Simple power analysis in causal mediation models for a dichotomous outcome based on the mediation proportion

Mediation models are widely used in many fields of research and have recently gained attention in epidemiology. The mediation proportion is a standard measure to evaluate what part of the total exposure effect on an outcome may be explained by a particular mediator and to examine how important that pathway is relative to the overall exposure effect. A common question is how large a sample size is needed to achieve high statistical power or, equivalently, what magnitude of effect can be detected. Current power and sample size calculations for mediation analysis are limited and additional research is needed. We therefore propose a computer-intensive power analysis using the mediation proportion. We conduct simulation studies to calculate statistical powers and sample sizes. And then, we illustrate our power analysis using an example from the Adult Health Study of atomic-bomb survivors and demonstrate that the method is relatively straightforward to understand and compute.