  A utility-based Bayesian population finding (BaPoFi) method was proposed by
Morita and M\"uller (2017, Biometrics, 1355-1365) to analyze data from a
randomized clinical trial with the aim of identifying good predictive baseline
covariates for optimizing the target population for a future study. The
approach casts the population finding process as a formal decision problem
together with a flexible probability model using a random forest to define a
regression mean function. BaPoFi is constructed to handle a single continuous
or binary outcome variable. In this paper, we develop BaPoFi-TTE as an
extension of the earlier approach for clinically important cases of
time-to-event (TTE) data with censoring, and also accounting for a toxicity
outcome. We model the association of TTE data with baseline covariates using a
semi-parametric failure time model with a P\'olya tree prior for an unknown
error term and a random forest for a flexible regression mean function. We
define a utility function that addresses a trade-off between efficacy and
toxicity as one of the important clinical considerations for population
finding. We examine the operating characteristics of the proposed method in
extensive simulation studies. For illustration, we apply the proposed method to
data from a randomized oncology clinical trial. Concerns in a preliminary
analysis of the same data based on a parametric model motivated the proposed
more general approach.
