Abstract: Biomedical and clinical research is gradually shifting from a traditional ?one-size-fits-all? approach to a new paradigm of personalized medicine. An important step in this direction is to identify the treatment-covariate interactions. Our setting may include many covariates of interest. Numerous machine learning methodologies have been proposed to aid in treatment selection in this setting. However, few have adopted formal hypothesis testing procedures. As such, we present a novel testing procedure based on an m-out-of-n bootstrap that can be used to sequentially identify variables that interact with a treatment. We study the theoretical properties of the method, and use simulations to show that it outperforms competing methods in terms of controlling the type-I error rate and achieving satisfactory power. The usefulness of the proposed method is illustrated using real-data examples, from a randomized trial and an observational study.

Key words and phrases: Double robustness, forward stepwise testing, m-out-of-n bootstrap, non-regular asymptotics, personalized medicine.