Objective Bayesian Analysis of Group-invariant Survival Models

Ferrara, Paul G., Department of Statistics, University of Virginia
Holt, Jeffrey, Department of Mathematics, University of Virginia
Spitzner, Dan, Department of Statistics, University of Virginia
Conaway, Mark, PBHS Public Health Sciences Admin, University of Virginia
Chang, Theodore, Department of Statistics, University of Virginia

The type of survival models under consideration in the current work are the class of parametric accelerated hazard and proportional hazard models, where the baseline hazard function can be viewed as being invariant under the action of a mathematical group. The main focus, regarding this class of survival model, is in performing Ob -jective Bayesian analysis, and in particular, performing inference based on the use of Reference priors. In order to perform this analysis, Reference priors are calculated for several versions of such models, and subsequent data analysis performed. To imple -ment the posterior sampling required for this analysis, in chapter 2, an alternative to Gilks Adaptive Rejection Metropolis Sampling (ARMS) is proposed in the presence of non - logconcavity of the full - conditionals within GIBBS sampling. The proposed algorithm, AARS, is described, and several theoretical results are proved regarding the proposed algorithm. It is claimed that the proposed algorithm has several advan -tages over the ARMS algorithm. Next, selection of the baseline hazard function, for the class of group - invariant survival models, is considered. It is proposed that a dece -dent of the Bayes Factor, called the Intrinsic Bayes Factors, be used to determine the most efficacious form of the baseline hazard function, for a given dataset. This form of the Bayes Factor allows the use of true non - informative priors, unlike the traditional Bayes Factor. Moreover, for the group invariant survival models under considera -tion, it is shown that use of Reference Priors results in considerable simplification in the calculation of the Intrinsic Bayes Factor. Lastly, for the class of group invariant survival models under consideration, weighted combinations of baseline hazard func -tions are considered as an alternative to modeling with a single, common, parametric baseline hazard function. The form of a Reference prior for such weighted - hazard models is derived, and subsequent data analysis is performed using this Reference prior. Lastly, the superiority of weighted models for data sets exhibiting bath - tub shaped, and I1oI1 - InoI1otoI1ic, empirical hazard functions is illustrated.

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PHD (Doctor of Philosophy)
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