The Poisson-Inverse-Gaussian regression model with cure rate: a Bayesian approach and its case influence diagnostics

This paper proposes a new survival model, called Poisson Inverse-Gaussian regression cure rate model (PIGcr), which enables different underlying activation mechanisms that lead to the event of interest. The number of competing causes of the event of interest follows a Poisson distribution and the time for the event follows an Inverse-Gaussian distribution. The model takes into account the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo was considered. Discussions on the model selection criteria, as well as a case deletion influence diagnostics are addressed for a joint posterior distribution based on the -divergence, which has several divergence measures as particular cases, such as Kullback-Leibler (K-L), -distance, norm and -square divergence measures. The procedures are illustrated in artificial and real data.