Bayesian Methods for Decision Making in Biomedical Applications

Abstract

This dissertation focuses on developing Bayesian survival analysis methodology for optimizing decision making and treatment methods in a variety of biomedical applications.

First, we develop a flexible Bayesian nonparametric regression model based on a dependent Dirichlet process and Gaussian process, DDP-GP, for optimizing precision dosing of intravenous busulfan in allogenic stem cell transplantation. Our analyses of a dataset of 151 patients identified optimal therapeutic dosage intervals that maximizes patient survival outcomes and varies substantively with age and complete remission status. Extensive simulations to evaluate the DDP-GP model in similar settings showed that its performance compares favorably to alternative methods. We provide an R package, DDPGPSurv, that implements the DDP-GP model for a wide range of survival regression analyses.

The second main contribution of this dissertation is the development of personalized dynamic treatment regimes (DTR) in continuous time. Traditional statistical methods for DTRs usually focus on estimating the optimal treatment or dosage at each given medical intervention, but overlook the important question of “when this intervention should happen.” We fill this gap by building a generative model for a sequence of medical interventions with a marked temporal point process (MTPP) and embedding this into a Bayesian joint framework where the other components model longitudinal medical measurements and time-to-event data. Moreover, we propose a policy gradient method to learn the personalized optimal clinical decision that maximizes patient survival by interacting the MTPP with the model on clinical observations while accounting for uncertainties in clinical observations. A signature application is to schedule follow-up visitations and assign a dosage at each visitation for patients after kidney transplantation. We demonstrate that the personalized decisions made by our method are interpretable and help improve patient survival, and provide an R package, doct, that broadly implements our framework.

Lastly, we introduce a Bayesian semiparametric model for learning biomarker trajectories and change points in Alzheimer's disease (AD). Through simulation and real data studies, we show that our model is able to reliably detect a pre-diagnosis longitudinal change point, evaluate the probability of AD progression, and account for heterogeneity by clustering subjects using longitudinal and diagnosis time data.