A mediator effect size in randomized clinical trials

To understand the process by which a treatment (T) achieves an effect on outcome (O) and thus to improve the effect of T on O, it is vital to detect mediators, to compare the impact of different mediators, and to develop hypotheses about the causal factors (all mediators) linking T and O. An index is needed to facilitate interpretation of the potential clinical importance of a mediator (M) of choice of T on treatment O in randomized clinical trials (RCTs). Ideally such a mediator effect size should (1) be invariant under any rescaling of M and O consistent with the model used, and (2) reflect the difference between the overall observed effect of T on O and what the maximal effect of T on O could be were the association between T and M broken. A mediator effect size is derived first for the traditional linear model, and then more generally for any categorical (ordered or non-ordered) potential mediator. Issues such as the problem of multiple treatments, outcomes and mediators, and of causal inferences, and the correspondence between this approach and earlier ones, are discussed. Illustrations are given of the application of the approach.