21-bias confounding 23 associationa-yangbf 09.4.23

8/14/2019 21-Bias Confounding 23 Associationa-YangBF 09.4.23

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23. Measuring association inepidemiology

Ben-Fu YangDept. Epidemiology

School of Public HealthJining Medical College

23 April 2009


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Most popular measures of association:Most popular measures of association:

absolute risk absolute risk relative risk relative risk odds ratioodds ratioattributable risk attributable risk

population attributable risk population attributable risk number needed to treat number needed to treat


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Definitions

Association

A statistical relationship between two or moreA statistical relationship between two or morevariablesvariables

Risk

Probability conditional or unconditional of theProbability conditional or unconditional of theoccurrence of some event in timeoccurrence of some event in time

Probability of an individual developing aProbability of an individual developing adisease or change in health status over a fixeddisease or change in health status over a fixedtime interval, conditional on the individual nottime interval, conditional on the individual notdying during the same time perioddying during the same time period

Absolute risk


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A 22 table can be useful for calculating some

measures of association

Table 23.1: A 22 table for risk

Disease present?

Exposed to

risk factor?a+b+c+db+da+cTotal

c+ddcNoa+bbaYes

Total NoYes


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Absolute risk

Number of cases of disease in those exposedNumber of cases of disease in those exposed

Number of individuals exposedNumber of individuals exposed

When using a 22 table, absolute risk can beWhen using a 22 table, absolute risk can becalculated ascalculated as a/(a+b)a/(a+b) ..

Example:Example:

If 90 people were exposed to a risk factor, and 20 of If 90 people were exposed to a risk factor, and 20 of them develop a particular disease, their absolute risk isthem develop a particular disease, their absolute risk is20/90=0.22 or 22%.20/90=0.22 or 22%.


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Relative risk

Disease incidence in exposed groupDisease incidence in exposed groupRelative risk=Relative risk=

Disease incidence in non-exposed groupDisease incidence in non-exposed group

RRRR =1=1RRRR >1>1RRRR


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Relative risk Table 23.3 : A 22 table showing miscarriage in first trimester and

bacterial vaginosis status for women undergoing in-vitro fertilization

Miscarriage in first trimester (Disease)

Bacterialvaginosis

(risk factor)207(a+b+c+d

)158(b+d)49(a+c)Total

146(c+d)119(d)27(c)No

61(a+b)39(b)22(a)Yes

Total NoYes


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d cc

baa

+

+

/

/95.1

185.0

361.0

146/27

61/22==

Proportion of disease in exposed group

RR= Proportion of disease in non-exposed group

==


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Attributable risk

Attributable risk is calculated as follows: Disease incidence in exposed group disease incidence in non-exposed

group

or, using a 22 table (a/a+b)-(c/c+d).

(22/61)-(27/146)=0.361-0.185=0.176AR=

Population attributable risk


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Odds ratio (OR )

In case-control study (CCS), we cannot calculate theCI or IR, therefore, cannot calculate the RR directly

OR as a measure of association between exposure &disease is used when data are collected in case-controlstudy

OR can be obtained however, from a cohort as wellas a case-control study and can be used instead of RR.


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Odds are ratio of two probabilitiesi.e. Probability that event occurs / 1-Probability

that event does not occur Odds refer to single entityIf an event has the probability P, then the

odds of the same event are P/1-P


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Derivation of OR in Cohort studyP D+ | E+ = (exposed developed the disease) =

a/(a+b)

P D-| E+ = (exposed did not develop the disease) =b/(a+b)

Odds of developing disease among exposed = D+|E+ /1-P D-|E+ = a/(a+b) = a/b

b/(a+b)

P D+ | E- = (non-exposed developed the disease) = c/(c

+ d)

P D-| E- = (non-exposed did not develop the disease) = d/(c+ d)

Odds of develo in disease amon non-ex osed =


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OR in case-control study

In case-control study RR cannot be calculateddirectly to determine the association betweenexposure and disease.

Dont know the risk of disease among exposedand un-exposed since we start recruiting cases and

controls.Can use OR as measure of association between

exposure and disease in a case control study.


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OR in case-control Study

Probability of case being exposed = P case

Probability of case being non-exposed =1-P case

Odds of case being exposed = P case /1- P case

Probability of control being exposed = P control

Probability of control being non-exposed =1-P control

Odds of control being exposed = P control / 1-P control


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Derivation of OR in case-control Study

Probability of being exposed among cases = a /(a + c)

Probability of being non-exposed among cases) = c /(a + c)

Odds of being exposed among cases = a/c

Probability of being exposed among controls = b/(b + d)

Probability of being unexposed among controls = d/(b + d)

Odds of being exposed among controls = b/d

OR = ad/bc


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Past surgery HCV status

HCV+ HCV-Yes 59 168No 54 48

113 216

ExampleOR in case-control Study


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Odds of Past surgery among HCV +

P 1 (Surgery among HCV +) = 59/113

1-P 1 (No surgery among HCV +) =54/113

Odds of surgery among HCV+ )

= 59/54 = 1.09

Odds of Past surgery among HCV -

P 2 (Surgery among HCV -) = 168/216

1-P 2 (No surgery among HCV -) = 48/216

Odds of surgery among HCV - = 168/48 = 3.5


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When is the OR a good estimate of RR? In CCS, only OR can be calculated as measure of

associationIn Cohort study, either RR or OR is a valid measure of

association

When a RR can be calculated from case control study?

*When exposure prevalence among studied cases insimilar and nearly similar to that of disease subjects in the

population from which cases are taken.*Prevalence of exposure among studied controls is

similar to that of non-diseased population from cases weredrawn.

*Rare disease (CI < 0.1)


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Causality

1 Dose-response is there an association between the

incidence of disease and the amount of exposure to the risk

factor?

2 Stength are subjects who have been exposed to the risk

factor much more likely to develop the disease than unexposed

subjects?

3 Disease specificity does the risk factor apply only to thedisease being studied?

4 Time relationship did exposure to the risk factor occur

before the disease developed?


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5 Biological plausibility is what we know about the

relationship between the risk factor and disease

consistent with what is already known about their

biology?

6 Consistency have other investigators working with

other populations at other times observed similar results?

7 Experimental evidence do randomized controlled

trials show that an intervention can cause outcomes

such as increased survival or decreased disease?

Causality (cont.)


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21. Bias and Confounding


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Types of Error

Random error Random error Systematic error:Systematic error:Selection biasSelection biasInformation biasInformation bias


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0

2

4

6

810

12

14

0 5 10 15 20 25 30 35

Size of induration, mm

Random Error Per Cent


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0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Size of induration, mm

Systematic Error Per Cent


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Sources of Selection Bias

Inappropriate population studiedInappropriate population studiedInadequate participationInadequate participationChange of classification of theChange of classification of thedeterminantdeterminantSelection of most accessible or of Selection of most accessible or of volunteersvolunteers


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Inadequate Participation

We want to study the association of We want to study the association of stigma with diagnosis of TBstigma with diagnosis of TB

We select a sample of the populationWe select a sample of the population20% of the sample agree to participate20% of the sample agree to participateWe find that there is no association of We find that there is no association of stigma with TBstigma with TBIs this true?Is this true?


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Inappropriate Population

We wish to measure the impact of HIV onWe wish to measure the impact of HIV ontuberculosistuberculosis

We study the trend of tuberculosis inWe study the trend of tuberculosis inEgypt from 1997 to 2001Egypt from 1997 to 2001We find no change in notification rateWe find no change in notification rate

We conclude that HIV has no impact onWe conclude that HIV has no impact onTBTBWere we right?Were we right?


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Classification of Determinant

We want to study the impact of poverty on theWe want to study the impact of poverty on thetrend of tuberculosistrend of tuberculosisWe select a poor district and a rich district andWe select a poor district and a rich district andcompare the notification of TB from 1991 tocompare the notification of TB from 1991 to20002000In the meantime, there is an urban renewalIn the meantime, there is an urban renewal

project in the poor districtproject in the poor districtWe find no difference between the districtsWe find no difference between the districtsCan we conclude that poverty is not related toCan we conclude that poverty is not related toTB?TB?


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Participation of Volunteers

We want to determine the prevalence of We want to determine the prevalence of HIV infectionHIV infection

We ask for volunteers for testingWe ask for volunteers for testingWe find no HIVWe find no HIVIs it correct to conclude that there is noIs it correct to conclude that there is noHIV?HIV?


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Minimizing Selection BiasStudy Design

Appropriate population selectionAppropriate population selectionHigh participation rateHigh participation rateDemonstration of lack of differenceDemonstration of lack of differencebetween participants and non participantsbetween participants and non participants


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Minimizing Selection Bias Analysis

Exclude from numerator and denominator Exclude from numerator and denominator Analyze by time at riskAnalyze by time at riskWorst and best case scenariosWorst and best case scenarios


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Source of Information Bias

Subject variationSubject variationObserver variationObserver variationDeficiency of toolsDeficiency of toolsTechnical errors in measurementTechnical errors in measurement


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Subject Variation

We want to determine the association of We want to determine the association of knowledge about TB and notification of TBknowledge about TB and notification of TBWe interview TB patients in a public clinic andWe interview TB patients in a public clinic andthose in a private practicethose in a private practiceThe public clinic has a program of healthThe public clinic has a program of healtheducationeducation

We find that those who know about TB areWe find that those who know about TB arenotified and those who do not are notnotified and those who do not are notIs it correct that there is an association betweenIs it correct that there is an association betweenknowledge about and notification of TB?knowledge about and notification of TB?


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Observer Variation

We carry out a case control study of We carry out a case control study of poverty and tuberculosispoverty and tuberculosis

We accept any case diagnosed by aWe accept any case diagnosed by adoctor doctor The doctor knows that poor people areThe doctor knows that poor people are

more likely to have TBmore likely to have TBCan this knowledge bias the result?Can this knowledge bias the result?


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Technical Errors

We want to test a new antigen for theWe want to test a new antigen for thediagnosis of tuberculosisdiagnosis of tuberculosis

We select a case control studyWe select a case control studyBy chance, the batch of the antigen we useBy chance, the batch of the antigen we usefor the cases has been left unrefrigeratedfor the cases has been left unrefrigerated

We find no difference in response to theWe find no difference in response to theantigen between cases and controlsantigen between cases and controls


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Minimizing Information Bias

Specify criteria in advanceSpecify criteria in advanceAnalyze directly according to criteriaAnalyze directly according to criteriaReduce numbers of observersReduce numbers of observersMonitor performance of observersMonitor performance of observersUse standardized tools for measurementUse standardized tools for measurement


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Confounding A Special Type of Bias

A factor associated with both the outcomeA factor associated with both the outcomeand a determinant (an etiological factor)and a determinant (an etiological factor)

Therefore associated with outcomeTherefore associated with outcomethrough its association with thethrough its association with thedeterminant (etiological factor)determinant (etiological factor)


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ConfoundingKnowledge about and Notification of TB

Recall the study of knowledge of andRecall the study of knowledge of andnotification of TBnotification of TB

TB patients are educated about TB in theTB patients are educated about TB in thepublic sector but not in the privatepublic sector but not in the privateEducated TB patients are notified andEducated TB patients are notified andthose not educated are notthose not educated are notThe real reason for notification is the typeThe real reason for notification is the typeof practice and not the knowledge of TBof practice and not the knowledge of TB


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Confounding

Determinant

(Type of Practice)

Outcome

(Notification)

Confounder (Knowledge)


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Confounding Age and tuberculosis

We find a higher proportion of reported TBWe find a higher proportion of reported TBcases in rich countries are older mencases in rich countries are older men

We conclude that advancing age is a riskWe conclude that advancing age is a riskfactor for tuberculosisfactor for tuberculosisIs this correct?Is this correct?


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Tuberculosis Notification RateNorway, by Age

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70

Per 100 000Per 100 000

Age, yearsAge, years

1927 1927

1947 1947

19801980

Nor Fore Lunge 1986;30 Nor Fore Lunge 1986;30


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Impact of Error or Bias

Random error will obscure a realRandom error will obscure a realdifferencedifference

Random error will require a larger sampleRandom error will require a larger samplesizesizeBias will result in false differenceBias will result in false difference

It cannot be overcome by statistics if It cannot be overcome by statistics if presentpresent

21-bias confounding 23 associationa-yangbf 09.4.23

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