quantitative measures in epidemiology - interfetpthailand · • both nominal and ordinal scale...

Quantitative Measures in Epidemiology

2

DEFINITION OF EPIDEMIOLOGY

“The study of the distribution and determinants of diseasefrequency"

(MacMahon, 1970)

“The study of the occurrence of illness"

(Cole, 1979)

3

QUANTITATIVE MEASURES OF DISEASE FREQUENCY

Basic elements of epidemiologic inference are defining, counting, and summarizingdisease outcomes

Outcomes: expressed as either categorical (eg. Disease occurrence or severity) or continuous variables

4

NOMINAL AND ORDINAL VARIABLES

• Both nominal and ordinal scale data can be summarized in frequency distributions

• Nominal scale data are usually further summarized as ratios, proportions and rates

• Ordinal scale data are usually further summarized with measures of central location and measures of dispersion

5

TYPES OF VARIABLES AND STATISTICS

Qualitative

Polychotomous(> 2 groups)

Categorical data

Variables

Quantitative

Nominal Ordinal

Dichotomous(2 groups)

Continuous dataMean

MedianModeRange

Inter-quartile rangeStandard deviation

RatioProportion

Rate

6

QUANTITATIVE MEASURES USED IN EPIDEMIOLOGY

• Measures of disease frequency reflect the relative occurrence of the disease in a population.

• Measures of association reflect the strength or magnitude of the statistical relationship between exposure status and disease occurrence.

• Measures of effect: Certain measures of association involving disease incidence are also measures of the exposure effect.

• Measures of impact* are used to predict the impact of an intervention on the disease occurrence in a population (extra number of cases attributable to, or prevented by, the exposure)

7

EPIDEMIOLOGIC APPROACH

• Case Definitions: – based on signs, symptoms

and results of tests

• Numbers and Rates

• Descriptive Epidemiology

• Analytic Epidemiology

QUANTITATIVE METHODS

• Measurement of variables

• Estimation of population parameters

• Testing of statistical hypothesis

8

EPIDEMIOLOGIC DATA• A common form of epidemiologic data is a

rectangular database.• Each row contains information about one individual--

i.e., record, observation.• Each column contains information about one

characteristic--i.e., variable.• In an outbreak investigation, we usually create a

database called a “line listing”.• In a line listing, each row represents a case. Columns

contain identifying information, clinical details, descriptive epidemiologic factors, and possible etiologic factors.

9

Neonatal listeriosis, General Hospital A, Costa Rica, 1989

Symptom Delivery AdmittingID Sex Date DOB Type Outcome Symptoms

1 F 6/2 6/2 Vaginal Lived dyspnea2 M 6/8 6/2 C-section Lived fever3 F 6/15 6/8 Vaginal Died dyspnea4 F 6/12 6/8 Vaginal Lived fever5 F 6/15 6/11 C-section Lived pneumonia6 F 6/20 6/14 C-section Lived fever7 M 6/21 6/14 Vaginal Lived fever8 F 6/18 6/15 C-section Lived fever9 M 6/20 6/15 C-section Lived pneumonia

10 M 6/19 6/16 Forceps Lived fever11 M 7/21 7/21 Vaginal Died dyspnea

Source: Schuchat 1991

An example of “line lis

ting”.

10

SUMMARIZING DIFFERENT TYPES OF VARIABLES

When categories are used, the measurement scale is called a nominal scale.

Vaccination Number

Yes 76

No 125

Total 201

When points on a numerical scale are used, the scale is called an ordinal scale.

11

FREQUENCY DISTRIBUTION

• With larger databases, we usually summarize variables into tables called “frequency distribution”.

• A frequency distribution shows the values a variable can take, and the number of people with each value.Example

12

Distribution of Students by Levels of Blood Sugar, n=100

Bl. sugar (mg%) Number Relative freq Cumulative relative freq

52-55 4 4 4

56-59 12 12 16

60-63 16 16 32

64-67 27 27 59

68-71 13 13 72

72-75 19 19 91

76-79 4 4 95

80-83 5 5 100

Total 100 100 100Example of “frequency

distribution”.

13

In what circumstance that we should measure by counting absolute number?

14

0

2

4

6

8

10

18 -

24 M

ay

25 -

31 M

ay

1 - 7

Jun

8 - 1

4 Ju

n

15 -

21 J

un

22 -

28 J

un

29 J

un -

5 Ju

l

6 - 1

2 Ju

l

13 -

19 J

ul

20 -

26 J

ul

27 J

ul -

2 Au

g

3 - 9

Aug

10 -

16 A

ug

17 -

23 A

ug

24 -

30 A

ug

31 A

ug -

6 Se

p

7 - 1

3 Se

p

14 -

20 S

ep

21 -

27 S

ep

28 S

ep -

4 O

ct

5 - 1

1 O

ct Weekly interval

NS 1NS 2

2 / 2 Kit.

Epidemic curve and spot mapof mumps cases, kindergarten “A” ,May–September 1999

(N=38)

1 child case 1 officer case

1 / 1 1 / 2 3 / 2 3 / 1

2 / 1

Laosirithaworn, 1999

Distribution

15

Example: Investigation of increasing death from unintentional fall, Thailand

• The injury surveillance (IS) data from Lampang regional hospital showed increasing number of death from unintentional fall after 1998

• FETP was notified and went to investigate• IS report and medical records were

reviewed and relatives of the deaths were interviewed

Source: Jiraporn Plaitho, 2002

16

Number of deaths from unintentional fall by year and age-group, Lampang hospital 1997-2001


Age 1997 1998 1999 2000 2001

0-14 yr 1 0 1 1 1

15-59 yr 12 7 15 12 20

>=60 yr 15 10 16 17 22

17

Population of Lumpang province 1997-2001

Age 1997 1998 1999 2000 2001

0-14 yr 161,221 162,430 159,550 158,160 153,343

15-59 yr 479,933 493,553 500,146 509,278 513,012

>=60 yr 90,002 93,184 94,983 82,914 99,441


18

Number of deaths from unintentional fall by age-group, Lampang hospital 1997-2001

0

5

10

15

20

25

1997 1998 1999 2000 2001

0-14 yrs 15-59 yrs >=60 yrs0-14yr3%

>=60yr53%

14-59yr44%

Number

N=150


19

Death rate of unintentional fall by age-group, Lumpang hospital 1997-2001

0

5

10

15

20

25

1997 1998 1999 2000 2001

0-14 yrs 15-59 yrs >=60 yrs

14-59yr44%>=60yr

53%

0-14yr3%

Rate per 100,000 pop

N=150


rate ?

20

DISEASE FREQUENCY

Disease frequency is usually measured as a proportion or rate in which:

• Numerator reflects the number of cases or events of interest

• Denominator reflects the size of a population from which those cases or events are identified

21

TYPES OF FREQUENCY MEASURES

Distinguished by type of numerator• Incidence: the numerator reflects

the number of new cases identified during a given period.

• Prevalence: the numerator reflects the number of existing casesidentified at a point in time.

22

Incidence and Prevalence

23

PREVALENCE MEASURES

Prevalence is the frequency of existing cases

24

Prevalence is calculated by:

Number of people with the disease or condition at a specific time

P =Total population at a specific time

25

1 existing case at a point in time in a population of 5 babies

1Prevalence = = 0.2 = 20%

5

• Point prevalence is:

The proportion of the population affected by a disease at a specific point in time

26

PERIOD PREVALENCE

• Period prevalence is calculated by:

Number of incident and prevalent cases identified during a given period

• P =Size of the total population

during the period

27

3 existing case during a period of time in a population of 5 babies

3Period revalence = = 0.6 = 60%

5

• Period prevalence is:

The proportion of the population affected by a disease anytime during a given period

28

INTERPRETATION OF PREVALENCE

• Because prevalence reflects both incidence rate and disease duration, it is not as useful as incidence for studying causes of disease.

• It is useful for measuring disease burden on a population, especially if those who have the disease require specific medical attention.

29

RELATIONSHIP BETWEEN PREVALENCE AND INCIDENCE

Prevalence is less useful than incidence in etiologic studies, because it is a function of incidence rate ( ) and duration of disease ( )

Assumption: prevalence, incidence rate and mortality rate remain constant over time, no in- and out-migration

( )TIP

P=

−1

TI

30

RELATIONSHIP BETWEEN PREVALENCE AND INCIDENCE

If the disease is rare,

= mean duration of diseaseAssumption: prevalence, incidence rate and

mortality rate remain constant over time, no in- and out-migration

( )TIP ≈

T

31

FACTORS INFLUENCING OBSERVED PREVALENCE

Increase/Decrease

Out-migration of cases

Longer duration of the diseaseHigh case fatality rateDecrease in incidence

In-migration of healthy people

Improved diagnostic facilitiesBetter reportingImproved cure rate

Source: WHO, 1994

32

The proportion of infants who are born alive with a defect of the ventricular septum of the

heart is a prevalence or incidence?

33

Risk and Rate

34

INCIDENCE MEASURES: RISK AND RATE

Distinguished by type of denominator• Risk (cumulative incidence, incidence

proportion): probability of the event• Incidence rate (incidence density): rate

estimate expresses the “rate” at which the events occur in the population at risk at any given point in time

35

RISK AND INCIDENCE PROPORTION

• Risk is measured on the same scale and interpreted in the same way as a probability.

• We use risk to describe the probability that a person will develop a given disease.

• Risk is used in reference to a single person• Incidence proportion is often used in

reference to a group of people• We use average taken from population to

estimate the risk experience by individuals

36

RISK ESTIMATION (SIMPLE METHOD)

• Risk (R) is:

The probability of an individual at risk developing the disease during a given period

Number of incident cases of disease occurring in a specified period

R = A/N =Number of people at risk at the start

of the specified period

• Assumption: all N people are followed for the entire time period, i.e., follow up is complete

37

When did your last health check up?

If you can choose to have either total cholesterol equal 7 or 8 mmol/l*, which level do you want?

Why?

*High total cholesterol defined as a total cholesterol level of 6.2 mmol/l or highermmol/l = mg% X 0.02586

If you interview SARS patients, will you wear full PPE (personal protection equipments),

compared to interview measlespatients? Why?

38

HYPOTHETICAL COHORT

Incidence is best understood in the context of prospective (cohort) studies

• In a typical cohort, censored observations can occur when individuals dying from other diseases or recruited later in the accrual period of the study, or migration

39

Hypothetical cohort of 10 persons followed for up to 24 months, Jan 96-Dec 98

Modified from fig. 2-1 in M. Szklo, F. Nieto. Epidemiology Beyond the Basics. Maryland: Aspen Publishers; 2000

Individuals12345678910

Jan-

96

Mar-9

6

May-

96

Jul-9

6

Sep-

96

Nov-

96

Jan-

97

Mar-9

7

May-

97

Jul-9

7

Sep-

97

Nov-

97

Jan-

98

Death

Censored observation

Follow-uptime

40

The same hypothetical cohort, started from the beginning of the study

0 4 8 12 16 20 24

12345678910

Individuals

Months of follow-up

1172092416213103

Total time under observation

Death


Follow-uptime

Modified from fig. 2-1 in M. Szklo, F. Nieto. Epidemiology Beyond the Basics. Maryland: Aspen Publishers; 2000

41

0 4 8 12 16 20 24

12345678910

Individuals

Months of follow-up

1172092416213103


Death


Follow-uptime

Death = 6

Pop. at start = 10

Risk estimated from simple method

Risk of dying = 6/10 = 0.6 in 2 years

42

INTERPRETATION OF RISK• The only way to interpret a risk is to know

the length of the time period over which the risk applies.

• This time period may be short or long, but without identifying it, risk values are not meaningful

• Over a very short time period, the risk of any particular disease is usually extremely low. What is the probability that a given person will develop a disease in the next 5 minutes?

43

ATTACK RATEAn attack rate (AR) is a risk of becoming

afflicted with a condition during an epidemic period, applied to a defined population observed for a limited time.

• Attack rate is calculated by:

Number of incident cases during an epidemic period

AR =Population at risk at the beginning

of the epidemic period

44

SECONDARY ATTACK RATE

Is the attack rate among susceptible people who come into direct contact with primary cases

• Secondary attack rate is calculated by:

Number of incident cases among contacts of primary cases during the epidemic period

=Total number of contacts

45

RATE (INCIDENCE DENSITY)

• The occurrence of new cases at a point in time t, per unit of time, relative to the size of the population at risk at time t

• Denominator for incidence rate is total person-time for the study period (the sum of person-time contributed to by each individual)

46

INCIDENCE RATE ESTIMATIONWhen data on the timing of events or losses

are available from a defined cohort• We used incidence rate to measure

disease occurrence by dividing number of cases by a measure of time

• Because the instantaneous rate for each individual cannot be directly calculated, average incidence over a period of time for a population is used

47

TIME MEASURE IN INCIDENCE RATE

• This time measure is the summation, across all individuals, of time experienced by population being followed

• This denominator should include all of the time that each person was at risk of getting the outcome

• Average incidence rate can be calculated based on individual data or aggregate FU data

48

Rate: the occurrence of an event in a population over time

Number of incident cases of disease occurring in a specified period

I =Amount of person-time experienced by

population at risk in the same period

INCIDENCE RATE ESTIMATION BASED ON INDIVIDUAL DATA

49

0 4 8 12 16 20 24

12345678910

Individuals

Months of follow-up

1172092416213103


Death


Follow-uptime

Total number of event = 6

Total amount of FU time

for all individuals is = 115

Rate = 6/115 = 0.052 per person-month

= 5.2 per 100 person-month

= 0.63 per person-year

50

INCIDENCE RATE ESTIMATION BASED ON AGGREGATE DATA

Using the estimated average population as the denominator

Number of eventRate = Average population

Typically used to estimate mortality based on vital statistics information

51

ESTIMATE AVERAGE POPULATIONAssume that the period is not long and

population and its demographic composition in the area of interest are stable

• Population at the middle of the period• Average of the population at the

beginning and at the end of the period• Subtracting one half of the events and

losses from the initial population

52

0 4 8 12 16 20 24

12345678910

Individuals

Months of follow-up

1172092416213103


Death


Follow-uptime

n = (10+1)/2 = 5.5

n = 10 - 0.5(6+3) = 5.5

Rate = 6/5.5 = 1.09 per 2 person-yearor

0.55 per person-year

53

0 4 8 12 16 20 24

12345678910

Individuals

Months of follow-up

1172092416213103


Death


Follow-uptime

Why rate from individual data = rate from aggregate data?

Rate in 1st 12 months = 3/85 = 0.035 or

0.42 per person-year

Rate in 2nd 12 months = 3/30 = 0.1 or

1.2 per person-year

54

COMPARISON OF INCIDENCE PROPORTION (RISK) AND INCIDENCE RATE

Property Risk Rate

Smallest value 0 0

Greatest value 1 Infinity

Units None 1/time

Interpretation Probability Inverse of waiting time

55

In Thailand, speed limit for 4-wheel cars on an express way is 110 km/hr

What measure?

Compute to meters per minute

The unit of time in the denominator is arbitrary and has no implication

for any period of time over which the rate is measured or applies

56

INTERPRETATION OF RATE

• Incidence rate is a measure of occurrence that takes the ratio of events to the total time in which the events occur. Unit is the reciprocal of time (time-1)

• Under steady-state conditions, a situation in which rates do not change with time, the reciprocal of the incidence rate equals the average time until an event occurs.

• An incidence rate of 3.57 cases per person-year. This value can be interpreted as an average waiting time of 0.28 years until the occurrence of the first case. (1/3.57 years = 0.28 years)

57

RELATION BETWEEN RISK AND RATE

Risk = Incidence Rate X Time

• This simplest formula is an approximation that works well as long as risk is < 20%

• Assumption: Incidence rate remains constant over the time period

58

Suppose we have a population of 1000 people who experience a mortality rate of 12 deaths per 1000 person-year for a 20-year period

At the end of 20-year period, how many deaths occur?

•The previous formula predicts that the risk of death over 20 years would be (12/1000)*20 = 0.24•This calculation neglects that size of population at risk decreases as deaths occur.

59

Year Number alive at start of year

Expected Deaths

Cumulative Deaths

1 1,000 12 122 988 12 243 976 12 364 964 12 475 953 11 596 941 11 707 930 11 818 919 11 929 908 11 103

10 897 11 11411 886 11 12412 876 11 13513 865 10 14514 855 10 15615 844 10 16616 834 10 17617 824 10 18618 814 10 19519 805 10 20520 795 10 215

Number of expected deaths over 20 years among 1000 people experiencing a mortality rate of 12 deaths per 1000 person-year

(Rothman 2002)

60

BASIC CONCEPTS OF MEASUREMENT

• Ratio: a ratio expresses the relationship between two numbers in the form x : y

• Proportion: a proportion is a fraction in which all elements of the numerator are included in the denominator

• Rate: a rate is an instantaneous change in one quantity per unit of time

61

Number of deaths in a year of children less than 1 year of age

= Number of live births in the same year

• Perinatal mortality: 28 wks gestation 1 wk of life

• Neonatal mortality: 1st month of life

• Post neonatal mortality: 1 month 1 year

INFANT MORTALITY RATIO (IMR)

62

MORTALITY MEASURES• As with incidence, the frequency of death can

be expressed as a risk (probability) in individuals or as a rate (hazard) in populations

• 3 types of mortality frequency measures:– case fatality: death from a specific disease

among cases with that disease– total mortality: all deaths in the total

population– disease-specific mortality: death from a

specific disease in the total population

63

CASE FATALITY

• Case fatality risk (CFR) is defined as:The probability of a case dying from the

disease during a given period• CFR is calculated by:

Number of deaths from a disease during a specified period after disease occurrence

CFR =Number of incident cases of the disease

during that period

64

TOTAL MORTALITY

• Total mortality risk, also called crude mortality risk (CMR), is calculated by:

Total number of deaths during a specified period

CMR =Total number of population at baseline

65

SPECIFIC MORTALITY

• Disease-specific mortality risk is calculated by:

Number of deaths from a disease during a specific period

=Total number of population at baseline

• Other specific mortality--e.g., age-specific mortality, sex-specific mortality

66

AGE SPECIFIC MORTALITY

• Age-specific mortality rate per year is calculated by:

Number of deaths among people in a specified age-group during a given year

=Average number of population in that

age-group of the same year

67

EXAMPLE

68

1234567

Individuals

Total time underobservation and in health (years)

0 1 2 3 4 5 6 7

7306173

Years of follow-up

healthy period

disease period

death

7-yr risk of disease (simple estimation) = 3/6 = 0.5 = 50%

69

1234567

Individuals


0 1 2 3 4 5 6 7

7306173

Years of follow-up

PT = 7+3+6+1+7+3 = 27 person-yearsAverage incidence rate for 7-year follow-up period =

healthy period

disease period

death

incident cases/PT = 3/27 = 0.11 / person year

70

1234567

Individuals


0 1 2 3 4 5 6 7

7306173

Years of follow-up

healthy period

disease period

death

Case fatality risk in 1 year after disease occurrence= death cases/incident cases = 1/3 = 0.33 = 33%

71

1234567

Individuals


0 1 2 3 4 5 6 7

7306173

Years of follow-up

healthy period

disease period

death

7-year total mortality risk = death cases/total pop. = 3/7 = 0.43 = 43%

72

Error! Error!

Cumulative Number of Reported Probable Cases Of SARSFrom: 1 Nov 20021 To: 2 June 2003, 18:00 GMT+2

- SARS Travel Recommendations Summary Table - 2 June

Country

Cumulativenumberof case(s)2

Number ofnew casessince lastWHOupdate2,3

Numberofdeaths

Numberrecovered4

Date lastprobablecasereported

Date for whichcumulativenumber of casesis current

Total 8384 27 770 5402

Notes:

Cumulative number of cases includes number of deaths.

As SARS is a diagnosis of exclusion, the status of a reported case may change over time. Thismeans that previously reported cases may be discarded after further investigation and follow-up.

Exercise: Compute case fatality ratio, case fatality risk, case fatality rate

73

The study of situation and mobilization of human resources for dental health, 2006

• Objective: To study mobilization of human resources for dental health

• Design: Survey by mailed questionnaires

• Source population: Registered dentists graduated in 1975, 1980, 1985, 1990

• Sampling: 50% of source population• Results: 31% responded (450/1448)

Source: Komet Wichawut, Division of Dental HealthDepartment of Health, 2006

74

Proportion of dentists employed in government workforce by work year in service, 2006

403020100

1.1

1.0

.9

.8

.7

.6

.5

1975

1980

1985

1990

Graduation Year

Work Year in Service

75All PIX from Royal Flora Expo 2006

quantitative measures in epidemiology - interfetpthailand · • both nominal and ordinal scale...

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