons NewYork, USA,(1998) 605

[21]. Ministry of Health”Health Service Utilization Survey in Turkey”, Ankara, urkey, (1995).

[22]. MEPS HC-003:1996 Panel Population Characteristics and Utilization Data , 1996[23]. Mosslakos, E.; Thompson, S.: “Voluntary Health Insurance in the European Union

“Copenhagen, Denmark(2002) [24]. Newhouse, J.P.; Manning, W.G.; Keeler, E.B.; Sloss, E.M.:“Adjusting capitation

rates using objective health measurers and prior utilization” , Health Care FinancingReview, 10(3):(1989)41-54.

[25]. Orros, G.; Webber, J.: “Medical Expense Insurance- An Actuarial Review”Presented to the Institute of Actuaries, London, UK,(1987)

[26]. Orros, G. : “Group Medical Expenses in the United Kingdom” Benefits &Compensation International May(1985)

[27]. Palsbo, S.:”Risk Assessment and Risk Adjustment: A Field Guide for People with Disabilities” The National Institute of Disability and Rehabilitation Research(NIDRR) December, (2001)

[28]. Philips, J. P.; Carstens, J. P.; Lewis, L.; Swanson, S.; Zwitter, N.: “StandardBenefits in Health Care Reform-The Impact and Cost” American Academy of Actuaries, Washinton DC, USA,(1993)

[29]. Savas,B.Serdar et al.In Thomson,S.and Mossialos, E., eds.”Health care systems intransition: Turkey. Copenhagen, Copenhagen, Denmark(2002)

[30]. Seminar description “Modernizing Our Ancient Pricing Methods” 2003 S. MSnow & Associates, Inc.http://www.smsnow.com/Sem_AncientPricing/APmain.htm#detailed Berlin, MAUSA (2003)

[31]. Van de Ven; W.P.M.M., Ellis, R.P.:”Risk adjustment in competitive health planmarkets” . Handbook of Health Economics. A.J. Culyer and J.P. Newhouse, ElsevierScience B.V. 1A:(2000)755 – 845

[32]. Van de Ven, W.P.M.M.; van Vliet, R.C.J.A.:“How can we prevent cream

skimming in a competitive health insurance market? The great challenge for the‘90’s” , in P. Zweifel and H.E. French, eds., Health Economics World-wide KluwerAcademic Publishers, the Netherlands,(1992)23-46.

[33]. Walling, R.; “Managed Care: A Brief Look at the Past” Paper Presented to theCasualty Actuarial Society Ratemaking Seminar Nashville, USA,(1999)

[34]. Wang, S.: “Aggregation of Correlated Risk Portfolios: Models & Algorithms”.Proceedings of the Casualty Actuarial Society,(1999)28



[35]. Zhao, Y., Ellis, R.P., Ash, A.S., Calabrese, D., Ayanian, J.A., Slaughter, J.P.,Weyuker, L., Bowen, B., “Measuring Population Health Risks Using Inpatient

Diagnoses and Outpatient Pharmacy Data” HSR: Health Services Research, Part II,(2001)



APPENDIX 1

Definiton of the Actuary

An actuary is a professional businessperson skilled in the application of mathematics to

financial problems.

An actuary applies specialized knowledge of the mathematics of finance, statistics and

risk theory to problems faced by:

• Insurance companies

• Pension plans

• Government regulators

• Social programs

• Individuals

Traditionally, actuaries have specialized in:

• Life insurance

• Annuities

• Property and casualty insurance

• Pension plans

• Other employee benefit plans

• Evidence in the courts about loss of future earnings

An actuary has a practical business sense, the creativity to apply training and experience

to new problems and provide innovative solutions, and the communication skills required to



convince both colleagues and clients. Actuaries help people plan better for the future by

controlling or reducing financial risks associated with:

• Sickness• Disability

• Dying too soon

• Living too long

• Unemployment

• Property loss and damage

• Investment policy

Some actuaries spend part of their time ensuring that companies and pension plans

comply with the consumer protection and tax legislation, which govern their operations. In

legislation, an actuary is defined as a member of an institute, as a profession, have rules of

professional conduct and standards of practice.

The actuarial profession has played a significant role in the process of health insurance

and it is hoped that the role will strengthen over time. The primary areas of responsibility of

an actuary with a carrier organization would be, among others:

Pricing of contribution

Determination of reserves

Determination of reinsurance arrangement

Advice on benefit design

Determination of capital requirements

Pricing and advise on provider remuneration arrangements

Analysis of claims data

In order for the actuary to perform these tasks professionally and efficiently an

understanding of the dynamics within the health care environment is required.

Members of Actuarial Profession have become the highest income class mathematicians

who are employed in various sectors of finance as well as insurance and risk management.



Many common applications of estimation as well as the industrial engineers,

statisticians are applied in actuarial literature and some specific applications have very special

properties that the industrial engineers will benefit.

Extreme Cases

Table 0-1 Earthquake predictions from the California DataMagnitude Estimated

incidence forDeath

Estimatedincidence forHospitalizatio

ns (*)

Estimatedincidence

foroutpatients

Number of Dead Number ofHospitalizations (*)

Number ofoutpatients

6 0.000014 0.0001 0.00042 168 672 5,0407 0.00031 0.0012 0.0093 3,720 14,880 111,6008 0.0048 0.0192 0.144 57,600 230,400 1,728,0009 0.068 0.2720 1 816,000 3,264,000 12,000,000

(*) Number of hospitalized people is assumed to be 4 times the number of deads and out patient treated number will be30 times the number of deads

Table 0-2 Real Earthquake dataIZMIT MEXCO KOBE NADA ERZNCAN DÜZCE

Population 1,500,000 18,000,000 1,500,000 80,000njured 43,000 50,000 26,800Dead 17,000 10,000 5,100 800Homeless 600,000 250,000 500,000Incidence for injury 0.029 0.0028 0.0179Incidence fordeath

0.011 0.0006 0.0034 0.0068 0.0058 0,01

Incidence forhomelss

0.400 0.0139 0.3333

According to the USA statistics [16] approximately 34,000 organ transplant(excluding

cornea transplants) are done to the population below 65 years which means 238 million

citizens producing an incidence rate of 0.00014 with a 189,000$ of average case size and

2,500 transplants for the population over 65 years which means 34 million citizen producing

an incidence rate of 0.000073 with a 263,000$ of average case size.



In Grazier K.L[15], depending on Group Private Insurance data USA, for all the large

medical expenditure cases below data is produced

Table 0-3 High costs incidence rates

AGE EXPOSEDNUMBER

AVERAGECOST

POSSIBILITYOF EXCEEDING25.000$

AVERAGECOST

POSSIBILITYOF EXCEEDING250.000$

0 20 317,319 46,246 0.004264 167,163 0.00016421 30 237,034 38,213 0.002536 145,546 0.00007231 40 362,143 39,294 0.003361 136,827 0.00007741 50 303,184 36,217 0.005700 132,088 0.00010251 60 169,052 31,556 0.014138 116,429 0.00018361 64 52,064 29,776 0.025680 98,078 0.00019265 69 32,655 25,195 0.016628 164,821 0.000092

70 120 44,774 25,628 0.010430 21,888 0.000067



APPENDIX 2

In the model there are 8 major sheets. The major sheets where all the iterations are done

are ‘dr’, ‘pres’,’ diagnostic’, ‘minortreat’, ’ hospital’ SHEETS

The formulas are

FORMULAS FROM RANGE B4:E7

B4. =+G4/C4

C4. =+I4/G4

B5. =+G5/C5

C5. =+I5/G5

B7. =+'YAŞ C NS YET'!T1

FORMULAS FROM RANGE G4:I5G4. =+'YAŞ C NS YET'!V1

H4. =+'YAŞ C NS YET'!W1

I4. =+H4-G4^2

G5. =+'YAŞ C NS YET'!X1

H5. =+'YAŞ C NS YET'!Y1

I5. =+H5-G5^2

FORMULAS FROM RANGE B8:B9

B8. =RiskBinomial(1, B7, RiskCorrmat(NewMatrixPc,1))

B9. =RiskOutput() + ROUND(RiskGamma(B4, C4,

RiskCorrmat(NewMatrixadet,1)),0)

FORMULAS FROM RANGE D9:AB9



D9. =+ IF(D11=0,0,RiskDiscrete($AD$2:$AD$13,$AE$2:$AE$13))

AB9. =+ IF(AB11=0,0,RiskDiscrete($AD$2:$AD$13,$AE$2:$AE$13))

FORMULAS FROM RANGE B12:C14

B12. =RiskOutput() + IF(B8=1,C12,0)

C12. =RiskOutput() + SUM(D12:AB12)

B14. =RiskOutput() + IF(B8=1,C14,0)

C14. =RiskOutput() + MAX(D14:AB14)

FORMULAS FROM RANGE B16:B21

B16. =RiskOutput() + RiskGamma($B$5,$C$5)

B17. =RiskOutput() +IF(B16>$D$5,$D$5-$E$5,IF(B16>$E$5,B16-$E$5,0))

B20. =RiskOutput() + IF(E11>$D$5,$D$5-$E$5,IF(E11>$E$5,E11-$E$5,0))

B21. =RiskOutput() + COUNTIF(D12:AB12,">0")

FORMULAS FROM RANGE D11:AB19

From D column to AB column below formulas are coppied

D11. =IF(D10>$B$9,0,RiskGamma($B$5,$C$5))

D12. =IF(D10>$D$4,0,IF(D10<=$E$4,0,IF(D11>$D$5,$D$5-

$E$5,IF(D11>$E$5,D11-$E$5,0))))

D13. =SUM($D$11:D11)

D14. =+IF(ISERROR(D15),0,D15)

D15. =+IF(D13<$E$6,0,IF(D13<$D$6,D13,$D$6)-$E$6)

D16. =+D11*(1-(MAX(D11-$D$5,0)/D11))-($E$5/D11)

D17. =+(D13-$E$6)*(1-(MAX(D11-$D$5,0)/D11))-($E$5/D11)

D18. =+($D$6-C13)*(1-(MAX(D11-$D$5,0)/D11))-($E$5/D11)



D19. =+($D$6-$E$6)*(1-(MAX(D11-$D$5,0)/D11))-($E$5/D11)

Formulas in ‘total sheet’ SHEETS

FORMULAS FROM RANGE A8:E14

B8. =RiskOutput() + +dr!B8+pres!B8+diagnostic!B8+minortreat!B8+hospital!B8

B9. =RiskOutput() +

+dr!B9*dr!B8+pres!B9*pres!B8+diagnostic!B9*diagnostic!B8+minortreat!B9*minortreat!B

8+hospital!B9*hospital!B8

D9. =RiskOutput() +

+IF(dr!B8=0,0,dr!B9)+IF(diagnostic!B8=0,0,diagnostic!B9)+IF(diagnostic!B8=0,0,diagnosti

c!B9)+IF(minortreat!B8=0,0,minortreat!B9)+IF(hospital!B8=0,0,hospital!B9)

B11. =RiskOutput() +

+dr!B11+pres!B11+diagnostic!B11+minortreat!B11+hospital!B11

C11. =RiskOutput() +

+dr!C11+pres!C11+diagnostic!C11+minortreat!C11+hospital!C11

B12. =RiskOutput() +

+dr!B12+pres!B12+diagnostic!B12+minortreat!B12+hospital!B12



B14. =RiskOutput() ++dr!B14+pres!B14+diagnostic!B14+minortreat!B14+hospital!B14



In AGE/GENDER sheet the representative average moments of the distributions are

calculated.

FORMULAS FROM RANGE A1:BJ36A1. =IF(A2=1,"DISTRIBUTE THE MEMBERS ACCORDING TO THE AGE AND

GENDER",IF(A2=1,"AGE AND GENDER ENTERIES WILL NOT BE USED","WRONG

CODE"))

T1. =IF($A$2=3,T$143,T$2)

U1. =IF($A$2=3,U$143,U$2)



V1. =IF($A$2=3,V$143,V$2)

W1. =IF($A$2=3,W$143,W$2)

X1. =IF($A$2=3,X$143,X$2)

Y1. =IF($A$2=3,Y$143,Y$2)

AC1. =IF($A$2=3,AC$143,AC$2)

AD1. =IF($A$2=3,AD$143,AD$2)

AE1. =IF($A$2=3,AE$143,AE$2)

AF1. =IF($A$2=3,AF$143,AF$2)

AG1. =IF($A$2=3,AG$143,AG$2)

AH1. =IF($A$2=3,AH$143,AH$2)

AL1. =IF($A$2=3,AL$143,AL$2)

AM1. =IF($A$2=3,AM$143,AM$2)

AN1. =IF($A$2=3,AN$143,AN$2)

AO1. =IF($A$2=3,AO$143,AO$2)

AP1. =IF($A$2=3,AP$143,AP$2)

AQ1. =IF($A$2=3,AQ$143,AQ$2)

AU1. =IF($A$2=3,AU$143,AU$2)

AV1. =IF($A$2=3,AV$143,AV$2)

AW1. =IF($A$2=3,AW$143,AW$2)

AX1. =IF($A$2=3,AX$143,AX$2)

AY1. =IF($A$2=3,AY$143,AY$2)AZ1. =IF($A$2=3,AZ$143,AZ$2)

BD1. =IF($A$2=3,BD$143,BD$2)

BE1. =IF($A$2=3,BE$143,BE$2)

BF1. =IF($A$2=3,BF$143,BF$2)

BG1. =IF($A$2=3,BG$143,BG$2)

BH1. =IF($A$2=3,BH$143,BH$2)

BI1. =IF($A$2=3,BI$143,BI$2)

T2. =SUMPRODUCT($E$6:$E$142,T6:T142)U2. =SUMPRODUCT($E$6:$E$142,U6:U142)

V2.

=SUMPRODUCT($E$6:$E$36,T6:T36,V6:V36)/SUMPRODUCT($E$6:$E$36,T6:T36)

W2.

=SUMPRODUCT($E$6:$E$36,T6:T36,W6:W36)/SUMPRODUCT($E$6:$E$36,T6:T36)



X2.

=SUMPRODUCT($E$6:$E$36,T6:T36,V6:V36,X6:X36)/SUMPRODUCT($E$6:$E$36,V6:

V36,T6:T36)

Y2.

=SUMPRODUCT($E$6:$E$36,T6:T36,V6:V36,Y6:Y36)/SUMPRODUCT($E$6:$E$36,V6:

V36,T6:T36)

AC2. =SUMPRODUCT($E$6:$E$142,AC6:AC142)

AD2. =SUMPRODUCT($E$6:$E$142,AD6:AD142)

AE2.

=SUMPRODUCT($E$6:$E$36,AC6:AC36,AE6:AE36)/SUMPRODUCT($E$6:$E$36,AC6:

AC36)

AF2.

=SUMPRODUCT($E$6:$E$36,AC6:AC36,AF6:AF36)/SUMPRODUCT($E$6:$E$36,AC6:

AC36)

AG2.

=SUMPRODUCT($E$6:$E$36,AC6:AC36,AE6:AE36,AG6:AG36)/SUMPRODUCT($E$6:

$E$36,AE6:AE36,AC6:AC36)

AH2.

=SUMPRODUCT($E$6:$E$36,AC6:AC36,AE6:AE36,AH6:AH36)/SUMPRODUCT($E$6:

$E$36,AE6:AE36,AC6:AC36)

AL2. =SUMPRODUCT($E$6:$E$142,AL6:AL142)AM2. =SUMPRODUCT($E$6:$E$142,AM6:AM142)

AN2.

=SUMPRODUCT($E$6:$E$36,AL6:AL36,AN6:AN36)/SUMPRODUCT($E$6:$E$36,AL6:

AL36)

AO2.

=SUMPRODUCT($E$6:$E$36,AL6:AL36,AO6:AO36)/SUMPRODUCT($E$6:$E$36,AL6:

AL36)

AP2.=SUMPRODUCT($E$6:$E$36,AL6:AL36,AN6:AN36,AP6:AP36)/SUMPRODUCT($E$6:$

E$36,AN6:AN36,AL6:AL36)

AQ2.

=SUMPRODUCT($E$6:$E$36,AL6:AL36,AN6:AN36,AQ6:AQ36)/SUMPRODUCT($E$6:

$E$36,AN6:AN36,AL6:AL36)



AU2. =SUMPRODUCT($E$6:$E$142,AU6:AU142)

AV2. =SUMPRODUCT($E$6:$E$142,AV6:AV142)

AW2.

=SUMPRODUCT($E$6:$E$36,AU6:AU36,AW6:AW36)/SUMPRODUCT($E$6:$E$36,AU

6:AU36)

AX2.

=SUMPRODUCT($E$6:$E$36,AU6:AU36,AX6:AX36)/SUMPRODUCT($E$6:$E$36,AU6

:AU36)

AY2.

=SUMPRODUCT($E$6:$E$36,AU6:AU36,AW6:AW36,AY6:AY36)/SUMPRODUCT($E$

6:$E$36,AW6:AW36,AU6:AU36)

AZ2.

=SUMPRODUCT($E$6:$E$36,AU6:AU36,AW6:AW36,AZ6:AZ36)/SUMPRODUCT($E$6

:$E$36,AW6:AW36,AU6:AU36)

BD2. =SUMPRODUCT($E$6:$E$142,BD6:BD142)

BE2. =SUMPRODUCT($E$6:$E$142,BE6:BE142)

BF2.

=SUMPRODUCT($E$6:$E$36,BD6:BD36,BF6:BF36)/SUMPRODUCT($E$6:$E$36,BD6:

BD36)

BG2.

=SUMPRODUCT($E$6:$E$36,BD6:BD36,BG6:BG36)/SUMPRODUCT($E$6:$E$36,BD6:BD36)

BH2.

=SUMPRODUCT($E$6:$E$36,BD6:BD36,BF6:BF36,BH6:BH36)/SUMPRODUCT($E$6:$

E$36,BF6:BF36,BD6:BD36)

BI2.

=SUMPRODUCT($E$6:$E$36,BD6:BD36,BF6:BF36,BI6:BI36)/SUMPRODUCT($E$6:$E

$36,BF6:BF36,BD6:BD36)

AE3.=SUMPRODUCT($E$6:$E$36,AC6:AC36,AE6:AE36)/SUMPRODUCT($E$6:$E$36,AC6:

AC36)

AF3.

=SUMPRODUCT($E$6:$E$36,AC6:AC36,AF6:AF36)/SUMPRODUCT($E$6:$E$36,AC6:

AC36)



APPENDIX 3

Fourier Algorithm

Sub Macro1()

'

' Macro1 Macro' Macro recorded 11.06.2000

'

Application.Run "ATPVBAEN.XLA!Fourier", ActiveSheet.Range("$B$2:$B$33"),

_

ActiveSheet.Range("$N$2:$N$33"), False, False

End Sub

Sub fftsht()Dim found As Integer, row As Integer

Dim s As String, power As Integer

found = False

row = 5

Workbooks.Open FileName:="C:\Fourier\inputfile.xls"

While Not found

row = row + 1

s = "I" & Trim$(Str$(row))

If Workbooks("inputfile.xls").Worksheets("tablolar").Range(s) = "Grand Total"

Then found = True

Wend

power = Int(Log(row - 6) / Log(2)) + 1

For i = 1 To 2 ^ power



Workbooks("fftsht.xls").Worksheets("n-fold").Range(Chr$(65 + row) & "2:" & Chr$(65 +

row) & Trim$(Str$(2 ^ power + 1))).Value

Workbooks("fftsht.xls").Worksheets("n-fold").Range(Chr$(67 + row) & "2:" &

Chr$(67 + row) & Trim(Str$(2 ^ power + 1))).Formula = "=IMPRODUCT(" & Chr$(65 +

row) & "2," & Chr$(66 + row) & "2)"

For i = 2 To row - 2

Application.Run "ATPVBAEN.XLA!Fourier",

Workbooks("fftsht.xls").Worksheets("n-fold").Range("$" & Chr$(67 + row) & "$2:$" &

Chr$(67 + row) & "$" & Trim(Str$(2 ^ power + 1))), _

Workbooks("fftsht.xls").Worksheets("n-fold").Range("$" & Chr$(68 + row) &

"$2:$" & Chr$(68 + row) & "$" & Trim(Str$(2 ^ power + 1))), True, False

Workbooks("fftsht.xls").Worksheets("n-fold").Range(Chr$(65 + i) & "2:" &

Chr$(65 + i) & Trim$(Str$(2 ^ power + 1))).Value = Workbooks("fftsht.xls").Worksheets("n-

fold").Range(Chr$(68 + row) & "2:" & Chr$(68 + row) & Trim$(Str$(2 ^ power + 1))).Value


"$2:$" & Chr$(68 + row) & "$" & Trim(Str$(2 ^ power + 1))).ClearContentsWorkbooks("fftsht.xls").Worksheets("n-fold").Range("$" & Chr$(65 + row) &

"$2:$" & Chr$(65 + row) & "$" & Trim(Str$(2 ^ power + 1))).ClearContents

Application.Run "ATPVBAEN.XLA!Fourier",

Workbooks("fftsht.xls").Worksheets("n-fold").Range("$" & Chr$(65 + i) & "$2:$" &

Chr$(65 + i) & "$" & Trim(Str$(2 ^ power + 1))), _


"$2:$" & Chr$(65 + row) & "$" & Trim(Str$(2 ^ power + 1))), False, FalseNext i

Workbooks("fftsht.xls").Worksheets("n-fold").Range("B" & Trim$(Str$(2 ^ power +

4))).Formula = "=B" & "$" & Trim$(Str$(2 ^ power + 3)) & "*B2"


4))).Copy




4)) & ":" & Chr$(63 + row) & Trim$(Str$((2 ^ power) * 2 + 4))).Select

ActiveSheet.Paste

Workbooks("fftsht.xls").Worksheets("n-fold").Range(Chr$(63 + row + 1) &

Trim$(Str$((2 ^ power) + 4)) & ":" & Chr$(63 + row + 1) & Trim$(Str$((2 ^ power) * 2 +

4))).Formula = "=SUM(B" & Trim$(Str$((2 ^ power) + 4)) & ":" & Chr$(63 + row) &

Trim$(Str$((2 ^ power) + 4)) & ")"

End Sub

Sub Macro2()

'

' Macro2 Macro

' Macro recorded 11.06.2000

'

'

Application.Run "ATPVBAEN.XLA!Fourier", ActiveSheet.Range("$T$2:$T$33"),

_

ActiveSheet.Range("$U$2:$U$33"), True, False

End Sub



CURRICULUM VITAE

Name: SALIH BULENT ERISHOME TEL:+90 216 3 40 37 35MOBILE TEL:+90 532 794 22 74E MAIL: [email protected]: BEYAZ KARANFIL SOKAK 19/8 ACIBADEM 81010ISTANBUL/TURKEYGENDER: MALEBIRTH DATE : DECEMBER,3RD 1967

EDUCATION1979-1985 KADIKÖY ANADOLU LISESI/ KADIKÖY ANADOLU SECONDARY-HIGHSCHOOL1985-1989 BS. IN MANAGEMENT ENGINEERING TECHNICAL UNIVERSITY,ISTANBUL (GRADUATION PROJECT: “CASH FLOW MANAGEMENT ANALYSIS”)1989-1992 MS. IN MARM. UNIV. BANKING AND INSURANCE FACULTY ININSURANCE (GRADUATION PROJECT: “MAJOR MEDICAL EXPENSE ANDUNLIMITED HEALTH INSURANCE BENEFITS”)EXPERIENCE1990-1996 Worked as specialist in System Research and Development department in chargeof actuarial subjects on life and health product development, system analysis1996-1999 MANAGER IN “TECHNICAL AND R&D” DEPARTMENT. ABOVESUBJECTS PLUS THE RE-INSURANCE AND POOLING WORK.1999- SENIOR MANAGERATTENDED SEMINARS ON VARIOUS SUBJECTS SUCH ASMARCH 1992 LIFE INSURANCE UNDERWRITING SEMINAR (FROM MUNICH RE)1994 AND 1995 2 MAIN COURSES FOR ISO 9001SEPTEMBER 1995 EDUCATION OF THE EDUCATORS (FROM ROTACONSULTANCY INC.)JUNE 1995 REACHING THE STARS (FROM TIME MANAGEMENT INTERNATIONALINC.)JUNE 1997 ACTUARIAL COURSE FOR ONE WEEK IN COLOGNEOCTOBER 2000 MAY 2001 MANAGEMENT TRAINING. (BY INTERCON)MARITAL STATUS

MARRIED SINCE 1991 AND HAS SON BORN JULY, 3RD 1995.



Page 143: [1] Comment [B4] BERIS

Edwin C. Hustead, Peter G. Hendee, Roland E. King, Mark E.Litow,Gerald R. Shea, Harry L. Sutton Jr.,George. Wagoner Jr ‘Medical SavingsAccounts Cost Implications and Design Issues’ ,American Academy of Actuaries ,1995 (V1SLTSL1 Medical Savings A c c o u n t s Costimplications and Design Issues.pdf)

Board of Directors of the CAS ‘Statement of Principles Regarding Property and CasualtyInsurance Ratemaking’, 1988(sppcrateStatement of Principles Regarding Property andCasualty Insurance Ratemaking.pdf)

Paul R. Fleischacker, Judith A. Discenza, Martin S. Huey, ‘Actuarial Issues Related to PrizingHealth plans Under Health Care Reform’ American Academy of Actuaries,1994(PRICINGHEALTH PLANS.pdf veya PRICING HEALTH PLAN RISK2.pdf)(daha cok grup buyuklugunden degil ama grup icindeki yas gruplarının oranındanbahsediyor ama yararlı olabilir ozellikle Appendix kısmı)Harold L Barney, Phyllis A Doran, Alice F Rosenblatt, Dale H Yamanoto, A Review of Premium Estimates in the Health Security Act, 1994(PREMIUM ESTIMATES.pdf)(Features that affect Primiums ve Methodology kısmı guzel)‘MEPS HC-003:1996 Panel Population Characteristics and Utilization Data’ , 1996(PanelPopulation Characteristics and Utilization Data for 1996 XXXXX.pdf)

‘Medical Expenditure Panel Survey Household Component: Public Use File 1’, 1997(medical expenditure population charac XXXXX.pdf)

‘Recommendations for Actuarial Advice Given With Respect to Self-Insured EmployeeBenefit Plans’, 1985(recomandations for actuarial adice given with respect to self insuredemployee benefit plans.pdf)

William F Bluhm, Peter Perkins, Janet M Carstens, Alan D Knapp, ‘ Actuarial SolvencyIssues of Health Plans in the United States’ 1994(HEALTH PLAN SOLVENCY.pdf)(Who takes the Risk ve Managing the Risk bolumleri genel bilgi verilen bir bolumdekullanılabilir)Julia T Philips, Janet M Carstens, Lucinda Lewis, Sheree Swanson, Norman Zwitter, ‘Standard Benefits in Health Care Reform-The Impact and Cost’ 1993(EFFEC OF standarthealth benefis IN USA.pdf)(Sizin calısmanıza benzer bir calısma bu calısmada 4 ayrı model simule edilmis ve buplanlar costları ile kıyaslanmıs)

Bunların dısında hcir.pdf de bulunan Health Care Index Report u , factse 50facts of health.pdf

dosyasında bulunan 50 Facts of Health yazısı ve monthly HMO premiums for singl e

premium.pdf de bulunan prim örnekleri konu anlatımı sırasında kullanılabilir gibi duruyor.

bulent eris model development for planning and forecasting in diagnostic and treatment systems...

Documents