A Dirichlet Process Mixture Regression Model for the Analysis of Competing Risk Events

Francesco Ungolo and Edwin R. van den Heuvel

Abstract: We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is characterized by a random effect following a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance predictive performance of the surrending rates.

Keywords: Competing Risks, Survival Analysis, Dirichlet Processes, Bayesian analysis, Lapse risk, MCMC