Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

1. EPI 5240:Introduction to EpidemiologyConfounding: concepts and general approachesNovember 9, 2009 Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

2. Earlier session introduced confounding • THERE MUST BE THREE VARIABLES!!! • ‘Usual approach’ is based on ‘causation triad’ • Related to exposure • Related to outcome • Not part of the causal pathway • These criteria aren’t ‘quite’ right • No-one actually uses this approach in real research • We will introduce new ideas and expand on the triad.

3. Confounding (1) Dementia Yes No Total Yes 400 600 1,000 No 100 900 1,000 500 1,000 1,000 CRUDE table Diabetes Risk in exposed: = 400/1000 = 0.4 Risk in Non-exposed = 100/1000 = 0.1 Risk ratio (RR) = 0.4/0.1 = 4.0

4. Confounding (2) 45-79 80-99 Dementia Yes No Total Yes 379 521 900 No 21 79 100 400 600 1,000 Dementia Yes No Total Yes 21 79 100 No 79 821 900 100 900 1,000 Risk in exposed: = 21/100 = 0.21 Risk in Non-exposed = 79/900 = 0.088 Risk ratio (RR) = 0.21/0.088 = 2.39 Risk in exposed: = 379/900 = 0.42 Risk in Non-exposed = 21/100 = 0.21 Risk ratio (RR) = 0.42/0.21 = 2.01 Best ‘guess’ of RR would be about 2.2, not 4.0!!

5. Confounding (3) • Previous example is confounding • The estimate of the effect of an exposure is distorted or confounded by a third factor. • We’ll come to ‘why’ in a minute. • Tables in previous slide are called stratified tables (here, age stratified). • Let’s consider a new situation based on the same crude table.

6. Confounding (4) 45-79 80-99 Dementia Yes No Total Yes 395 505 900 No 5 95 100 400 600 1,000 Dementia Yes No Total Yes 5 95 100 No 95 805 900 100 900 1,000 Risk in exposed: = 5/100 = 0.05 Risk in Non-exposed = 95/900 = 0.106 Risk ratio (RR) = 0.05/0.106 = 0.47 Risk in exposed: = 395/900 = 0.44 Risk in Non-exposed = 5/100 = 0.05 Risk ratio (RR) = 0.44/0.05 = 8.78 What is best ‘guess’ of RR? It depends on age. There is no single answer!

7. Confounding (5) • Previous example is effect modification • The effect of an exposure on an outcome depends on the level of a third variable • In this example: • For people under age 79, it looks like diabetes protects against dementia • For people over age 80, it looks like diabetes increases the risk of getting dementia, • No single number or statement is an appropriate summary when this pattern occurs. • Links statistically to interactions. • Gene-environment interactions are a ‘hot’ topic of study.

8. Confounding (5A) • We’re not going to talk more about effect modification today.

9. Confounding (6) • Why was there confounding? • Numerical/mathematical answer can be given but let’s talk more conceptually. • Does heavy alcohol drinking cause mouth cancer? • A case-control study was done which found an OR of 3.2 (95% CI: 2.1 to 4.9). • Does this prove the case? • Consider the following situations.

10. Confounding (7) Alcohol mouth cancer • This is what we are trying to prove. • But, we know that smoking can cause mouth cancer. • And, people who drink heavily tend, in general, to be heavy smokers. • So, we might have:

11. Confounding (8) Alcohol mouth cancer Smoking ??? • The association between alcohol and mouth cancer is explained away by the link to smoking. • Adjusted OR is 1.1 (95% CI: 0.6 to 2.0).

12. Confounding (9) • Confounding requires three or more variables. • Two variables, each with multiple levels, cannot produce confounding. • Three requirements for confounding • Confounder relates to outcome • Confounder relates to exposure • Confounder is not part of causal pathway between exposure and outcome

13. Confounding (9A) • Requirements aren’t this simple • For case-control study, you need: • Confounder is related to exposure in the control group (OR≠1.) • Confounder is related to the outcome in the unexposed group (OR≠1.)

14. Confounding (10) • In our initial dementia example, we have: • OR relating age and dementia in people without diabetes = 2.8 • OR relating age and diabetes in people without dementia = 68.5 • There is no suggestion that diabetes causes dementia because people are getting older.

15. Confounding (11) • In ‘real’ research, these three ‘rules’ are not applied to identify confounding. • Inefficient and prone to false negatives • Instead, we compute an adjusted RR or OR and compare this to the crude RR or OR [Change of Estimate method]. • If these differ enough to ‘matter’, then we say there is confounding. • Usual guideline is a 10% change.

16. Confounding (12) Dementia Yes No Total Yes 400 600 1,000 No 100 900 1,000 500 1,000 1,000 CRUDE table Diabetes Risk in exposed: = 400/1000 = 0.4 Risk in Non-exposed = 100/1000 = 0.1 Risk ratio (RR) = 0.4/0.1 = 4.0

17. Confounding (13) 45-79 80-99 Dementia Yes No Total Yes 379 521 900 No 21 79 100 400 600 1,000 Dementia Yes No Total Yes 21 79 100 No 79 821 900 100 900 1,000 Risk in exposed: = 21/100 = 0.21 Risk in Non-exposed = 79/900 = 0.088 Risk ratio (RR) = 0.21/0.088 = 2.39 Risk in exposed: = 379/900 = 0.42 Risk in Non-exposed = 21/100 = 0.21 Risk ratio (RR) = 0.42/0.21 = 2.01 How to ‘adjust’ the OR?

18. Confounding (14) • How to adjust? • Topic for later class • Basic idea is that a good ‘guess’ is in the middle between the two strata-specific OR’s • Take an average BUT weight the average in some way • USE board to explain weighted average.

19. Confounding (15) • Confounding can be complex and controversial • Presence of confounding can depend on analysis scale • Multiplicative vs. additive • Works best for simple situations (e.g. only three variables) • The basic idea is to look for the independent effect of each variable • BUT, suppose the etiology is more complex?

20. Web of Causation sample

21. Confounding (16) How do we deal with confounding? Prevention You need to ‘break’ one of the links between the confounder and the exposure or outcome ‘Treatment’ (analysis) Stratified analysis (like my simple example) Standardization (we’ll discuss this later) Regression modeling methods (covered in a different course ) 13/7/2008 21

22. Confounding (17) Prevention Randomization One of the big advantages of an RCT Restriction Limits the subject to one level of confounder (e.g. study effect of alcohol on mouth cancer ONLY in non-smokers) Matching Ensures that the distribution of the exposure is the same for all levels of confounder 13/7/2008 22

23. Confounding (18) Randomization Exposure <=> treatment Subjects randomly assigned to each treatment without regard to other factors. On average, distribution of other factors will be the same in each treatment group Implies no confounder/exposure correlation  no confounding. Issues Small sample sizes Chance imbalances Infeasible in many situations Stratified allocation 13/7/2008 23

24. Confounding (19) Restriction Limit the study to people who have the same level of a potential confounder. Study alcohol and mouth cancer only in non-smokers. Lack of variability in confounder means it can not ‘confound’ There is only one 2X2 table in the stratified analysis Relatively cheap 13/7/2008 24

25. Confounding (20) Restriction (cont) ISSUES Limits generalizibility Cannot study effect of confounder on risk Limited value with multiple potential confounders Continuous variables? Can only study risk in one level of confounder exposure X confounder interactions can’t be studied Impact on sample size and feasibility Alternative: do a regular study with stratified analysis Report separate analyses in each stratum 13/7/2008 25

26. Confounding (21) Matching The process of making a study group and a comparison group comparable with respect to some extraneous factor. Breaks the confounder/exposure link Most often used in case-control studies. Usually can’t match on more than 3-4 factors in one study Minimum # of matching groups: 2x2x2x2 = 16 We’ll talk more about matching on Nov. 30 KEY POINT: in a case control study, matching does not ‘fix’ confounding – you still have to use stratified analyses. 13/7/2008 26

27. Matching (1) Example study (case-control) Identify 200 cases of mouth cancer from a local hospital. As each new case is found, do a preliminary interview to determine their smoking status. Identify a non-case who has the same smoking status as the case If there are 150 cases who smoke, there will also be 150 controls who smoke. 27

28. Matching (1a) OR = Implies no smoking/outcome link and no confounding Outcome status Case Control +ve 150 150 -ve 50 50 Smoking 28

29. Matching (2) Two main types of matching Individual (pair) Matches subjects as individuals Twins Right/left eye Frequency Ensures that the distribution of the matching variable in cases and controls is similar but does not match individual people. 29

30. Matching (3) Matching by itself does not fully eliminate confounding in a case-control study! You must use analytic methods as well Matched OR Stratified analyses Logistic regression models In a cohort study, you don’t have to use these methods although they can help. But, matching in cohort studies is uncommon 30

31. Matching (4) Advantages Strengthens statistical analysis, especially when the number of cases is small. Increases study credibility for ‘naive’ readers. Useful when confounder is a complex, nominal variable (e.g. occupation). Standard statistical methods can be problematic, especially if many levels have very few subjects. 31

32. Matching (5) Disadvantages You can not study the relationship of matched variable to outcome. Can be costly and time consuming to find matches, especially if you have many matching factors. Often, some important predictors can not be matched since you have no information on their level in potential controls before doing interview/lab tests Genotype Depression/stress If matching factor is not a confounder, can reduce precision and power. 32

33. Confounding (22) Analysis options Stratified analysis Divide study into strata based on levels of potential confounding variable(s). Do analysis within each strata to give strata-specific OR or RR. If the strata-specific values are ‘close’, produce an adjusted estimate as some type of average of the strata-specific values. Many methods of adjustment of available. Mantel-Haenzel is most commonly used. 33

34. Confounding (23) Stratified analysis (cont) Strata specific OR’s are: 2.3, 2.6, 3.4 A ‘credible’ adjusted estimate should be between 2.3 and 3.4. Simple average is: 2.8 Ignores the number of subjects in the strata. If one group has very few subjects, its OR should contribute less information Weight by # of subjects in each group, e.g.: Mantel-Haenzel does the same thing with different weights 34

35. Confounding (24) Stratified analysis (cont) This approach limits the number of variables which can be controlled or adjusted. Also hard to apply it to continuous confounders But, gives information about strata-specific effects and can help identify effect modification. Used to be very common. Now, no longer widely used in research with case-control studies. Stratified analysis methods can be applied to cohort studies with person-time. 35

36. Confounding (25) Analysis options Regression modeling The most common approach to confounding Can control multiple factors (often 10-20 or more) Can control for continuous variables Logistic regression is most popular method for case-control studies Discussed in last class Cox models (proportional hazard models) are often used in cohort studies. 36

37. Summary: Confounding • Confounding occurs when a third factor explains away an apparent association • This is a major problem with epidemiological research • If you measure a confounder, you can adjust for it in the analysis • Many potential confounders are not measured in study and so can not be controlled [Unmeasured confounders]