A Semiparametric Approach to Model Effect Modification

Abstract

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.

Keywords:

• Dimension reduction
• Interaction
• Precision medicine
• Semiparametric efficiency
• Tangent space

Supplementary Materials

Estimation with multiple level treatments or exposures, proofs of Theorems 3.1–5.5, additional simulation results, and supplemental results for the mammography screening study are contained in the supplementary materials.

Additional information

Funding

Research reported in this article was partially funded through a Patient-Centered Outcomes Research Institute (PCORI) Award (ME-1409-21219). The views in this publication are solely the responsibility of the authors and do not necessarily represent the views of the PCORI, its Board of Governors or Methodology Committee.