Causal Power and its Relationship with the Relative Risk, Odds Ratio, and Risk Difference
Channel: Jake Shannin
Date: 2020-03-27

Epidemiologists quantify how a given exposure or treatment differently affects different populations (e.g. genders) using any of a variety of effect measures. The strength and even direction of heterogeneity of effect can depend on which effect measure they choose. We show that if the relative risk and causal power both indicate ("agree") that an exposure affects population P more strongly than population Q, then so will the odds ratio and risk difference. We use a Monte Carlo simulation to estimate how frequently effect measures agree when risks are chosen from given intervals. We give particular attention to the behavior of the odds ratio and risk difference when the relative risk and causal power disagree. We discuss epidemiological literature in which effect measures disagree and suggest guidelines for choosing and interpreting effect measures. We relate biological scenarios to each effect measure, finding that the relative risk is often more appropriate for treatments that decrease each population's risk while causal power applies more typically to exposures that increase each population's risk.