Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome.

Abstract

This paper develops a Bayesian model with a flexible link function connecting a binary treatment response to a linear combination of covariates and a treatment indicator and the interaction between the two. Generalized linear models allowing data-driven link functions are often called "single-index models" and are among popular semi-parametric modeling methods. In this paper, we focus on modeling heterogeneous treatment effects, with the goal of developing a treatment benefit index (TBI) incorporating prior information from historical data. The model makes inference on a composite moderator of treatment effects, summarizing the effect of the predictors within a single variable through a linear projection of the predictors. This treatment benefit index can be useful for stratifying patients according to their predicted treatment benefit levels and can be especially useful for precision health applications. The proposed method is applied to a COVID-19 treatment study.