Case-only approach to identifying markers predicting treatment effects on the relative risk scale

Retrospectively measuring markers on stored baseline samples from participants in a randomized controlled trial (RCT) may provide high quality evidence as to the value of the markers for treatment selection. Originally developed for approximating gene-environment interactions in the odds ratio scale, the case-only method has recently been advocated for assessing gene-treatment interactions on rare disease endpoints in randomized clinical trials. In this article, the case-only approach is shown to provide a consistent and efficient estimator of marker by treatment interactions and marker-specific treatment effects on the relative risk scale. The prohibitive rare-disease assumption is no longer needed, broadening the utility of the case-only approach. The case-only method is resource-efficient as markers only need to be measured in cases only. It eliminates the need to model the marker's main effect, and can be used with any parametric or nonparametric learning method. The utility of this approach is illustrated by an application to genetic data in the Women's Health Initiative (WHI) hormone therapy trial.