Bayesian sequential analysis for correlated time to event data: A computational approach

The computational and analytical burden of the Bayesian sequential decision problem has historically limited its application domain. Advances in decision-theoretic loss approximation through simulation (Carlin et al., 1998, Brockwell and Kadane, 2003, Muller et al., 2007) present an option for simpler, low-dimensional designs based upon optimization of the decision boundaries or discretization of the parameter space. The combination of these approaches and high performance computing (HPC) allow for the application of Bayesian sequential decision methodology to increasingly complex problems. For example, one such problem is the Weibull-Stable frailty model for correlated event times. The time requirement for sampling its joint posterior is non-trivial and practical simulation based approaches are infeasible without inclusion of a high level of a parallelization. With increasing public accessibility to HPC (e.g., cloud based providers such as Amazon, and Rackspace), the level of parallelization required is easily achievable. Using HPC, the utility and efficiency of the simulation based decision-theoretic methods in the context of loss functions, interim analysis, and correlated survival data is explored. This dissertation provides methodology for reaching Bayes optimal decisions for the Weibull-Stable model in a matter of hours, rather than months.