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Bayesian paradigm takes advantage of well fitting complicated survival modelsand feasible computing in survival analysis owing to the superiority intackling the complex censoring scheme, compared with the frequentist paradigm.In this chapter, we aim to display the latest tendency in Bayesian computing,in the sense of automating the posterior sampling, through Bayesian analysis ofsurvival modeling for multivariate survival outcomes with complicated datastructure. Motivated by relaxing the strong assumption of proportionality andthe restriction of a common baseline population, we propose a generalizedshared frailty model which includes both parametric and nonparametric frailtyrandom effects so as to incorporate both treatment-wise and temporal variationfor multiple events. We develop a survival-function version of ANOVA dependentDirichlet process to model the dependency among the baseline survivalfunctions. The posterior sampling is implemented by the No-U-Turn sampler inStan, a contemporary Bayesian computing tool, automatically. The proposed modelis validated by analysis of the bladder cancer recurrences data. The estimationis consistent with existing results. Our model and Bayesian inference provideevidence that the Bayesian paradigm fosters complex modeling and feasiblecomputing in survival analysis and Stan relaxes the posterior inference.

Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model