A Sequential Significance Test for Treatment by Covariate Interactions

Abstract: Due to patient heterogeneity in response to various aspects of any treatment program, biomedical and clinical research is gradually shifting from the traditional "one-size-fits-all" approach to the new paradigm of personalized medicine. An important step in this direction is to identify the treatment by covariate interactions. We consider the setting in which there are potentially a large number of covariates of interest. Although a number of novel machine learning methodologies have been developed in recent years to aid in treatment selection in this setting, few, if any, have adopted formal hypothesis testing procedures. In this article, we present a novel testing procedure based on m-out-of-n bootstrap that can be used to sequentially identify variables that interact with treatment. We study the theoretical properties of the method and show that it is more effective in controlling the type I error rate and achieving a satisfactory power as compared to competing methods, via extensive simulations. Furthermore, the usefulness of the proposed method is illustrated using real data examples, both from a randomized trial and from an observational study.