21-bias Confounding 23 Associationa-yangbf 09.4.23

23. Measuring association in epidemiology Ben-Fu Yang Dept. Epidemiology School of Public Health Jining Medical College 23 April 2009

Most popular measures of association: absolute risk  relative risk  odds ratio  attributable risk  population attributable risk  number needed to treat 

Definitions Association 

A statistical relationship between two or more variables

Risk 

Probability conditional or unconditional of the occurrence of some event in time



Probability of an individual developing a disease or change in health status over a fixed time interval, conditional on the individual not dying during the same time period

Absolute risk

A 2×2 table can be useful for calculating some measures of association Table 23.1: A 2×2 table for risk

Disease present? Exposed to Yes No risk factor? Total

Yes a c a+c

No b d b+d

Total a+b c+d a+b+c+d

Absolute risk Number of cases of disease in those exposed Number of individuals exposed When using a 2×2 table, absolute risk can be calculated as a/(a+b). Example: If 90 people were exposed to a risk factor, and 20 of them develop a particular disease, their absolute risk is 20/90=0.22 or 22%.

Relative risk Disease incidence in exposed group Relative risk= Disease incidence in non-exposed group

RR=1 RR>1 RR<1

Relative risk Table 23.3: A 2×2 table showing miscarriage in first trimester and bacterial vaginosis status for women undergoing in-vitro fertilization

Miscarriage in first trimester (Disease) Yes No Total Bacterial vaginosis (risk factor)

Yes

22(a)

39(b)

61(a+b)

No

27(c)

119(d)

146(c+d)

Total

49(a+c)

158(b+d)

207(a+b+c+d )

Proportion of disease in exposed group RR= Proportion of disease in non-exposed group

a/a+b 22 / 61 0.361 = = 1.95 = = c/c+d 27 / 146 0.185

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

disease incidence in non-exposed

or, using a 2×2 table (a/a+b)-(c/c+d).

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

Population attributable risk

Odds ratio (OR) In case-control study (CCS), we cannot calculate the CI 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-control study 

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



Odds are ratio of two probabilities i.e. Probability that event occurs / 1-Probability that event does not occur

 

Odds refer to single entity If an event has the probability P, then the odds of the same event are P/1-P

Derivation of OR in Cohort study P 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 = = a/(a+b) = a/b D+|E+/1-P D-|E+ b/(a+b) P D+|E- = (non-exposed developed the disease) + d)

= c/(c

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

OR in case-control study  In case-control study RR cannot be calculated

directly to determine the association between exposure and disease.  Don’t know the risk of disease among exposed and 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.

OR in case-control Study Probability of case being exposed = Pcase Probability of case being non-exposed =1-Pcase Odds of case being exposed = Pcase/1- Pcase Probability of control being exposed = Pcontrol Probability of control being non-exposed =1-Pcontrol Odds of control being exposed = Pcontrol/ 1-Pcontrol

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

Example OR in case-control Study Past surgery Yes No 

HCV status HCV+ HCV59 168 54 48 113 216

Odds of Past surgery among HCV+ P1 (Surgery among HCV+)

= 59/113

1-P1 (No surgery among HCV+) Odds of surgery among HCV+

)

=54/113 = 59/54 = 1.09

Odds of Past surgery among HCVP2 (Surgery among HCV-)

= 168/216

1-P2 (No surgery among HCV-) = 48/216 Odds of surgery among HCV-

= 168/48 = 3.5

When is the OR a good estimate of RR? In CCS, only OR can be calculated as measure of association  In 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 in similar 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 were drawn. *Rare disease (CI < 0.1)

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 the disease being studied? 4 Time relationship – did exposure to the risk factor occur before the disease developed?

Causality

(cont.)

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?

21. Bias and Confounding

Types of Error Random error  Systematic error:  Selection bias  Information bias 

Random Error Per Cent 14 12 10 8 6 4 2 0 0

5

10

15

20

25

30

Size of induration, mm

35

Systematic Error Per Cent 14 12 10 8 6 4 2 0 0

5

10

15

20

Size of induration, mm

25

30

Sources of Selection Bias   



Inappropriate population studied Inadequate participation Change of classification of the determinant Selection of most ‘accessible’ or of volunteers

Inadequate Participation 

  



We want to study the association of stigma with diagnosis of TB We select a sample of the population 20% of the sample agree to participate We find that there is no association of stigma with TB Is this true?

Inappropriate Population     

We wish to measure the impact of HIV on tuberculosis We study the trend of tuberculosis in Egypt from 1997 to 2001 We find no change in notification rate We conclude that HIV has no impact on TB Were we right?

Classification of Determinant  

  

We want to study the impact of poverty on the trend of tuberculosis We select a poor district and a rich district and compare the notification of TB from 1991 to 2000 In the meantime, there is an ‘urban renewal’ project in the poor district We find no difference between the districts Can we conclude that poverty is not related to TB?

Participation of Volunteers 

  

We want to determine the prevalence of HIV infection We ask for volunteers for testing We find no HIV Is it correct to conclude that there is no HIV?

Minimizing Selection Bias Study Design   

Appropriate population selection High participation rate Demonstration of lack of difference between participants and non participants

Minimizing Selection Bias Analysis   

Exclude from numerator and denominator Analyze by ‘time at risk’ ‘Worst’ and ‘best’ case scenarios

Source of Information Bias    

Subject variation Observer variation Deficiency of tools Technical errors in measurement

Subject Variation     

We want to determine the association of knowledge about TB and notification of TB We interview TB patients in a public clinic and those in a private practice The public clinic has a program of health education We find that those who know about TB are notified and those who do not are not Is it correct that there is an association between knowledge about and notification of TB?

Observer Variation 







We carry out a case control study of poverty and tuberculosis We accept any ‘case’ diagnosed by a doctor The doctor knows that poor people are more likely to have TB Can this knowledge ‘bias’ the result?

Technical Errors 

 



We want to test a new antigen for the diagnosis of tuberculosis We select a case control study By chance, the batch of the antigen we use for the cases has been left unrefrigerated We find no difference in response to the antigen between cases and controls

Minimizing Information Bias     

Specify criteria in advance Analyze directly according to criteria Reduce numbers of observers Monitor performance of observers Use standardized tools for measurement

Confounding A Special Type of Bias 



A factor associated with both the outcome and a determinant (an etiological factor) Therefore associated with outcome through its association with the determinant (etiological factor)

Confounding Knowledge about and Notification of TB    

Recall the study of knowledge of and notification of TB TB patients are educated about TB in the public sector but not in the private Educated TB patients are notified and those not educated are not The ‘real’ reason for notification is the type of practice and not the knowledge of TB

Confounding Confounder (Knowledge)

Determinant (Type of Practice)

Outcome (Notification)

Confounding Age and tuberculosis 





We find a higher proportion of reported TB cases in rich countries are older men We conclude that advancing age is a risk factor for tuberculosis Is this correct?

Tuberculosis Notification Rate Norway, by Age Per 100 000

700 600

1927

500 400

1947

300 200 100

1980

0 0

10

20

30

40

Age, years Nor Fore Lunge 1986;30

50

60

70

Impact of Error or Bias 



 

Random error will obscure a real difference Random error will require a larger sample size Bias will result in false difference It cannot be overcome by ‘statistics’ if present