Multiple regression analysis Analysis of confounding and effectmodification

1. Multiple regression analysisAnalysis of confounding and effectmodification • Martin van de Esch, PhD

2. Literature • Fletcher & Fletcher (2005) Ch. 1, 2 • Guyatt et al (2008) Ch. A5, B9.1 • Andy Field Ch. 5 (143-217) • http://www.youtube.com/watch?v=TwwyyA3wIdw

3. Content • Checking assumptions (confounding and effect modification)

4. Definitions • Bias: A systematic error in the design, recruitment, data collection or analysis that results in a mistaken estimation of the true effect of the exposure and the outcome • Confounding: A situation in which the effect or association between an exposure and outcome is distorted by the presence of another variable. Positive confounding (when the observed association is biased away from the null) and negative confounding (when the observed association is biased toward the null) both occur • Effect modification : a variable that differentially (positively and negatively) modifies the observed effect of a risk factor on disease status.  Different groups have different risk estimates when effect modification is present

5. Introduction • “Error” in research: • Effectmodification (interaction) • The combined effect of two or more independent variables on an outcome variable • Confounding • Influence on the association between determinant and outcome variable by an independant variable related to the determinant and the outcome variable

6. Confounding confounder Association (causal, marker), also in non-exposed Association determinant (exposure) outcome Association of our interest

7. Effect modification Effect modifier Association (causal, marker), also in non-exposed Association 1 2 3 determinant (exposure) outcome Association of our interest 6

8. Three conditions for being a confounder of the association between determinant and outcome variable Smoking (confounder, independent factor) Positive association 1 Appearens of larynx cancer  2 together 3 Alcohol intake(determinant, expositionfactor) Positive association 1 = independent determinant 2 = association present 3 = no causal relationship

9. walktime 100m (s) Proprioception O poor ▲ accurate Muscle strength (Nm/kg) Muscle strengh, activity limitation and proprioception 8

10. b = unstandardized regression coefficient • ** Variables centered around the mean † SE = Standard Error of the Estimate ‡ GUG = Get Up and Go test

11. Biomechanical model of activity limitations Dekker et al 2013

12. Effectmodification and confounding with a crosstab

13. Example • Case-control study: assocation between alcohol-use and myocard infarction • OR = (71  48) / (52  29) = 2.26 (=‘ruwe OR’)

14. 95% CI of crude OR • 95%-CI of OR: • EXP(LN(2.26) ± 1.96 (1/71+1/52+1/29+1/48)) indicating 1.3 tot 4.1 • Question: Is smoking an effectmodificator of the association between alcohol intake and MI? • Is the association between alcohol intake and MI different between smokers and non-smokers?

15. Example: effectmodification (interaction) • How to test? • Stratification on variable smoking

16. Example: effectmodification • OR non-smoker = (8  44) / (17  22) = 0.94 • 95% CI = (0.4 - 2.5) • OR smoker = (63  4) / (35  7) = 1.03 • 95 % CI = (0.3 - 3.8)

17. Confounding • Question: Is smoking a confounder of the association between alcohol-intake and MI? • Is the effect of alcohol on MI (partly) caused (explained) by smoking? • How to test • Comparison between the crude association with the corrected (pooled) association

18. Condition for confounding • Smoking is associated with alcohol • Smoking is associated with MI • OR for stata of the suspected confounder

19. How do we calculate the pooled association? • According to the Mantel-Haenszel method: • Notation:

20. Mantel-Haenszel OR

21. Example confounding • In our example: • ORMI = 0.97

22. Example confounding • Summary • ORcrude = 2.26 • ORpooled = 0.97 • Confounding, beacuse ORcrude  ORpooled • We present the pooled OR • Almost 100(1-a)%-CI for ORMI (don’t remember the formula). In the example: • ORMI = 0.97 (0.4 - 2.1)

23. Summary effectmodification and confounding • Effectmodification (interaction) • The combined effect of two or more independent predictor variables on an outcome variable. • Confounding • Influence on the association between determinant and outcome variable by an independant variable related to the determinant and the outcome variable • Conclusion: there is no average association, crude association is not present for an individual subject within the study population. • In publication: present two associations (one OR for smokers and one OR for non-smokers)

24. Summary effectmodification and confounding • Confounding: The association between determinant and outcome is influenced, moderated by a third variable • Confounder is related to determinant and outcome.

25. summary effectmodification and confounding • Compare crude assocoation with corrected association • When these is a difference (>10%): confounding is assumed!

26. Example 2 • Question: Is gender an interactor (moderator) of the association between alcohol inake and MI? • Is there a difference between male and female in the assocation between alcohol intake and MI?

27. Example 2 • OR male = (38  43) / (34  20) = 2.40 95 % BI: (1.2 - 4.9) • OR female = (33  5) / (18  9) = 1.02 • 95% BI: (0.3 - 3.5) • Modification because OR1  OR2 • Presentation of stratum specific OR's: • “The" OR does not exist

28. Example 2 • Question: is gender a confounder?

29. Summary examples • Smoking is a confounder which can be corrected by stratified analyses • Gender is an effect modificator (moderator): modification will be studied and the influence of the interactor will be presented in each stratum

30. Stratified analyses • Confounding and modification can be studied by splitting the data into strata: stratified analyses

31. General procedure • Calculation of "crude" association and ratio’s (OR/RR/RV) • Stratify always for one variable and calculate the specific measure • Compare the measure of each stratum with each other: • Strong differences – moderation • No differences – no moderation

32. 4. calculate the total/ composite measure • compare crude and composite measures • - When "crude" measure  composite measure: no confounding • Present "crude" measure and CI • - When "crude" measure  composite measure: Confounding and present the composite measure + CI

33. "Beyond stratified analysis” • In case of more then one potential confounder or interactor; what to do? • Multipele regression analysis

34. Confounding in (logistic) regression analysis

35. Confounding in case of (logistic) regression analysis • In regression analyses more than one confounder is possible: how to act? • Step wise or other ways of input in the regression model: depending on type of analysis (association or prediction) • Type of analysis is based on the hypothesis

36. Effectmodification in case of logistic regression-analysis Interact= group x age Group is dichotomized or ordinal

37. Confounding in regression analysis • Confounding: adding a variable to the regression model – does B coefficient change with > 10%? • Statistical approach • confoundes are known from literature, from correlation analses or confounder analyses

38. Confounding in regression analysis • Present the model without and with confounders

39. Effectmodification and regression-analysis • Effect modification: adding the interaction variable to the regression model • Is the addition of the interaction significant? • In the presence of a significant interaction: present crude model and model with interaction. Explain what the interaction means (use graphs)

40. Example: confounding by linear regression analysis

41. Effecmodification by linear regression analysis: example

42. Questions?