Epidemiologic Methods Sample Size and Power Calculations for Additive Interactions

Interactions measured on the additive scale are more relevant than multiplicative interaction for assessing public health importance and also more closely related to notions of mechanistic synergism. Most work on sample size and power calculations for interaction have focused on the multiplicative scale. Here we derive analytic expressions for sample size and power calculations for interactions on the additive scale. We give formulae for detecting additive interaction on the risk scale from a cohort study, formulae for detecting additive interaction using the relative excess risk for interaction from a logistic regression with cohort data, and formulae for detecting additive interaction for the relative excess risk for interaction from a logistic regression with case-control data. When main effects of both exposures are positive, power to detect positive interaction on the additive scale will be greater than that on the multiplicative scale. Excel spreadsheets are provided for power and sample size calculations for additive, multiplicative, and case-only interaction estimates.