Bayesian inference and cure rate modeling for event history data

TL;DR

This paper introduces a Bayesian approach using advanced MCMC techniques for cure rate models in event history data, effectively handling complex likelihood landscapes and improving estimation accuracy over traditional methods.

Contribution

It develops a novel Bayesian inference method with a parallel tempering MCMC algorithm for cure models, addressing multimodality and flat likelihood issues.

Findings

The proposed algorithm explores multimodal posteriors effectively.

It provides robust point estimates superior to EM-based maximum likelihood.

Application to real recidivism data demonstrates practical utility.

Abstract

Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully Bayesian approach in order to overcome these issues. Posterior inference is carried out by constructing a Metropolis-coupled Markov chain Monte Carlo (MCMC) sampler, which combines Gibbs sampling for the latent cure indicators and Metropolis-Hastings steps with Langevin diffusion dynamics for parameter updates. The main MCMC algorithm is embedded within a parallel tempering scheme by considering heated versions of the target posterior distribution. It is demonstrated via simulations that the proposed algorithm freely explores the multimodal posterior distribution and produces robust point estimates, while it outperforms maximum likelihood estimation via the Expectation-Maximization algorithm. A by-product of our Bayesian implementation is to control the False Discovery Rate when classifying items as cured or not. Finally, the proposed method is illustrated in a real dataset which refers to recidivism for offenders released from prison; the event of interest is whether the offender was re-incarcerated after probation or not.