Jiang Qian

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Director, Data and Statistical Science
AbbVie Inc


A Bayesian Weibull Survival Model

This dissertation explores a Bayesian Weibull survival model used to analyze data from clinical trials, and examines the Gibbs sampling scheme employed to estimate posterior distributions. I review the definition and some properties of a Weibull survival distribution, introduce two parameterizations for comparing treatments in a clinical trial, and discuss various treatment comparison measures. It is difficult to use the Weibull model to analyze and evaluate the posterior distributions of the parameters analytically. Therefore, I use an approximation based on Monte Carlo integration to obtain the posterior distributions of the parameters and predictive measures to compare the treatments. A mixture model with a Weibull component and a surviving fraction is introduced. I employ a Gibbs sampling procedure incorporating the Adaptive Rejection Sampling Method, to obtain the posterior distribution of parameters and the predictive measure of vaccine efficacy. This dissertation shows the practicality of the Bayesian Weibull survival modeling. I use the Weibull model to analyze data collected at several interim analysis times during a Non-Small Cell Lung Cancer (NSCLC) clinical trial. I also provide posterior distributions of parameters, give the numerical results about the relative efficacy of treatments, and address the sensitivity issue about the prior choice. I employ the mixture model to analyze data from a Haemophilus Influenzae type B vaccine trial, and to explore various methodological and computational aspects. I use a Gibbs sampling scheme to calculate the predictive protective efficacy (PE) of the vaccine. I also address the sensitivity of the choice of prior distribution.