12.4 - Interaction Revisited

Let's start with two definitions.

Effect modification
Effect modification occurs when a factor (an effect modifier) modifies the causal relationship between a risk factor and the outcome.

For example, immunization status is a strong effect modifier of the relationship between exposure to a specific pathogen and subsequent disease from that pathogen. As an effect modifier, immunization status then modifies the biologic response of the person. The presence of effect modification supports a causal relationship because it implies a biologically plausible process.

Statistical interaction
Statistical interaction is a term that is often used to describe a similar feature of data. Statistical interaction is consistent with effect modification but does not necessarily mean that there is a difference in the biologic response depending on exposure status.

Consequences of not identifying an effect modifier

If effect modification is not recognized, the estimator of the association of the risk factor with the outcome (e.g., RR) becomes a weighted average between the RR in one level of X (e.g., immunized) and the RR from another level of X (not immunized).

Methods to take effect modification into account

When designing and conducting a study:

  1. Conceptualize which factors (variables) might be effect modifiers
  2. Do not match on a potential effect modifier
  3. Collect information on potential effect modifiers (the more the better!)
  4. Consider powering the study to be able to test effect modifiers (rule of thumb – 4 times the sample size as would be required to test the presence of effect modification)

In the analysis of a study:

  1. Conceptualize potential effect modifiers, using your knowledge of the area of research, prior experience (from yourself and others). Ask a sequence of questions (e.g. For exposure E, disease D and factor X, a potential effect modifier: is there an association between E and D? is it biologically plausible that the association betwen E and D differs for levels of X? can such a difference be detected in this study?)
  2. Estimate a crude (unadjusted) association between exposure and disease.
  3. Stratifiy by potential effect modifiers to get stratum specific estimators. Compare/test significance of differences between stratum-specific estimators.
  4. Use a statistical model with interaction term.


  1. If the stratum-specific estimators are significantly different from each other, the stratified variable is likely to be a major effect modifier.
  2. Statistical methods (Breslow-Day Test for Homogeneity of the ORs from Extended Mantel-Haenszel method, -2 log likelihood test from logistic regression) are available to test the statistical significance of potential effect modifiers, and to calculate the estimators of Exposure-Disease association according to the levels of significant effect modifiers.
  3. Most epidemiological studies are not designed to have enough statistical power to statistically identify potential effect modifiers (often not the primary objective).

Absence of evidence is not the same as Evidence of absence.

“The interactions between Exposure and race, sex… in association with Disease were statistically tested by introducing interaction-terms into the logistic regression models, and none of them were found to be statistically significant at p < 0.15 level”.

An effect modifier is a real or hypothesized relationship in nature, not just observed in a dataset, as compared to a confounder. Once identified as an effect modifier, a variable is not treated as a confounder.


Here is an example of effect modification:

Diabetes and incident CHD - Females


Incident CHD
Row Pct
Col Pct
0 1 Total
0 1191 25 1216
1 93 13 106
Total 1248 38 1322

\(CI_0 = 2.06\%\)

\(CI_1 = 12.26\%\)

RR = 6.00

Odds ratio = 6.66

Diabetes and incident CHD - Males


Incident CHD
Row Pct
Col Pct
0 1 Total
0 1003 70 1073
1 77 12 89
Total 1080 82 1162

\(CI_0 = 6.52\%\)

\(CI_1 = 13.48\%\)

RR = 2.07

Odds ratio = 2.23

Combining both sexes, the OR = 4.30. Thus, sex modifies the effect of diabetes on incident CHD.