Approximate Bayesian inference for mixture cure models

TL;DR

This paper develops a Bayesian inference method for mixture cure models in survival analysis, combining INLA and MCMC techniques to efficiently analyze populations with cured and susceptible individuals, even with censored data.

Contribution

It introduces an innovative approach integrating INLA with MCMC for mixture cure models, leveraging uncensored data to improve inference accuracy.

Findings

Effective Bayesian inference for mixture cure models.

Incorporation of uncensored data enhances model accuracy.

Applicable to censored and non-censored survival data.

Abstract

Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible individuals. The statistical analysis of these models focuses on examining the probability of cure (incidence model) and inferring on the time-to-event in the susceptible subpopulation (latency model). Bayesian inference on mixture cure models has typically relied upon Markov chain Monte Carlo (MCMC) methods. The integrated nested Laplace approximation (INLA) is a recent and attractive approach for doing Bayesian inference. INLA in its natural definition cannot fit mixture models but recent research has new proposals that combine INLA and MCMC methods to extend its applicability to them (Bivand et al., 2014, G\'omez-Rubio et al., 2017, G\'omez-Rubio and Rue, 2018}. This paper focuses on the implementation of INLA in mixture cure models. A general mixture cure survival model with covariate information for the latency and the incidence model within a general scenario with censored and non-censored information is discussed. The fact that non-censored individuals undoubtedly belong to the uncured population is a valuable information that was incorporated in the inferential process.