Joint modelling of recurrent events and survival: a Bayesian nonparametric approach

Heart failure (HF) is one of the main causes of morbidity, hospitalization and death in the western world and the economic burden associated with HF management is relevant and expected to increase in the future. We consider hospitalization data for heart failure in the most populated Italian Region, Lombardia. Data were extracted from the administrative data warehouse of the regional healthcare system. The main clinical outcome of interest is time to death and research focus is on investigating how recurrent hospitalizations affect the time to event. The main contribution of the paper is to develop a joint model for gap times between consecutive re-hospitalizations and survival time. The probability models for the gap times and for the survival outcome share a common patient specific frailty term. Using a flexible Dirichlet process model for the random effects distribution accounts for patient heterogeneity in recurrent event trajectories. Moreover, the joint model allows for dependent censoring of gap times by death or administrative reasons and for the correlations between different gap times for the same individual. It is straightforward to include covariates in the survival and/or recurrence process through the specification of appropriate regression terms. The main advantages of the proposed methodology are wide applicability, ease of interpretation and efficient computations. Posterior inference is implemented through Markov chain Monte Carlo methods.