Date of Award

Summer 2025

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Ray Bai

Abstract

Survival analysis is a cornerstone of biomedical and clinical research and plays an important role in fields as diverse as engineering, actuarial science, and sociology. In this dissertation, we develop new semiparametric Bayesian methodology for three problems from survival analysis: 1) adjustment for treatment crossover in randomized controlled trials (RCTs), 2) multilevel modeling of clustered survival outcomes when the cluster size is also informative, and 3) divide-and-conquer Bayesian inference for massive survival data. Our methods are semiparametric in the sense that we assume the covariates have a linear effect with regard to the log-hazard or the log- survival time; however, we make minimal assumptions about the baseline hazard or the residual error distribution of the log-survival time.

In Chapter 2, we present a unified three-state model (TSM) framework for evalu- ating treatment effects in clinical trials in the presence of treatment crossover. Treat- ment crossover occurs when patients switch from their randomly assigned treatment to a different trial treatment. Researchers have proposed diverse methodologies to es- timate the treatment effect that would have hypothetically been observed if treatment crossover had not occurred. Our proposed TSM framework unifies existing methods, effectively identifying potential biases, model assumptions, and inherent limitations for each method. The TSM framework also facilitates the creation of new methods to adjust for confounding effects from treatment crossover. To illustrate this capability, iii we introduce a new Bayesian imputation method that falls under its scope. Using a piecewise constant prior for the hazard, our proposed method directly estimates the hazard function with increased flexibility.

In Chapter 3, we introduce a Bayesian method to jointly model the time-to- event outcome and cluster size for multilevel survival data. We use Dirichlet process mixtures (DPMs) for both the cluster size model and the survival model, allow- ing us to infer covariate effects and predict survival probabilities without imposing strong assumptions about the underlying data distributions. The two models are joined through a shared random effect, thus capturing potential informative cluster size (ICS). ICS arises when the cluster sizes are not independent of the measured outcomes. To the best of our knowledge, this is the first Bayesian semiparametric method for handling ICS.

In Chapter 4, we propose new distributed inference methods for Bayesian survival analysis based on piecewise exponential (PWE) models. To alleviate the computa- tional burden of fitting these models when sample size is large, we propose to use divide-and-conquer (D&C) Markov chain Monte Carlo (MCMC). We consider D&C MCMC for both the PWE model with independent observations and the mixed effects PWE model for clustered observations. For clustered survival data, we propose a novel data partitioning scheme to handle imbalanced cluster sizes. Our D&C MCMC algorithms greatly reduce the cost of running MCMC on large survival datasets, thus facilitating more efficient posterior inference.

Rights

© 2025, Zile Zhao

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