  Individualized treatment rules (ITR) can improve health outcomes by
recognizing that patients may respond differently to treatment and assigning
therapy with the most desirable predicted outcome for each individual. Flexible
and efficient prediction models are desired as a basis for such ITRs to handle
potentially complex interactions between patient factors and treatment. Modern
Bayesian semiparametric and nonparametric regression models provide an
attractive avenue in this regard as these allow natural posterior uncertainty
quantification of patient specific treatment decisions as well as the
population wide value of the prediction-based ITR. In addition, via the use of
such models, inference is also available for the value of the Optimal ITR. We
propose such an approach and implement it using Bayesian Additive Regression
Trees (BART) as this model has been shown to perform well in fitting
nonparametric regression functions to continuous and binary responses, even
with many covariates. It is also computationally efficient for use in practice.
With BART we investigate a treatment strategy which utilizes individualized
predictions of patient outcomes from BART models. Posterior distributions of
patient outcomes under each treatment are used to assign the treatment that
maximizes the expected posterior utility. We also describe how to approximate
such a treatment policy with a clinically interpretable ITR, and quantify its
expected outcome. The proposed method performs very well in extensive
simulation studies in comparison with several existing methods. We illustrate
the usage of the proposed method to identify an individualized choice of
conditioning regimen for patients undergoing hematopoietic cell transplantation
and quantify the value of this method of choice in relation to the Optimal ITR
as well as non-individualized treatment strategies.
