Generated effect modifiers (GEM's) in randomized clinical trials

In a randomized clinical trial (RCT), it is often of interest not only to estimate the effect of various treatments on the outcome, but also to determine whether any patient characteristic has a different relationship with the outcome, depending on treatment. In regression models for the outcome, if there is a non-zero interaction between treatment and a predictor, that predictor is called an "effect modifier". Identification of such effect modifiers is crucial as we move towards precision medicine, that is, optimizing individual treatment assignment based on patient measurements assessed when presenting for treatment. In most settings, there will be several baseline predictor variables that could potentially modify the treatment effects. This article proposes optimal methods of constructing a composite variable (defined as a linear combination of pre-treatment patient characteristics) in order to generate an effect modifier in an RCT setting. Several criteria are considered for generating effect modifiers and their performance is studied via simulations. An example from a RCT is provided for illustration.