  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.
