1. 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

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

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

4. 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)

5. 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

6. 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.

7. 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)

8. 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

9. 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

10. 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

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

12. Qualitative interaction (example 2)D
M=0 E

13. 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

14. 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”

15. 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 ( ). Ann Occup Hyg, e-pub January 20, 2011; PMID: