Publication Date

Spring 5-16-2026

Abstract

Bayesian methods provide a flexible framework for time-to-event analysis by incorporating prior information. The power prior offers a systematic way to borrow information from historical data. This approach is especially valuable in clinical research, where historical data can enhance inference in early-phase trials with limited sample sizes. This dissertation develops Bayesian approaches for two-arm survival studies using both closed-form and simulation-based methods. The closed-form inference is derived under exponential and Weibull survival models. Under the proportional hazards framework, the posterior is derived through a normal approximation to the log hazard ratio, allowing inference on the treatment effect when the variance is unknown. MCMC methods are implemented using both parametric and piecewise exponential models to accommodate censoring and flexible survival distributions. The study evaluates the impact of historical borrowing on power and Type I error across different scenarios, demonstrating that appropriate use of power priors can improve efficiency while maintaining Type I error control.

Degree Name

Statistics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Fletcher Christensen

Second Committee Member

Jianrong Wu

Third Committee Member

James Degnan

Fourth Committee Member

MingAn Yang

Language

English

Keywords

Bayesian clinical trial design, survival analysis, Cox proportional hazards model, power prior, Markov chain Monte Carlo (MCMC), power prior, piecewise exponential model

Document Type

Dissertation

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