Efficient interaction analysis in randomized controlled trials

Abstract Identifying treatment-covariate interaction is an initial step toward revealing treatment effect heterogeneity and advancing precision medicine. However, when the covariate of interest is continuous, the definition of treatment-covariate interaction can be ambiguous or rely on questionable model assumptions. To tackle this challenge, we introduce a model-free framework for interaction analysis in randomized controlled trials, advocating the adoption of a clearly defined target parameter for interaction and thereby avoiding assumptions about the functional form of the data-generating mechanism. To ensure feasibility for most randomized controlled trials encountered in practice, we study interaction analysis under covariate-adaptive randomization, including simple and stratified randomization, and minimization methods. We observe that the usual method for interaction analysis can either exaggerate or understate uncertainty, leading to asymptotically conservative or anti-conservative results. We modify the usual method with a consistent variance estimator. Furthermore, by acknowledging the dependence structure of treatment assignment induced by covariate-adaptive randomization, we compute the semiparametric efficiency bound and introduce a novel semiparametric efficient method for analyzing our specified interaction effect. We demonstrate that our semiparametric efficient inference procedure, equipped with nonparametric and machine learning techniques for adjusting baseline covariate information, is both efficient and widely applicable.