implementation of semi-parametric bayesian …particularly in medicine (survival analysis) and...

International Journal of Research in Engineering, Science and Management

Volume-3, Issue-5, May-2020

www.ijresm.com | ISSN (Online): 2581-5792

88

Abstract: The aim of this study is to implement semi parametric

Bayesian analysis for survival of HIV patients, on data obtained

from Debre Berhan Referral Hospital, Ethiopia of HIV-positive

patients enrolled in ART, the time of an event occurring were

taken. The study subjects were enrolled between the Period

January 2012 to January 2018, and attending treatment until the

first month of2018 and all subjects include in this study were

greater than or equal to 16 years old. A total of 1036 patients, who

fulfill the inclusion criteria were selected for the study. Data were

explored using basic descriptive statistics and the censoring status

of categorical variables was presented. Kaplan-Meier estimation

technique was used to asses survival by each covariates category.

semi parametric Bayesian analysis, Cox proportional hazard

model (cox PH) for the survival data analysis were used along with

their prior selection, model estimation, model diagnosis and

Markov Chain Monte Carlo algorithm was used for data

simulation. The base line CD4 cell count, baseline weight, sex, age,

functional status, marital status, WHO-clinical stage, educational

level, age, religion, residence, opportunistic infection were the

covariates in this study. Semi parametric Bayesian analysis

method with cox proportional hazard was used. During model

diagnosis with MCMC and time to death analysis all variables

were significantly determine survival time of patients except

opportunistic infection and regimen class 4. In this time to event

(time to death) data 113(10.90734%) were practicing the event

with median of age 32.00, mean of age is 34.02, first quartile of age

is 27 and third quartile of age is 40. The variables age, WHO

clinical stages, marital status, functional status, baseline CD4,

regimen class, residence were significantly determines the survival

time of patients. Whereas opportunistic infection have no

significance impact on survival time. The variable residence is also

can affect survival time of patients such as 91.44% chance that the

hazard rate of patients live in urban is greater than that of patients

in rural. Analysis of time to death of HIV/AIDS patient by semi

parametric Bayesian is effective. Markov chain diagnostic show

good convergence and almost perfect mixing. But covariate

opportunistic infection and category 4 in regimen class were not

poor in MCMC convergence.

Keywords: MCMC algorithm, Proportional hazard, Semi

parametric Bayesian, Survival data.

1. Introduction

HIV refers to human immunodeficiency virus; it is a

collection of virus those most likely mutated decades ago from

a virus that infected chimpanzees to a virus that infects humans.

It began to spread beyond the African continent in the late

1970s and is now endemic worldwide. HIV causes disease

because it attacks critical immune defense cells and over time

overwhelms the immune system. When HIV positive people

live without treatment, HIV infection starts to cause symptoms

in an average of eight to ten years with opportunistic infection,

opportunistic infection is caused when people have weak

immune function. The period from infection to the cause of

symptom is known as latent period where as the period started

from symptomatic phase up to death referred to as acquired

immune deficiency syndrome (AIDS) or HIV disease Sandra

Gonzalez Gompf (2018). HIV infection leads to low levels of

CD4+T cells that in turn make the body susceptible to

opportunistic infections. According to the UNAIDS (United

Nation for International Development) report, it was estimated

that 33.2 million people lived with the disease worldwide, and

that AIDS killed an estimated 2.1 million people, including

330,000 children. In 2008, an estimated 33.4 million people

were living with HIV/AIDS worldwide; nearly 70% of these

were found in sub-Saharan Africa Sandra Gonzalez Gompf

(2018).

The introduction of ART in 1996 was a turning point for

thousands of people with sophisticated health car. Roughly 75%

of AIDS patients in need of antiretroviral therapy (ART) in the

world still have no access, and most of them live in Africa

(World Health Organization 2006). This despite the fact that the

three by five initiative of the World Health Organization

(WHO), as well as the resources provided by the Global Fund,

greatly facilitated access to ART in all regions of the world and

boosted ART programs in most of sub-Saharan Africa, where

the number of persons treated was multiplied by more than

eight in just 2 years [World Health Organization (WHO) 2006].

The clinical benefit of ART for AIDS patients, in terms of

mortality reduction and improved quality of life, is well

established but shows regional variations, with higher case

fatality rates in poor countries. There are several predictors of

mortality for patients on ART: viral load, CD4 count, total

Implementation of Semi-Parametric Bayesian

Analysis for Survival of HIV/AIDS Patients in

the Case of Debre Berhan Referral Hospital

A. R. Muralidharan1*, Gethahun Mulugeta2

1,2Assistant Professor, P.G. Department of Biostatistics, College of Natural and Computational Science, Debre

Berhan University, Debre Berhan, Ethiopia *Corresponding author: [email protected]




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lymphocytes, body mass index (BMI), and adherence.

Although these determinants tend to be similar across the

world, there are some striking differences in their relative

frequency, example, the much lower baseline CD4 counts of

patients starting ART in poor countries Isidore Sieleunou. et al.

(2009).

Globally an estimated 34 million people were living with

HIV at the end of 2010. United Nation for International

Development and world health organization estimates since the

availability of effective treatment some 2.9 million lives have

been saved. About 68% of all people living with HIV resided in

sub Saharan Africa, a region with only 12% of the global

population in 2010. Ethiopia is the seriously affected countries

in sub Saharan Africa with more than 1.3 million people living

with HIV and an estimated 277,800 people requiring treatment.

The overall Adult HIV prevalence was 1 .4% and 1.5% in 2005

and 2011. The government of Ethiopia launched its free based

ART initiative in 2003 and free initiative in 2005.peoples ever

started ART were 150,136,208,784 and 268,934 respectively in

2008, 2009 and 2010. Peoples who were on ART on the same

year were 109,930,152,472and 207,733 respectively. (Nurilign

Abebe, 2014) The first HIV infection in Ethiopia was reported

in 1984 from stored sera which later expended as an epidemic

similar to elsewhere in sub-Saharan Africa. The 2005

Demographic and Health Survey estimated national adult HIV

prevalence of Ethiopia to be between 0.9%- 2.1%, with

infection levels highest in the Gambella (6%) and Addis Ababa

(4.7%) regions. Recent expansion of surveillance data and

improved analysis has lowered the 2005 estimate drastically.

Antenatal care surveillance data showed declining HIV

prevalence rate in urban areas being 10.1% and stable trend in

rural (1.8%). The highly vulnerable groups include young

women living in urban areas, commercial sex workers and

members of military and policy. In rural areas no significant

gender difference in risk of infection. (Worku, Pattern and

determinants of survival in, 2009) Statistics show that

approximately 40 million people are currently living with HIV

infection, and an estimated 40 million have died from this

disease since the beginning of the epidemic. HIV has been

particularly devastating in sub-Saharan Africa, which accounts

for almost 70% of new HIV infections globally. However,

infection rates in other countries also remain high. Sandra

Gonzalez Gompf, (2018).

Medical and epidemiological studies are mostly conducted

with an interest in measuring the occurrence of an outcome

event. Studies conducting survival analysis, however, are

focused toward measuring time to event or outcome. Time to

event could vary from time to fatal event that is death, or time

to occurrence of a clinical endpoint such as disease, or

attainment of a biochemical marker. Survival analysis studies

originated with the publication of John Graunt’s Weekly Bills

of Mortality in London. First life table was prepared by Healy.

Survival analysis is also known as lifetime data analysis, time

to event analysis, reliability and event history analysis

depending on focus and stream where it is used. However,

survival analysis is plagued by problem of censoring in design

of clinical trials which renders routine methods of

determination of central tendency redundant in computation of

average survival time. The present essay attempts to highlight

different methods of survival analysis used to estimate time to

event in studies based on individual patient level data in the

presence of censoring. (Shankar Prinja, 2010).

The three most commonly used semi parametric Bayesian

survival models, PH, proportional odds (PO), and accelerated

failure time (AFT), is developed and illustrated on several a real

and simulated data sets (Hanson). In this study the focused is

on Semi-parametric Bayesian models along with associated

Bayesian statistical methods. The Semi-parametric nature of the

model allows considerable generality and applicability. But

enough structure for useful interpretation and understanding

particular application in the medical research. Semi-parametric

is a model with two parts, that are parametric (such as

regression coefficients). Particularly in medicine (survival

analysis) and nonparametric parts (such as hazard function).

Semi-parametric models are quite popular, for being a good

compromise between too restrictive parametric and too non-

informative non-parametric models. The popularity of Semi-

parametric approaches for analyzing univariate survival data

begins with the seminal paper of cox (1972) on the proportional

hazard model, Following the path of cox several other survival

analysis following hem (K.Dey 2012). In many practical

situations, a parametric model cannot be expected to describe

in an appropriate manner the chance mechanism generating an

observed dataset, and unrealistic features of some common

models could lead to unsatisfactory inferences. In these cases,

we would like to relax parametric assumptions to allow greater

modeling flexibility and robustness against misspecification of

a parametric statistical model. In the Bayesian context such

flexible inference is typically achieved by models with

infinitely many parameters. These models are usually referred

to as Bayesian Nonparametric (BNP) or Semi parametric (BSP)

models depending on whether all or at least one of the

parameters is infinity dimensional, While BSP and BNP

methods are extremely powerful and have a wide range of

applicability within several prominent domains of statistics. A

direct benefit of MCMC algorithms approach is that the

sampling algorithms can be made dramatically more

efficient(Jara).

2. Objectives

The general objective of this study is to implement the Semi

parametric Bayesian analysis for survival of HIV patients who

follow in the ART.

Specific Objectives

1. To asses time to death of HIV/AIDS patients

2. To apply the semi parametric Bayesian analysis on

survival HIV

3. To identifying factors that affect survival of




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HIV/AIDS patients who were in ART clinic.

3. Data and Methodology

Location of Debre Berhan is a city and woreda in central

Ethiopia. Located in the Semien Shewa Zone of the Amhara

Region, about 120 kilometers north east of Addis Ababa on the

paved highway to Dessie, the town has a latitude and longitude

of 9°41′N 39°32′ECoordinates, 9°41′N 39°32′E and an

elevation of 2,840 meters was an early capital of Ethiopia and

afterwards, with Ankober and Angolalla, was one of the capitals

of the kingdom of Shewa. It is the administrative center of the

Semien Shewa Zone of the Amhara Region. Debre Birhan is

located in Ethiopia (Amhara region) and time zone

Africa/Addis Ababa. Places in the near are Debre Sīna, Abomsa

and Fichē.

The study population was included HIV positive adults

whose age is started from 16 and above initiated ART treatment

in the Debre Berhan Referral Hospital. All patients who have

initiated to ART and their baseline CD4 cell count, baseline

weight who started first line regiment class wasincluded in the

study population, while patient started ART with their age is

less than 16 years old and patient who starts ART before

January 2013 and after January 2018 are not included in the

study population. All patients who fulfill the inclusion criteria

were included in the study. When the data is recording from

medical charts Identification numbers were used to each

individual patients to make it easy to identify individuals

visiting profile by keeping patients medical secrete.

Study Variables

The interest of the study is survival analysis; the data have

the nature of time-to-event, from the time started medication in

the ART clinic to the occurrence of an event (or occurrence of

death).

Response Variable

Time to event of interest is the dependent variable. This data

is with the “Right censored observation”. This was computed

as the time difference between the event occurred and the time

of the ART started (initiated).

Death (Code: Event=1 No Event =0)

Explanatory variables

4. Data analysis

This study aimed at Implementation of the semi-parametric

Bayesian for survival of HIV patients. In order to address the

objectives of the study, 1036 patient population of Debre

Berhan referral hospital patients of HIV in the ART treatment

were taken. In the case of analysis the SAS (Statistical Analysis system) software with PHREG procedure were used. In the

semi parametric Bayesian analysis selected model was cox

(PH) with constant prior known as uniform prior for models

parameter. In this section results obtained from descriptive data

analysis and from Semi parametric Bayesian will be presented.

Baseline Demographic Factors

The baseline covariates of this study were compared by cross

tabulation. It shows the distribution of patients in each category.

And also association of explanatory covariates is checked by

Pearson chi-square test. Table of this result are shown below.

Table 2 Patients with their censoring status 60.4% of censored

patients were females and 6.3 % of females were died and 28.7

% of males were censored, 4.6% of male patients were died.

Regarding functional status 91.0% of working patients were

censored, 85.0% of working patients were died, 8.1% of

ambulatory patients were censored, 9.7% of ambulatory patients were died, 0.9% of bed ridden patient were censored,

5.3% of bed ridden patients were died. the other classification

of the patients were WHO clinical stages there are four clinical

stages these are stage I 47.9% of patients in stage I were

censored, 18.6% of patients in stage I were died, the in

in stage II 20.7% of patients in stage II were censored, 29.2%

Table 1

Explanatory Variables (Code)

Table 1a

Measures Taken (Time, weight and CD4 Count)

Variable Names Time Weight CD4 count

Measures Taken In months Baseline Weight of the patients Baseline CD4 cell count

Table 1b

Age

Age 16-25 26-35 36-45 46-55 56-65 >65

Code 1 2 3 4 5 6

Table 1c

Sex

Sex Marital status Religion Education Residence Functional status Opportunistic illness Code

Female Single Orthodox No education Rural Working Yes 0

Male Married Muslim Primary Secondary and Urban others No 1

--- Other Protestant Tertiary school level ------ 2

Table 1d

WHO Stages and Regimen classes

Code 0 1 2 3 4

WHO Clinical Stages Stage 1 Stage2 Stage3 Stage4 ---

Regimen Classes AZT-3TC-NVP, AZT-3TC-EFV TDF-3TC-EFV TDF-3TC-NVP, ABC-3TC- NV




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of patients in stage II were died in stage III 26.9% of patients in

stage III were censored,46.0% of patients in stage III were died,

in stage IV 4.6% of patients in stage IV were censored, 6.2% of

patients in stage IV were died. In opportunistic infection 4.6%

of patients without opportunistic infection were censored,

100.0% of patients without opportunistic infection were died,

95.4% of the patients with opportunistic infection were

censored and 0.0% of the patients with opportunistic infection

were died. The other category of patients is regimen class 8.4% of censored patients were use AZT-3TCNVP, 0.8% of died

patients were use AZT-3TC-NVP,3.0% of censored patients

were use AZT-3TC-EFV, 0.2% of censored patents were use

AZT-3TC-EFV. 72.2% of censored patients were use TDF-

3TC-EFV. 8.3% of died patients were use TDF-3TC-EFV.

3.2% of censored patients were use TDF-3TC-NVP. 1.6% of

censored patients were used TDF-3TC-NVP, 5.9% of censored

patients were use ABC-3TC-NVP. The patients were classified

based on their educational status 14.4% of not educated patients

were censored, 15.9% of not educated patients were died. The

second category in educational level is primary educational

level 47.7% of primary educated patients were censored, 48.7% of primary educated patients were died. 30.3% of secondary

educated patients were censored, 26.5% of secondary educated

patients were died, 7.6% of tertiary educated patients were

censored, 8.8% of tertiary educated patients were died. Patients

Censoring status with marital status 30.4% of single patients

were censored, 17.7% of single patients were died. The second

categories of marital status 40.2% of Married patients were

censored, 40.7% of married patients were died. 29.4% of other

category of marital status of patients were censored, 41.6% of

other category of marital status of patients were died. The

patient based on religion as 93.3% of orthodox patients were censored, 94.7% of orthodox patients were died. 2.0%of

Muslim patients were censored, 0.9% of Muslim patients were

died.4.8% of protestant patients were 1.5% of patients live in

rural area were censored, 1.8% of patients live in rural area were

died. 98.5% of patients live in urban area censored and 98.2%

of patients live in urban area were died. In table 4.1 the last

column is Pearson chi-square test and level of significance,

these shows us censoring status of patients association with

other covariate.

From Table 3 in the case of opportunistic infection the

patients were classified as patients with opportunistic infection

and patients without opportunistic infection in the number of

patients without opportunistic infection in their functional

status is working patients without opportunistic infection were

12.8%, working patients with opportunistic infection were 77.5

and 2.1%,of widowed and divorced patients with opportunistic

infection, 7.5%of widowed and divorced patients without

opportunistic infection. 4.1% of censored patients without

opportunistic infection whereas 85.0% of censored patients

with opportunistic infection. 10.9% of died patients without

opportunistic infection, death patients with opportunistic

infection were 0.0%. Patients in educational level 2.4% of not

educated patients were without opportunistic infection 12.2%

of not educated patients with opportunistic infection.7.4%of

primary educated patients were without opportunistic infection,

40.3%.of primary educated patients were with opportunistic

infection, 3.9% of secondary educated patients were without

opportunistic infection, 26.1%vof secondary educated patients

were without opportunistic infection, 1.3%of tertiary educated

patients were with opportunistic infection In marital status 3.6%

of single patients were without opportunistic infection, 25.5%of

single patients were with opportunistic infection, 5.5% of

married patients were without opportunistic infection, 34.7% of

married patients were with opportunistic infection. 5.9% of

widowed and divorced patients were with opportunistic

infection, 24.8% of widowed and divorced patients were with

opportunistic infection. Patient’s category in religion 14.1% of

orthodox patients were without opportunistic infection, 79.3%

of orthodox patients were with opportunistic infection, 0.2% of

Muslim patients were without opportunistic infection, 1.6% of

Muslim patients were with opportunistic infection, 0.7% of

Protestant patients were without opportunistic infection, and

Table 2

Cross table for Censoring status with covariates

Covariate\Category Censoring Status(Count)

Chi-Square (P-Value) Censored

N (%)

Death

N (%) Covariate Category

Functional Status Working 840(81 .1) 96(9.3) 15.428(0.040)

Other 83(8.0) 17(1.6)

Educational Status No education 133(12.8) 18(1.7) 0.872*(0.832)

Primary 440(42.5) 55(5.3)

Secondary 280(27.0) 30(2.9)

Tertiary 70(6.8) 10(1.0)

Marital Status Single 281(27.1) 20(1.9) 10.543(0.005)

Married 371(35.8) 46(4.4)

Others 271(26.2) 47(4.5)

Religion Orthodox 861(83.1) 107(10.3) 0.699*(0.176)

Muslim 18(1.7) 1(0.1)

Protestant 44(4.2) 5(0.5)

Residence Rural 14(1.4) 2(0.2) 0.042*(0.837)

Urban 909(8.7) 111(10.7)

Sex Female 626(60.4) 65(6.3) 4.8090(0.28)

Male 297(28.7) 48(4.6)

*no significance association between censoring status with covariate at 0.05 level




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4.1% of protestant patients were with opportunistic infection.

The residence of patients 0.3% of Patients who live in rural

were without opportunistic infection, 1.3% of patients live in

rural were with opportunistic infection, 14.7% of patients live

in urban were without opportunistic infection, 83.6% of patients

live in urban area were with opportunistic infection. The sex of

patients is the other categorical variable 8.6%of Female patients

were without opportunistic infection, 58.1% of female patients

were with opportunistic infection. 6.4% of male patients were

without opportunistic infection, 26.9% of male patients were

with opportunistic infection. Table 4.2 last column is Pearson

chi-square with level of significance. Tells us association

between covariates with opportunistic infection. From the

covariates in table 4.2 sex, marital status, censoring status and

functional status show association with opportunistic infection

of patients.

Table 4 shows that the patients number in each clinical stage

with respect to the other factor such as sex, age, censoring

status, opportunistic infection, functional status, educational

level, marital status, religion, and residence of patients number

of females patients in stage I were 32.7%, number of females

patients in stage II 14.3%, number of females patients in stage

Table 3

Cross table for Opportunistic infection with Covariates

Covariate\Category Opportunistic infection (Count)

Chi-Square (P-Value) Yes

N(%)

No

N(%) Covariate Category

Functional Status Working 133(12.8) 803(77.5) 4.17(0.041)

Other 22(2.1) 78(7.5)

Censoring Censored 42(4.1) 881(85.0) 715.475(0.00)

Death 113(10.9) 0(0.00)

Educational Status No education 25(2.4) 126(12.2) 1.861*(0.602)

Primary 77(7.4) 418(40.3)

Secondary 40(3.9) 270(26.1)

Tertiary 13(1.3) 67(6.5)

Marital Status Single 37(3.6) 264(25.5) 6.46(0.040)

Married 57(5.5) 360(34.7)

Others 61(5.9) 257(24.8)

Religion Orthodox 146(14.1) 822(79.3) 0.34*(0.844)

Muslim 2(0.2) 17(1.6)

Protestant 7(0.7) 42(4.1)

Residence Rural 3(0.3) 13(1.3) 0.173*(0.677)

Urban 152(14.7) 868(83.8)

Sex Female 89(8.6) 602(58.1) 6.707(0.010)

Male 66(6.4) 279(26.9)

*no significance association between Opportunistic infection status with covariate at 0.05 level

Table 4

Cross table for WHO clinical stages with covariates

Covariate\Category WHO clinical stages (Count)

Chi-Square (P-Value)

Sta

ge I

Sta

ge I

I

Sta

ge I

II

Sta

ge I

V

Covariate Category

Functional Status Working 445(43.0) 204(19.7) 255(24.6) 32(3.1) 62.849(0.00)

Other 18(1.7) 20(1.9) 45(4.3) 17(1.6)

Opportunistic Infection No 40(3.9) 43(4.2) 64(6.2) 8(0.8) 27.893(0.00)

Yes 423(40.8) 181(17.5) 236(22.8) 41(4.0)

Censoring Censored 442(42.7) 191(18.4) 248(23.9) 42(4.1) 36.03(0.00)

Death 21(2.0) 33(3.2) 52(5.0) 7(0.7)

Educational Status No education 57(5.5) 34(3.3) 48(4.6) 12(1.2) 10.103*(0.342)

Primary 221(21.3) 110(10.6) 143(13.8) 21(2.0)

Secondary 145(14.0) 69(6.7) 83(8.0) 13(1.3)

Tertiary 40(3.9) 11(1.1) 26(2.5) 3(0.3)

Marital Status Single 138(13.3) 62(6.0) 83(8.0) 18(1.7) 4.144*(0.657)

Married 179(17.3) 89(8.6) 132(12.7) 17(1.6)

Others 146(14.1) 73(7.0) 85(8.2) 14(1.4)

Religion Orthodox 434(41.9) 212(20.5) 278(26.8) 44(4.2) 3.945*(0.341)

Muslim 9(0.9) 4(0.4) 4(0.4) 2(0.2)

Protestant 20(1.9) 8(0.8) 18(1.7) 3(0.3)

Residence Rural 5(0.5) 6(0.6) 5(0.5) 0(0.0) 3.350*(0.341)

Urban 458(44.2) 218(21.0) 295(28.5) 49(4.7)

Sex Female 339(32.7) 148(14.3) 176(17.0) 28(2.7) 19.627(0.00)

Male 124(12.0) 76(7.3) 124(12.0) 21(2.0)

*no significance association between WHO clinical stages status with covariate at 0.05 level




93

III 17%, number of females patients in stage IV 2.0%. In the

other hand number of male patients in stage I were 12.0%,

number of males patients in stage II were 7.3%, number of male

patients in stage III were 12.0%, number of males patients in

stage IV were 2.0%. Functional status of patients 43% of

working patients were in stage I, 19.7% of working patients

were in stage II, 24.6% of working patient working patients in

stage III, 3.1% of working patients were in stage IV. In category

other 1.7% of patients in other functional status were in stage I,

1.9% of patients in other functional status were in stage II,

4.3%of patients in other functional status were in stage III, 4.3%

of patients in other functional status were in stage IV. The

patients with or without opportunistic infection in each clinical

stages were stage I 3.9% of patients were without opportunistic

infection, in stage II 4.2%, in stage III 6.2, in stage IV 0.8%,

patients were without opportunistic infection. The other one

patients with opportunistic infection were in stage I 40.8%,

stage II 17.5%, in stage III 22.8%, in stage IV 4.0% of patients

were with opportunistic infection. When we see observation

based on educational level there were four level of education

these were not educated patients in this class 5.5% of patients

were in stage I, 3.3% not educated patients were in stage II,4.6

of non-educated patients were in stage III,1.2% of non-educated

patients were in stage IV. The other one patients primary school

level of education 21.3% were in stage I,10.6% of patients were

in stage II, 13.8*% of the patients were in stage III, 2.0% of the

primary school educational level patients were in stage IV.

Secondary school educated patients were 14.0% of the patients

in secondary school level of education were in stage I, 6.7% of

secondary school educational level patients were in stage II, 8

% of the secondary school level patients were in stage III, 1.3%

of secondary school level education patients were in stage IV.

In the marital status of patients 1 .3% of the single patients were

in stage I, 6.0% of the single patients were in stage II, 8.0% of

the single patients were in stage III, 1.7% of the single patients

were in stage IV. 17.3% of married patients were in stage

I,8.6% of married patients were in stage II, 12.7% of married

patients were in stage III, 1.6% of married patients were in stage

IV. 14.1% of patients in other group were in stage I, 7.0% of

others were in stage II, 8.2% of others were in stage III, 1.4%

of other was in stage IV. The religion of patient 41.9% of

orthodox patients were in stage I, 20.5% of orthodox patients

were in stage II, 26.8% of orthodox patients were in stage III,

4.2%of orthodox patients were in stage IV. 0.9% of Muslim

patients were in stage I, 0.4% of Muslim patients were in stage

II, 0.4% of Muslim Patients were in stage III, 0.2% of Muslim

patients were in stage IV. protestant patients in stage I were

1.9%, 0.8% of the protestant patients were in stage II, 1.7% of

protestant patients were in stage III, 0.3% of protestant patients

were in stage IV. In the residence of patients 0.5% of patients

live in rural area was in stage I, 0.6% of patients live in rural

area were in stage II, 0.5% of patients were in stage III, 0.0% of

patients live in rural area were in stage IV. 44.2% of patients

live in urban area was in stage I, 21.0% of patients in urban area

were in stage II, 28.5% of patients live in urban area were in

stage III, 4.7% of patients live in urban area were in stage IV.

The chi-square test of WHO clinical stage with other co-vitiates

shows there is significant association between WHO clinical

stage and functional status, censoring status, marital status and

residence of patients.

Table 5 shows that number of patient population in each

regimen class with respect to other covariates and their

category. There were five types of baseline regimens class for

adult patients were used in the hospital. That is AZT-3TC-NVP

in this 5.5% of the patients use this drug were females, 3.7% of

males patients were users of AZT-3TC-NVP, the drug AZT-

3TC-EFV was the second it was used by 2.0% females and

1.2% male patients. The next one is TDF-3TC-EFV it was used

by 53.4% female, 27.1% male patients; the fourth one is TDF-

3TC-NVP it was used by 5.5% females and 1.4% males. The

last regimen is ABC-CTC-NVP the users of this drug were

0.2% of females and 0.1% of males. On the bases of functional

status 8.4% of the working patients were used AZT-3TC-NVP,

3.0% of the working patients were used AZT-3TC-EFV, 72.6%

of working patients were users of TDF-3TC-EFV,6.2% of the

working patients were users of TDF-3TC-NVP. 0.2% of the

working patients were users of ABC-3TC-NVP, 0.7% of

patients who were not able to work were users of TDF-3TC-

NVP, 0.1% of patients in the others were users of ABC-3TC-

NVP. 8.4% of patients in stage I were use AZT-3TC-NVP,

0.7% of patients in stage I were user of AZT-3TC-EFV.37.2%

of patients in clinical stage I were use TDF-3TC-EFV, 2.4% of

patients in stage I were users of AZT-3TC-NVP,0.1% of

patients in stage I were users of ABC-3TC-NVP, 2.7% of

Patients in stage II were users of AZT-3TC-NVP, 1.0% of

patients in stage II were users of AZT-3TC-EFV, 15.5% of

patients in stage II were users of TDF-3TC-EFV, 2.3% of

patients in stage II were users of the TDF-3TC-NVP.0.1% of

patients in stage I were users of ABC-3TC-NVP, 1.8% of

patients in stage III were users of AZT-3TC-NVP,1.5% of

patients were in stage III were users of AZT-3TC-EFV,23.5%

of patients in stage III were users of TDF- 3TC-EFV,2.0% of

patients in stage III were users TDF-3TC-NVP, 0.1% of

patients in stage Iv were users of ABC-3TC-NVP. In stage IV

0.3% of patients were users of AZT-3TC-EFV,4.3% of patients

in stage IV were users of TDF-3TC-EFV, 0.1% of patients in

stage IV were users ofTDF-3TC-NVP. 1.4% of Patients without

opportunistic infection were users of AZT-3TC-NVP, 0.2% of

patients without opportunistic infection were users of AZT-

3TC-EFV, 11.6% of patients without opportunistic infection

were users of TDF-3TC-EFV, 1.8% of patients without

opportunistic infection were users of TDF-3TC-NVP. 7.8% of

Patients with opportunistic infection were users of AZT-3TC-

NVP, 3.0% of patients with opportunistic infection were users

of AZT-3TC-EFV,68.9% of patients with opportunistic

infection were users of TDF-3TC-EFV, 5.3% of patients with

opportunistic infection were users of opportunistic infection

were users of TDF-3TC-NVP,0.3% of patients with




94

opportunistic infection were users of ABC-3TC-NVP.8.4% of

censored patients were users of AZT-3TC NVP,3.0% of

censored patients were users of AZT-3TC-EFV, 72.2% of

censored patients were users of TDF-3TC-EFV,5.2% of

censored patients were users of TDF-3TC-NVP,0.3% of the

censored patients were users of ABC-3TC-NVP. 0.8% of the

died patients were users of AZT- 3TC-NVP, 0.2% of died

patients were users of AZT-3TC-EFV, 8.3% of died patients

were users of TDF-3TC-EFV, 1.6% of died patients were users

ofTDF-3TC-NVP. In the case of educational level of patients

0.9% of not educated patients were users of AZT-3TC-NVP,

0.4% of patients who were not educated were users of AZT-

3TC-EFV, 12.6% of not educated patients were users of TDF-

3TC-EFV, 0.7% of not educated patients were users of TDF-

3TC-NVP. 4.4% of primary educated patients were users of

AZT-3TC-NVP, 1.6% of primary educated patients were users

of AZT-3TC-EFV, 38.0% of the primary educational level

patients were users of TDF-3TC-EFV, 3.5% of the patient in

the primary school level of education were users of TDF-3TC-

NVP, 0.2% of the primary educated patients were users of

ABC-3TC-NVP. In the secondary school level of education of

patients 3.1 % of the patients were users of AZT-3TCNVP,

0.8% of the patients in the secondary level of education were

users of AZT-3TC-NVP, 23.6% of the patients were users of

TDF-3TC-EFV, 2.5%of patients in secondary level of

education were users of TDF-3TC-NVP. In the tertiary level of

education 0.8% were users of AZT-3TC-NVP, 0.4% of the

patients in the tertiary level of education were users of AZT-

3TCEFV, 6.3% of the patients in the tertiary level of education

were users of TDF-3TC-EFV, 0.2% of patients in tertiary level

of education were users of TDF-3TC-NVP,0.1% of the patients

in the tertiary level of education were users of ABC-3TC-NVP.

Patients in the marital status distributed as 2.6% os single

patients were users of AZT-3TCNVP,1.1% of single patients

were users of AZT-3TC-EFV,23.1% of single patients were

users of TDF-3TC-EFV,2.1% of single patients were users of

TDF-3TC-NVP,0.2% o single patients were users of ABC-

3TC-NVP.3.4% of married patients were users of AZT-3TC-

NVP,1.3% of married patients were users of AZT-3TC-

EFV,32.8% of patients were users of TDF-3TCEFV,2.7% of

patients were users of TDF-3TC-NVP ,0.1 % of married

patients were users of ABC-3TC-NVP. 3.2% of other patients

were users of AZT-3TC-NVP, 0.9% of patients in the other

were users of AZT-3TC-EFV, 24.6% of the patient in the other

were users of TDF-3TCEFV, 2.0% of the other patients were

users of TDF-3TC-NVP.

The patients number in each religion with respect to the

regimen expressed as 8.3% of the Orthodox patients were users

of AZT-3TC-NVP, 3.0% of Orthodox patients were users of

AZT- 3TC-EFV, 75. 2% of Orthodox patients were users of

TDF-3TC-EFV, 6.2% of Orthodox patients were users of TDF-

3TC-NVP, and 0.3% of Orthodox patients were users of ABC-

3TCNVP.0.2% of Muslim patients were users of AZT-3TC-

NVP, 1.4% of Muslim patients were users of TDF-3TC-EFV.

0.7% of protestant patients were users of AZT-3TC-NVP, 0.2%

of protestant patients were users of AZT-3TC-EFV, 0.5% % of

Table 5

Cross table for regimen class with covariates

Covariate\Category Regimen Class

Chi-Square (P-Value)

AZ

T-3

TC

-NV

P

AZ

T-3

TC

-EF

V

TD

F-3

TC

-EF

V

TD

F-3

TC

-NV

P

AB

C-3

TC

-NV

P

Covariate Category

Functional Status Working 87(8.4) 31(3.0) 752(72.6) 64(6.2) 2(0.2) 2.617*(0.624)

Other 8(0.8) 2(0.2) 82(7.9) 7(0.7) 1(0.1)

WHO

Stage 1 45(4.3) 7(0.7) 385(37.2) 25(2.4) 1(0.1)

28.788(0.004) Stage 2 28(2.7) 10(1.0) 161(15.5) 24(2.3) 1(0.1)

Stage 3 19(1.8) 16(1.5) 243(23.5) 21(2.0) 1(0.1)

Stage 4 3(0.3) 0(0.0) 45(4.3) 1(0.1) 0(0.0)

Opportunistic Infection No 14(1.4) 2(0.2) 120(11.6) 19(1.8) 0(0.0) 12.462(0.014)

Yes 81(7.8) 31(3.0) 714(68.9) (5.3) 3(0.3)

Censoring Censored 87(8.4) 31(3.0) 748(72.2) 54(5.2) 3(0.3) 14.491(0.006)

Death 8(0.8) 2(0.2) 86(8.3) 17(1.6) 0(0.0)

Educational Status No education 9(0.9) 4(0.4) 131(12.6) 7(0.7) 0(0.0) 13.137*(0.359)

Primary 46(4.4) 17(1.6) 394(38.0) 36(3.5) 2(0.2)

Secondary 32(3.1) 8(0.8) 244(23.6) 26(2.5) 0(0.0)

Tertiary 8(0.8) 4(0.4) 65(6.3) 2(0.2) 1(0.1)

Marital Status Single 27(2.6) 11(1.1) 239(23.1) 22(2.1) 2(0.2) 3.786*(0.876)

Married 35(3.4) 13(1.3) 340(32.8) 28(2.7) 1(0.1)

Others 33(3.2) 9(0.9) 255(24.6) 21(2.0) 0(0.0)

Religion Orthodox 86(8.3) 31(3.0) 784(75.7) 64(6.2) 3(0.3) 5.322*(0.723)

Muslim 2(0.2) 0(0.0) 14(1.4) 3(0.3) 0(0.0)

Protestant 7(0.7) 2(0.2) 36(3.5) 4(0.4) 0(0.0)

Residence Rural 3(0.3) 1(0.1) 9(0.9) 3(0.3) 0(0.0) 6.696*(0.153)

Urban 92(8.9) 32(3.1) 825(79.5) 68(6.6) 3(0.3)

Sex Female 57(5.5) 21(2.0) 533(53.4) 57(5.5) 3(0.3) 9.512(0.050)

Male 38(3.7) 12(1.2) 281(27.1) 14(1.4) 0(0.0)




95

protestant patients were users of TDF-3TC-NVP,0.4%% of

protestant patients were users of TDF-3TC-NVP. The residence

of patients with two categories is 0.3%of the patients in rural

area were users of AZT-3TC-NVP,0.1% of the patients in rural

area were users of AZT-3TC-EFV,0.9% of patients in rural area

were users of TDF-3TC-EFV,0.3% of patients in rural area

were users of TDF- 3TC-NVP.8.9% of the patients in urban

area were users of AZT-3TC-NVP,3.1% of patients were live

in urban users ofAZT-3TC-EFV, 79.6% of the patients in urban

area were users of TDF-3TC-EFV,6.6% of the patients live in

urban were users of TDF-3TC-NVP,0.3% of the patients live in

urban were users of ABC-3TC-NVP. Table 4.4 shows the chi-

square test and level of significance. The association between

regimen class and functional status, censoring status, marital

status and sew shows significant association.

Descriptive statistics for continuous variables

The data set in this study contains survival time of patients in

ART clinic from start up to occurrence of an event with the

minimum 1 month to the maximum 61 months. The first

quartiles of survival time are 7, third quartile of survival time is

40, the median of survival time is 20, the mean of the survival

time is 23. The weight of patients has minimum of 13 maximum

of 89. The first quartile of weight is 46, third quartile of weight

is 49, mean and median of weight is 52. The age of patients

have minimum 16 year, maximum 71 years. Median of age is

32.00, mean of age is 34.02, first quartile of age is 27, third

quartile of age is 40.

Table 6

Descriptive statistics for continuous variables

In Table 6, the mean of age is 34.02027 with its standard error

0 .3178348the minimum value of age is 16 the maximum values

of age is71. The mean of the time is 23.74807 with standard

error, the minimum value of time is 1 month, and the maximum

time in month is 61 months. When we see survival time of

patients, among total of 1036 study subjects 7.43243% of the

patients were died during the first 12 months, 3.7645% of

deaths occurred within the first three months after initiation of

ART. Another 2.027% of the patients were died in the

following three months of follow up; that is a total of 5.792%

of the patients deaths were occurred within six months. In the

last six months, 1.641% of the patients were died.

Descriptive statistics by using Kaplan-Meier plot

Figure 1 shows the trend among sex for female, the observed

and predicted are go in same direction from 0 to 55. Then there

was a little devotion but in the case of male there is fluctuation

in their line. On the other hand, survival of patient is affected

by sex.

Fig. 1. The Kaplan Meier survival estimates by sex

Fig. 2. Kaplan-Meier plot for Survival by Regimen class

Figure 2 shows that survival is affected by regimen class.

Patients who use AZT-3TC-NVP have less survival time than

that of patients use AZT-3TC-NVP.

Fig. 3. Kaplan-Meier plot for opportunistic infection

In figure 3, survival time is affected by opportunistic

infection. Survival of patient with opportunistic infection has

less survival time than that of patients without opportunistic

infection.

Fig. 4. Histogram for age group

In the figure 4, the category shows the age of patients in

group two contain highest number of patients from the other

group which is 26-35 age group.it followed by age group three

then group one, in this graph age group six contains smallest




96

number of observation. ART treatment and the curve show an

asymmetric distribution of age.

5. Results

In this study the main objective is to implementing the Semi-

parametric Bayesian analysis. Thus this study includes the data

set contains, 1036 patient under the ART treatment. To

implement the method of simulation of the data Markov chain

(MC) were used. In the simulation process the diagnostic plot

were produced, then the mixing and convergence of Markov

chain were examined by visual assessments of the plots. The

three types of plots are Trace plot, autocorrelation plot and

density plot; these are placed for each of the parameters

included in the model. It is imperative that these (and other

diagnostics) be examined before any conclusions are drawn

from the simulated posterior sample). The results shown on the

next page are almost perfect for most of the parameters. The

trace plot shows excellent mixing, the autocorrelation decreases

to near zero, and the density is bell-shaped or has the shape of

normally distributed data. The trace plots are centered near their

respective posterior mean and traverse the posterior space with

small fluctuations. These results exhibit convergence of the

Markov chain to its stationary distribution. The explanation of

convergence and mixing of Markov chain is presented for each

parameter as follows.

Diagnosis plot for Bayesian analysis

In the Bayesian analysis the parameters were examined by

using Graphical methods. The figure for some of the parameters

were depicts time difference diagram to examine convergence,

Autocorrelation and the density of the parameters. In assessing

the properties of convergence for the posterior distribution there

is a carful assessment method, it is known as Markov chain

mixing and convergence.

Fig. 5. Sex and Opportunistic Infection

As an explanation is made on the methodology the MCMC

process is used to converge the given data. Figure 5 shows that

the model is converge well in sex of males. The trace plot shows

excellent mixing, the autocorrelation decreases to near zero,

and the probability density is bell shaped, it attains almost the

perfect shape of Markov chain. The trace plots are centered near

their respective posterior mean (around negative 0.2) and

traverse the posterior space with small fluctuations. Whereas

the three of the plot are show in the case of opportunistic

infection was poorly mix and these plot are fail to fulfill Markov

chain plots shape.

Fig. 6. Regimen class for AZT-3TC-EFV and TDF-3TC-EFV

Figure 6 displays the trace plot, the autocorrelation function

plot and posterior density plot generated by Markov Chain. In

both regimen class the trace plot show excellent mixing, the

autocorrelation decreases to near zero, and the density has the

shape for Markov chain diagnostic plot. The trace plots are

centered near their respective posterior mean and traverse the

posterior space with small fluctuations.

Fig. 7. Regimen class

Figure 7 shows good mixing in TDF-3TC-NVP that is second

figure, but poor mixing and convergence in the ABC-3TC-NVP

that is first figure. In the other word the effectiveness of regimen

is different from one another. That mean the survival time is

affected by regimen class of patients.

Fig. 8. WHO Clinical stages

Figure 8 shows that the three WHO clinical stages diagnostic

plots. The trace plot shows excellent mixing, the

autocorrelation decreases to near zero, and the density plot

shows excellent shaped of Markov chain. The trace plots are

centered near their respective posterior mean and traverse the

posterior space with small fluctuations.




97

Fig. 9. Baseline Weight and CD4 count

Figure 9, three types of plot are displays these plots are good

convergence and good mixing of Markov chain. These are

examining the trace plot show well mixing, density plot shows

good convergence, the autocorrelation function plot show low

correlation. Figure 4. 8. For almost perfect convergence with

excellent Markov chain mixing. In the figure 8 for Baseline

CD4 and Baseline weight are shows the three diagnostic plots

for both of the parameters are perfect mixing of Markov chain.

Trace plots of samples versus the simulation index can be useful

in assessing convergence and also shows that the chain is

mixing well. It may be noted that if the chain does not converge

to its stationary distribution, then there will be long burn-in

period. One can observe from a trace plot that there On the basis

of figure 4, 6, 7, 8 and 9 we conclude that,

Markov chain (MC) has reached convergence.

MC has reached stationary as the distribution of points is

not changing as the chain progress.

The burn-in is a size of 2000. This means that the initial

2000 observations has been discarded.

Trace plot is perfect and the center of the chain is around

0.4 with small fluctuations which indicates that the MC

has reached the right distribution.

The chain is mixing well as it is exploring the distribution

by traversing to areas where its density is very low.

Result from posterior sample: As a consideration of semi

parametric model in Bayesian analysis, by using the variable

time-to-event the analysis were carried out. In this analysis

from the model information table the dependent variable is

time, the censoring status (cen), among the coded variables the

code 0 is for the censored and the code 1 is for the event of not-

censored category. The model is cox (PH) along with method

of tie handling is Breslow. From the Burn-in phase 2000 with

the MC sample size 10,000 were carried out. The observed

sample was 1036 and the event were 113(11%) whereas

censored observation 923(89.09%) were found. From this

censored data or category were more than 89% and the rest were

the event category.

Table 7 reports the statistics, posterior mean, credible

intervals, and high probability density (HPD) intervals for each

of the parameters based on the posterior sample of 10000.

Because the priors used are non-informative, the mean,

standard deviation and credible interval are fairly close to the

corresponding maximum likelihood estimates (estimate,

standard error, 95% CI).

Table 7

Posterior summary and posterior interval and maximum likelihood

estimates

Table 7, shows the mean and standard deviation of the

posterior samples are comparable to the MLE and its standard

error, respectively, this is happen because of the use of the

uniform prior. By referencing male, there is a 23.49% chance

that the hazard rate of male is less than that of the hazard rate

of fe male. The result is consistent with the fact that the average

survival time of female is less than that of males. The posterior

mean of age is 0.00667 it indicates there is a 0.667% chance

that the hazard rate of patients is increased by 0.667% as age is

increased by 1. By referencing workers, the posterior mean of

other functional status is 0.6042. There is a 60.42% chance that

the hazard rate of other functional status patients is greater than

that of working patients. The average survival time of working

patients is greater than that of other functional status patients.

The mean of baseline CD4 cell count is 0.00041it shows that

there is 0.41% chance that the baseline CD4 cell count can

decrease the hazard rate of the patients in 0.41% when Base line

CD4 is increased by 1, in other word the base line CD4 cell

increased by 1, the hazard rate of patients increases by 0.41%

rate. The base line weight mean is 0.0126. There is

a1.26%chance that the patients hazard rate decrease as Base

line weight increased by 1. By referencing rural, the mean of

the urban patients is 9144, there is a 91.44% chance that the

hazard rate of patients live in Urban is greater than that of

patients live in rural. By referencing stage I, WHO clinical stage

show that the hazard rate of patients has difference from each

other. the WHO stage 2, there is a 49.99%chance that the hazard

rate of Stage1 is less than that of stage I, The result is consistent

with the fact that the average survival time of patients in

stage1is greater than that of the survival time of patients in

stages 2. There is a 78.67% chance that the hazard rate of WHO

clinical stage stage3 is greater than that of stage 1. The average

survival time of patients in stage3 is less than that of stages1.

The result is consistent with the fact that the average survival

time of patients in stage 4 is less than that of stage1. By

referencing no education, there is a 33.00% chance that the

hazard rate of primary school educated patients less hazard rate

than that of not educated patients. The result is consistent with

the fact that the average survival time of primary educated

patients is greater than that of not educated patients. There is a

53.56% chance that the hazard rate of secondary educated

patients is greater than that of not educated patients. The result




98

is consistent with the fact that the average survival time of

secondary educated patients is less than that of not educated

patients. There is an 86.67% chance that the hazard rate of

tertiary educated patients greater than that of not educated

patients. By referencing regimen AZT-3TC-NVP, there is a

92.29% chance that the hazard rate of patients who use TDF-

3TC-EFV is greater than that of patients who were use AZT-

3TC-NVP. The result is consistent with the fact that the average

survival time of patients who were use AZT-3TC-NVP is

greater than that of patients who were use TDF-3TC-

EFV.There is a 98.98% chance that the hazard rate of patients

who were use TDF-3TC-NVP is greater than that of patients

who were use AZT-3TCNVP.


time of TDF-3TC-NVP users is less than that of AZT-3TC-

NVP users.by referencing single, there is a 50.37% chance that

the hazard rate of married patients is greater than that of single

patients. The result is consistent with the fact that the average

survival time of married patients is less than that of single

patients. There is a 46.88% chance that the hazard rate of

widowed and divorced patients less than that of single patients.


time of divorced and widowed patients is greater than that of

single patients. By referencing ortho9dox, the values -10.85%

and -84.32% are indicates that the religion of the patients has

no significance impact on the hazard rate of patients, that is the

survival time of the patients does not affected by the religion of

the patients. In the table 4.6 we can see that the likelihood

estimate and its standard error and posterior mean and its

standard deviation of the parameters, in both values for

likelihood estimate and values for posterior mean are lie in

between confidence limit and the higher probability density

intervals. In those maximum likelihood estimates all estimated

values are found in between the confidence limit. The sign of

parameter estimate of these parameters differ from each other.

And also the length of their confidence limit is different from

each other.in the other hand posterior mean and likelihood

estimate are approximately equal

Uniform Prior for model parameters is a default prior

in phreg SAS procedure for Semi parametric Bayesian

analysis, it is constant for all parameters

The fit Statistics gives the information about fitted

model in terms of DIC (Deviance Information

Criterion) and pD (effective number of parameters).

Table 8

Posterior Summary

Table 8 shows that effective sample size the effective sample

size is the test used to compare the covariates with their sample.

The sample of this covariate is show approximately equal to the

sample of the variables given by simulation it is known as good

sample, if it is larger or smaller than that of given sample it is

poor sample. The efficiency of the variables is small it is less

than 1 so the sampling method for each variable is good.

6. Discussion, Conclusion and Recommendation

Discussion: In this study semi-parametric Bayesian analysis

for time-to-event data from ART follow up was presented. The

method of semi-parametric Bayesian analysis for survival of

HIV, cox proportional hazard, prior elicitation and Markov

chain sampling were considered. As Bayesian analysis is based

on prior distribution, prior selection is the first step. In our

findings also the first step was to decide which kinds of prior is

important to perform the analysis with the aim of the study. The

Bayesian analysis method used proper prior if there exist

previous study similar to current study by their variable and the

model which is need to apply in the study. Then posterior

distribution form the first study is used as prior distribution.

Therefore, since there is no previous study to get prior

information for our study, the prior distribution was selected by

default. In other word improper prior or flat prior was used. The

second step of this study is Checking or diagnostics of Markov

chain convergence and mixing. To perform this process SAS

phreg procedure was used. From the variable which were not

significantly converge and mix Markov chain was opportunistic

infection, where as other variables such as sex, age, functional

status, WHO clinical stages, regimen class, educational level,

marital status, religion, residence, baseline weight and baseline

CD4 were satisfy the Markov chain mixing and convergence

criteria. The first objective of this study is implementation of

semi parametric Bayesian for survival of HIV patients. In this

analysis after diagnosis of Markov chain convergence and

posterior sample was produced. The posterior mean and

standard deviation were comparable with likelihood estimation

and standard error respectively. As an example residence is not

affect survival time of patients in the posterior mean whereas it

has impact on survival time of patients in maximum likelihood

estimation. The data which is taken from ART was analyzed by

using different plots and descriptive statistical analysis methods

such as cross tabulation for categorical covariates and mean,

minimum, maximum and standard error for continues co-

variable were carried out. In the other hand Kaplan-Meier plots

for survival of patients with each covariates by using stata

version 12.0(for Kaplan-Meier plot), SPSS version 20 (for

descriptive statistics) and SAS version 9.4 (for inferential

statistical analysis). The Kaplan-Meier plot suggests that

survival time of patients affected by age, sex, WHO clinical

stages, regimen class, opportunistic infection, marital status and

residence. From the semi parametric Bayesian model sex of

patient, age of patients, baseline CD4 cell count, Baseline body

weight, regimen class, WHO clinical stages, residence religion,




99

marital status and educational level are significant predictor of

the survival time of the patients or time to death of patient.

When we see all this covariate in Kaplan-Meier plot all

covariates have significant impact on survival time. But in semi

parametric Bayesian analysis, opportunistic infection is not

affect survival time of patients, in our point of view the number

of patients with opportunistic infection covers large (93.3%) but

there is no uncensored, whereas patients number without

opportunistic infection was with smaller (%) with all event. In

this variable the result from KM and semi parametric Bayesian

is contradict in opportunistic infection. Semi parametric

Bayesian for cox model used partial likelihood estimate and

generates a chain of posterior distribution samples by the Gibbs

Sampler. Summary statistics, convergence diagnostics, and

diagnostic plots are provided for each parameter. In the proc.

phreg procedure for Bayesian analysis. Since we were not

specifying prior for our model parameters the default prior for

Bayesian is uniform prior. The uniform prior is a flat prior on

the real line with a distribution that reflects ignorance of the

location of the parameter, placing equal probability on all

possible values the regression coefficient can take. When we

use the uniform prior, the expect Bayesian estimate to resemble

the classical results of maximizing the partial likelihood as the

likelihood. This study found that patient survival under ART

was significantly associated with WHO clinical stage, baseline

CD4 cell count, base line body weight, regimen class, sex, and

opportunistic infection was not associated with survival time.

The finding of this study was similar to other study Isidore

Sieleunou et al. (2009). In the other hand association of

explanatory variable with explanatory variables were done by

using Pearson chi-square this shows that association between

regimen classes and WHO clinical stage, opportunistic

infection, censoring status, educational level and residence was

significant. But Regimen class has no association with sex,

marital status and functional status of patients. Censoring status

of Patient is associated with sex, marital status, and functional

status. Opportunistic infection is associated with functional

status, sex, censoring status and marital status. WHO clinical

stage is associated with functional status, opportunistic

infection, censoring status, educational level, residence and sex.

The time is affected by CD4 cell count of the patients. Age of

patients is also affect survival time, as the age increase by one

unite survive time is decreased by 0.667 percent. CD4 cell

count is associated with survival time; if CD4 cell count is large

the hazard rate is low. In this study baseline CD4 cell has a

0.041percent of the hazard rate decrease if CD4 cell is increase

.it is supported by Ketema Kebebe and Eshetu Wencheko

(2011). Patients with smaller weight have higher hazard rate.

Conclusions: This study was about HIV/AIDS patient‟s

survival with semi parametric Bayesian analysis. The method

of data analysis by using Bayesian semi-parametric was

effective for our study data. This analysis method has its own

potential advantage that is we can jointly model the baseline

hazard and the regression coefficients, and then accurately

compute posterior model probabilities and their standard errors

using MCMC simulation techniques. Bayesian inference is

done after the posterior distribution samples have achieved to

the convergence of Markov chain. Factors that affect survival

time of patients in the ART treatment in this study were sex,

age functional status, WHO clinical status, regimen class,

residence, baseline CD4 cell count, and baseline body weight.

The diagnostic plots for Markov chain were trace,

autocorrelation and probability density plots, these three plots

were show the good mixing and convergence of MC. The non-

informative improper prior in all of the highest posterior density

(HPD) intervals for the regression coefficients of the covariates

contain 0. This indicates a moderate association between time

to death and covariates for these data, as was expected. The

posterior distribution of the parameters appears quite symmetric

at the mode. The partial likelihood of the COX model in

PHREG procedure generates a chain of posterior distribution

samples by Gibbs sampler and it is first fits the Cox model by

maximizing the partial likelihood along with 95% confidence

intervals for regression parameters. The Fit Statistics give the

information about fitted model in terms of DIC (Deviance

Information Criterion) and pD (effective number of

parameters). Generally, the hazard rate of patients were affected

by residence, sex, age, functional status, WHO clinical stages,

regimen class, baseline CD4, base line body weight and for

each categories in categorical variable. As an example,

regarding covariate residence living in an urban country is

associated with poor survival time after starting ART treatment.

That is the result indicates that after referencing individual

covariates, the hazard rate of HIV patients lives in urban

country 91.44 percent times larger than that of individual live

in rural country. Likewise regarding the sex of patients there is

a 22.96 chance that the hazard rate of the male is smaller than

that of females. The result is consistent with the fact that the

survival time of male’s patients is greater than that of female

patients. In the other hand covariate religion has no significant

impact on survival of patients.

Recommendation: From this study we can recommend the

following points 1. The survival or time to event analysis for

rare event or the data with large number of censored observation

is analyzed by using Bayesian semi parametric model. 2.In this

study male have less hazard rate than female, it may because

due to lack of giving awareness since by nature female are

easily exposed to HIV/AIDS than male. 3. Female income or

type of job for living leads them to loss their care to live with

HIV. So they need special awareness to manage themselves. 4.

In the other hand this study shows patients live in urban area

have less survival time than who living in rural area, hence it is

suggested that the care to taken based on area of living 5.

Regarding regimen class of patients who takes AZT-3TC-NVP

have high survival time than patients who take other regimens.

In this case at the beginning of ART treatment patients need

special attention taken until they adapt with the regimen and

how to survive with the disease. 6. Finally, this study needs to




100

suggest that Debre Berhan Referral Hospital to maintain a

record for baseline clinical and demographic status of patients,

for a research in future.

References

[1] Alemu A. W, Sebastian M. S. (2010), Determinants of survival in adult

HIV patients on antiretroviral therapy in Oromiyaa, Ethiopia. Global

Health Action. 3: 5398

[2] Alejandro Jara, Applied Bayesian Non- and Semi-Parametric Inference

using DP package

[3] Amanuel Alemu Abajobir, et al. (2014) Survival Status of HIV positive

Adults on Antiretroviral treatment in Debre Markos Referral Hospital,

Nothwest Ethiopia: Retrospective Cohort study.

[4] Andinet Worku, (2009), “Pattern and determinants of survival in adult

HIV patients on antiretroviral therapy, Ethiopia,

[5] Bachani D, Garg R, Rewari B. B et al. (2010), “Two-year treatment

outcomes of patients enrolled in India‟s national first-line antiretroviral

therapy programme. Natl Med J India. 23:7–12

[6] Carlin, B. P. and Chib, S. (1995) Bayesian model choice via Markov chain

Monte Carlo methods‟, Journal of the Royal Statistical Society, Series B:

Methodological 57, 473–484.

[7] Ketema Kebebew and Eshetu Wencheko, (2011), Survival analysis of

HIV-infected patients under antiretroviral treatment at the Armed Forces

General Teaching Hospital, Addis Ababa, Ethiopia.

[8] Shankar Prinja, Nidhi Gupta and Ramesh Verma, (2010) Censoring in

Clinical Trials: Review of Survival Analysis Techniques, Indian J

Community Med; 35(2): 217–221.

implementation of semi-parametric bayesian …particularly in medicine (survival analysis) and...

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