Bayesian Outcome Weighted Learning

TL;DR

This paper introduces a Bayesian formulation of outcome-weighted learning (OWL) for estimating optimal individualized treatment rules, providing a probabilistic approach to uncertainty quantification and demonstrating its effectiveness through simulations.

Contribution

It develops a Bayesian version of OWL using a pseudo-likelihood and Gibbs sampling, enabling uncertainty estimation in treatment rules.

Findings

Bayesian OWL accurately estimates optimal treatment rules.

The method effectively quantifies uncertainty in treatment recommendations.

Simulation studies show competitive performance with existing methods.

Abstract

One of the primary goals of statistical precision medicine is to learn optimal individualized treatment rules (ITRs). The classification-based, or machine learning-based, approach to estimating optimal ITRs was first introduced in outcome-weighted learning (OWL). OWL recasts the optimal ITR learning problem into a weighted classification problem, which can be solved using machine learning methods, e.g., support vector machines. In this paper, we introduce a Bayesian formulation of OWL. Starting from the OWL objective function, we generate a pseudo-likelihood which can be expressed as a scale mixture of normal distributions. A Gibbs sampling algorithm is developed to sample the posterior distribution of the parameters. In addition to providing a strategy for learning an optimal ITR, Bayesian OWL provides a natural, probabilistic approach to estimate uncertainty in ITR treatment recommendations themselves. We demonstrate the performance of our method through several simulation studies.