Approximate Bayesian inference for mixture cure models
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Approximate Bayesian inference for mixture cure models E. Lázaro1
· C. Armero1
· V. Gómez-Rubio2
Received: 15 March 2019 / Accepted: 12 September 2019 © Sociedad de Estadística e Investigación Operativa 2019
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 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. Keywords Accelerated failure time mixture cure models · Complete and marginal likelihood function · Gibbs sampling · Proportional hazards mixture cure models · Survival analysis Mathematics Subject Classification 62F15 · 62N99 · 62N02 · 62P10
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E. Lázaro [email protected]
1
Department of Statistics and Operations Research, Universitat de València, Valencia, Spain
2
Department of Mathematics, Universidad de Castilla-La Mancha, Albacete, Spain
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1 Introduction Survival analysis is an area of statistics dedicated to researching time-to-event data. This is one of the oldest areas of statistics, which dates back to the 1600s with the construction of life tables. The study of time-to-event data seems simple and traditional because its main interest is focused on nonnegative random variables. But this is very far from being the case. The fact that survival times are always positive keeps it away from the normal distribution framework, censoring and truncation schemes produce non-traditional likelihood issues, and the special elements that generate the dynamic nature of events occurring in time make survival analysis an interesting and exciting area of research and application, mainly in the biomedical field. Cure models in survival analysis deal with target populations in which a part of the individuals cannot experience the event of interest. This type of models has largely been developed as a co
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