1. Amsterdam Rehabilitation Research Center | Reade Multiple regression analysis Analysis of confounding and effectmodification Martin van de Esch, PhD

2. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Content Checking assumptions (confounding and effect modification)

4. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 5 Confounding determinant (exposure) confounder outcome Association (causal, marker), also in non-exposed Association of our interest

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

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

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

10. Amsterdam Rehabilitation Research Center | Reade Table 2. Results of the regression of functional ability (walking-time, GUG-time‡ and WOMAC-PF) on muscle strength and joint proprioception. Walking- timeGUGWOMAC-PF Variables**b* (SE) † p- value b* (SE) † p- value b* (SE) † p- value Intercept91.7311.9129.19 Muscle strength-68.13 (8.90).000-13.99 (1.70).000-18.23 (4.37).000 Proprioception-1.56 (1.27).225-0.513 (0.24).0390.01 (0.62).987 Muscle strength * Proprioception - 11.61(3.10 ).000-3.05 (0.59).000-0.94 (1.51).534 R 2 =0.54 F=23.23 p<.001 R 2 =0.57 F=25.76 p<.001 R 2 =0.30 F=8.81 p<.001 b = unstandardized regression coefficient ** Variables centered around the mean † SE = Standard Error of the Estimate ‡ GUG = Get Up and Go test

11. Amsterdam Rehabilitation Research Center | Reade Biomechanical model of activity limitations Dekker et al 2013

12. Amsterdam Rehabilitation Research Center | Reade Effectmodification and confounding with a crosstab

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

14. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Example: effectmodification (interaction) How to test? Stratification on variable smoking

16. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Condition for confounding Smoking is associated with alcohol Smoking is associated with MI OR for stata of the suspected confounder

19. Amsterdam Rehabilitation Research Center | Reade How do we calculate the pooled association? According to the Mantel-Haenszel method: Notation:

20. Amsterdam Rehabilitation Research Center | Reade Mantel-Haenszel OR

21. Amsterdam Rehabilitation Research Center | Reade Example confounding In our example: ORMI =0.97

22. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade summary effectmodification and confounding Compare crude assocoation with corrected association When these is a difference (>10%): confounding is assumed!

26. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Example 2 Question: is gender a confounder?

29. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Stratified analyses Confounding and modification can be studied by splitting the data into strata: stratified analyses

31. Amsterdam Rehabilitation Research Center | Reade General procedure 1. Calculation of "crude" association and ratio’s (OR/RR/RV) 2. Stratify always for one variable and calculate the specific measure 3. Compare the measure of each stratum with each other: Strong differences – moderation No differences – no moderation

32. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade "Beyond stratified analysis” In case of more then one potential confounder or interactor; what to do? Multipele regression analysis

34. Amsterdam Rehabilitation Research Center | Reade Confounding in (logistic) regression analysis

35. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Effectmodification in case of logistic regression- analysis Interact= group x age Group is dichotomized or ordinal

37. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Confounding in regression analysis Present the model without and with confounders

39. Amsterdam Rehabilitation Research Center | Reade 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. Amsterdam Rehabilitation Research Center | Reade Example: confounding by linear regression analysis

41. Amsterdam Rehabilitation Research Center | Reade Effecmodification by linear regression analysis: example

42. Amsterdam Rehabilitation Research Center | Reade Questions? 41