Lecture 6: Introduction to effect modification (part 2) Jeffrey E. Korte, PhD BMTRY 747: Foundations of Epidemiology II Department of Public Health Sciences Medical University of South Carolina Spring 2015

Interaction (additive model) D=absolute risk of disease No interaction Interaction

Interaction (multiplicative model) D=absolute risk of disease No interaction Interaction

Interaction (multiplicative model) D=absolute risk of disease 140 120 100 80 60 40 20 1000 100 10 D M=1 M=0 E No interaction (showing linear y-axis) No interaction (showing log y-axis)

Which scale to use? Choice of additive versus multiplicative models is somewhat arbitrary, depending on Analytic strategy Coding of important variables (e.g. continuous versus categorical outcome) Predictive fit of different candidate models One key is to understand and interpret any interactions in different analyses

Which scale to use? Multiplicative scale is the default This is mostly an artifact of the popularity of: Mantel-Haenszel methods Logistic regression Proportional hazards regression etc.

Which scale to use? However: additive interaction may be most useful when considering public health impact of prevention Additive interaction can be assessed even when using multiplicative models Positive additive interaction can occur even in the presence of negative multiplicative interaction (see example next slide)

Positive additive, negative multiplicative (may be important to check both scales to aid interpretation) Family history Smoking Incidence/100 Attributable risk/100 (exposed) Relative risk Absent No 10.0 Reference 1.0 Yes 40.0 30.0 4.0 Present 100.0 60.0 2.5

Additive interaction may be important (even when there is no multiplicative interaction) Family history Smoking Incidence/100 Attributable risk/100 (exposed) Relative risk Absent No 5.0 Reference 1.0 Yes 10.0 2.0 Present 20.0 40.0

Quantitative and qualitative interaction Quantitative interaction Effect size is stronger in one level But both levels show an association in the same direction Qualitative interaction Exposure increases risk in one level, but decreases risk (or no association) in the other level If present, this interaction always exists on both additive and multiplicative scales

Qualitative interaction (example 1) D E M=1 M=0

Qualitative interaction (example 2) D M=0 E

Stratified analyses With multiple strata, you might see cutpoints with effect modification above and below the cutpoint Level 1: RR=1.3 Level 2: RR=1.4 Level 3: RR=2.8 Level 4: RR=2.7 Level 5: RR=3.1

One more reminder Be cautious with small sample size The interaction may be significant in the multivariate model, but is basically due to small numbers Need to conduct sensitivity analysis to assess likelihood of “spurious interaction”

Discussion of article Frost G, Darnton A, Harding A-H. “The effect of smoking on the risk of lung cancer mortality for asbestos workers in Great Britain (1971-2005). Ann Occup Hyg, e-pub January 20, 2011; PMID: 21252055