Christensen, FletcherWu, JianrongDegnan, JamesYang, MingAnAlmutiri, Sara2025-12-152025دور القيادة التحويلية الخضراء فى دعم الميزة التنافسية للمستشفيات السعوديةhttps://hdl.handle.net/20.500.14154/77518Bayesian 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.162en-USBayesian clinical trial designsurvival analysisCox proportional hazards modelpower priorexponential survival distributionWeibull survival distributionMarkov chain Monte Carlo (MCMC)piecewise exponential model.Power and Type I errorThesis