Assessing Interaction in Case-Control Studies: Type I Errors When Using Both Additive and Multiplicative Scales

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Epidemiologic researchers often explore effect modification in case-control studies on more than one statistical scale, an approach that one expects would increase the rate of false-positive findings of interaction. For example, researchers have measured effect modification by using both a multiplicative interaction coefficient (M) in a logistic regression model and a measure of interaction on the additive scale such as the interaction coefficient from an additive relative risk regression model (A). We performed computer simulations to investigate the degree to which type I error may be inflated when statistical interactions are evaluated by using both M and A. The overall type I error rate was often greater than 5% when both tests were performed together. These results provide empiric evidence of the limited validity of a common approach to assessing etiologic effect modification. When the scale has not been specified before analysis, interaction hypothesis tests of effect modification should be interpreted particularly cautiously. Researchers are not justified in choosing the interaction test with the lowest P value.

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