Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

TL;DR

This paper introduces a Bayesian survival analysis model using dependent Dirichlet processes and Stan, enabling flexible modeling of multivariate survival data with complex structures and dependencies.

Contribution

It proposes a generalized shared frailty model with dependent Dirichlet processes for flexible baseline survival functions, automating posterior sampling with Stan.

Findings

Model validated on bladder cancer data

Estimates align with existing results

Demonstrates feasibility of complex Bayesian survival modeling

Abstract

Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling 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 of survival modeling for multivariate survival outcomes with complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects so as to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis and Stan relaxes the posterior inference.