A Semiparametric Approach to Model Effect Modification

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version. Supplementary materials for this article are available online.