4.4. effect modification

4.4. effect modification

1. 2014 Page 1 68 Effect modification (Interaction) Goals of stratification of data Evaluate and reduce/remove confounding Evaluate and describe effect modification Description of effect modification A change in the magnitude of an effect measure (between exposure and disease) according to the level of some third variable What two “classes” of effect measures have we used so far in the course?

2. example Effect modification: #1 Disease incidence by exposure and age – Does the relationship between exposure and disease change over the value of the potential confounder (age)? How? 69 2014 Page 2

3. Effect modification: example #2 Disease incidence by exposure and age Does the relationship between exposure and disease change over the value of the potential confounder (age)? How? Rothman ’86 (p 178) 2014 Page 3 70

4. 2014 Page 4 contrast Effect modification: with confounding Confounding A bias that an investigator hopes to remove A nuisance that may or may not be present in a given study design Properties of a confounding variable: (Rothman, p123): a) be a risk factor for disease among the non-exposed; b) be associated with the exposure variable; and c) not be an intermediate step in the “causal pathway” 71

5. 2014 Page 5 contrast Effect modification: with confounding Effect modification A more detailed description of the “true” relationship between the exposure and the outcome Effect modification is a finding to be reported (even celebrated), not a bias to be eliminated Effect modification is a “natural phenomenon” that exists independently of the study design The presence and interpretation of effect modification depends upon the choice of effect measure (ratio vs. difference) 72

6. 2014 Page 6 73 Some lingo Covariate Confounder, potential confounder Effect modification, interaction Intermediate variable

7. 2014 Page 7 Effect modification: contrast with confounding Note that for any association under study, a given factor may be: Both a confounder and an effect modifier or A confounder but not an effect modifier or An effect modifier but not a confounder or neither 74

8. 2014 Page 8 Examples of confounding/effect modification 76 Level 1 Level 2 Crude/ collapsed/ Combined “unadjusted” Uniform estimate (OR MH ) / “adjusted” Confounding present Interaction present 4.0 4.0 4.0 4.0 NO NO 4.0 0.25 1.0 1.0 NO YES 1.0 1.0 8.4 1.0 YES NO 4.0 0.25 1.0 2.0 YES (?relevance) YES

9. 77 2014 Page 90

10. Effect modification: test of homogeneity Null hypothesis: The individual stratified estimates of the effect do not differ from some uniform estimate of effect (such as a Mantel Haenszel estimator) Notation: – N is the number of strata (N=2 in our smoking/matches example); – MH ln^R i is the natural logarithm of the estimated (hence the “^”) effect measure for each stratum (OR i in our example); – ln^R is the natural logarithm of the uniform effect estimate (e.g. OR in – X 2 (N-1) is chi-square with (N-1) degrees of freedom; our example—the computer will use the maximum likelihood estimate) One formula to test homogeneity: X 2 (N-1) = ∑ [ln(^ R i ) – ln(R MH )] 2 Var[ln(^ R i )] N i= 1 78 JC: Comment on choice of signifciance level for test of homogeneity 2014 Page 10

11. 2014 Page 11 Paradox If effect modification is present, a uniform estimator of effect (such as OR MH ) cannot (or at least should not) be reported. However, in order to determine if effect modification is present, it is necessary to calculate the value of a uniform estimator of effect (such as OR MH ) because it is needed in the calculation of the test of homogeneity. 79

12. 2014 Page 12 Effect modification: test of homogeneity (or is heterogeneity?) Comments If the test of homogeneity is “significant” (=“reject homogeneity”) this is evidence that there is heterogeneity (i.e. no homogeneity) and that effect modification may be present. (Null hypothesis: The individual stratified estimates of the effect do not differ from some uniform estimate of effect) The choice of a significance level (e.g. p < 0.05) is somewhat open to interpretation. One “conservative” approach, because of inherent limitations in the power of the test of homogeneity, is to treat the data as if interaction is present for p < 0.20). In other words, one would rather err on the side of assuming that interaction is present (and reporting the stratified estimates of effect) than on reporting a uniform estimate that may not be true across strata. 80

13. UC Berkeley 34 2014 Page 13

14. 81 2014 Page 14

15. Additive versus multiplicative scale effect modification Notation: R XZ No additive interaction if (R11 – R01) = (R10 – R00) ○ Rewrite as: (R11-R01)-(R10-R00)=0 In words: Difference in risk for (X=1 vs. X=0) when Z=1 is equal to difference in risk for (X=1 vs. X=0) when Z=0 Note: the values R11, R10, etc. are risks (not counts) 2014 Page 15

16. Additive versus multiplicative scale effect modification Notation: R XZ No multiplicative interaction if (R11/R01)=(R10/R00) Rewrite as: (R11/R01)/(R10/R00)=1 In words: Ratio of risks/rates when X=1 vs. X=0 when Z=1 is equal to ratio of risks/rates when X=1 vs. X=0 when Z=0 2014 Page 16

17. 2014 Page 17 Effect modification is scale-dependent Evidence for effect modification/statistical interaction if the RR or the AR differs between two groups However, effect modification/statistical interaction is scale-dependent If you do not have interaction on the additive scale (AR is homogenous) then you will have interaction on the multiplicative scale (RR must be heterogeneous) If you do not have interaction on the multiplicative scale (RR is homogenous) then you will have interaction on the additive scale (AR must be heterogeneous) Note: It is common to have evidence of interaction on both scales.

18. Example No additive scale interaction if (R11-R01)-(R10-R00)=0 No relative scale interaction if (R11/R01)/(R10/R00)=1 ● Additive scale: (60-20) - (50-10) = Interaction not present on the additive scale ● Relative scale: (60/20) / (50/10)=0.6 Interaction present on the relative scale Z=1 Z=0 X=1 60 50 X=0 20 10 2014 Page 18

19. Example No additive scale interaction if (R11-R01)-(R10-R00)=0 No relative scale interaction if (R11/R01)/(R10/R00)=1 ● Additive scale: (60-20) - (30-10) = 20 Interaction present on the additive scale ● Relative scale: (60/20) / (30/10)=1 Interaction not present on the relative scale Z=1 Z=0 X=1 60 30 X=0 20 10 2014 Page 100