  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.
