Subgroup-effects models for the analysis of personal treatment effects

Abstract

The emerging field of precision medicine is transforming statistical analysis from the classical paradigm of population-average treatment effects into that of personal treatment effects. This new scientific mission has called for adequate statistical methods to assess heterogeneous covariate effects in regression analysis. This paper focuses on a subgroup analysis that consists of two primary analytic tasks: identification of treatment effect subgroups and individual group memberships, and statistical inference on treatment effects by subgroup. We propose an approach to synergizing supervised clustering analysis via alternating direction method of multipliers (ADMM) algorithm and statistical inference on subgroup effects via expectation-maximization (EM) algorithm. Our proposed procedure, termed as hybrid operation for subgroup analysis (HOSA), enjoys computational speed and numerical stability with interpretability and reproducibility. We establish key theoretical properties for both proposed clustering and inference procedures. Numerical illustration includes extensive simulation studies and analyses of motivating data from two randomized clinical trials to learn subgroup treatment effects.