Approximate Bayesian inference for mixture cure models

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 for 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 but in its natural definition cannot fit mixture models. This paper focuses on the implementation of a feasible INLA extension for fitting standard mixture cure models. Our proposal is based on an iterative algorithm which combines the use of INLA for estimating the process of interest in each of the subpopulations in the study, and Gibbs sampling for computing the posterior distribution of the cure latent indicator variable which classifies individuals to the susceptible or non-susceptible subpopulations. We illustrated our approach by means of the analysis of two paradigmatic datasets in the framework of clinical trials. Outputs provide closing estimates and a substantial reduction of computational time in relation to those using MCMC.