Power series cure rate model for spatially correlated interval-censored data based on generalized extreme value distribution

In this work, we propose a flexible cure rate model to allow for spatial correlations by including spatial frailty in the interval-censored data setting. The proposed model is quite flexible and generalizes the Bernoulli, geometric, Poisson, and logarithmic models. It can be tested for the best fit in a straightforward way. Our approach enables different underlying activation mechanisms that lead to the event of interest, and the number of competing causes that can be responsible for the occurrence of the event of interest follows a flexible exponential discrete power series distribution. MCMC methods are used in Bayesian inference for the proposed models and Bayesian comparison criteria are used for model comparison. Moreover, we conduct influence diagnostics through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions in the analysis results. Finally, the proposed models are used to analyze a real dataset.