A Bayesian cure rate regression model using Hamiltonian Monte Carlo methods

Abstract

In this paper, we propose a flexible cure rate survival model by assuming the number of competing causes, related to the event of interest, to follow generalized Poisson distribution. The generalized Poisson distribution has several important properties, e.g. it can effectively model both underdispersed (mean > variance) and overdispersed (mean < variance) mechanisms present in the data. Further, it includes the promotion time cure model as a special case. In this work, for a non-cure subject, we model the time to event of interest with the piecewise exponential distribution. We emphasize that the piecewise exponential distribution has a greater flexibility to model failure times, and can be considered as a distribution-free alternative to the parametric distributions based assumptions. Inferences for the model parameters are considered via full Bayesian analysis. Further, a detailed simulation study is performed with different parameter settings, sample sizes and censoring percentages to study the behavior of the estimators. Finally, a data set from the medical area is analyzed for further illustration.