A Bayesian Cure Rate Model for Repeated Measurements and Interval Censoring

We extend a recently published multivariate Bayesian cure rate model to handle interval censoring and a varying number of measurements per individual. The model assumes an unknown number of latent causes of the event in question at each repeated measurement. This number is assumed to be distributed Poisson, with rate a function of covariates multiplied by a subject-specific frailty term. The observed event time is the minimum of the event times of the latent causes, and may only be recorded as contained within a given time interval. If the number of latent causes of the event is zero for an individual at a measurement, then that individual will not experience the event at that measurement. We present the model for a general frailty distribution and lifetime distribution. Our model formulation also allows covariates to describe the lifetime distribution. We illustrate the model using a data set from NASA’s Hypobaric Decompression Sickness Databank. We model the time to onset of grade IV venous gas emboli in hypobaric environment using both a gamma frailty distribution and an inverse Gaussian frailty distribution. We compare the two frailty models using the conditional predictive ordinate (CPO) statistic.