A general long-term aging model with different underlying activation mechanisms: Modeling, Bayesian estimation, and case influence diagnostics

In this paper we propose a general cure rate aging model. Our approach enables different underlying activation mechanisms which lead to the event of interest. The number of competing causes of the event of interest is assumed to follow a logarithmic distribution. The model is parameterized in terms of the cured fraction which is then linked to covariates. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. Moreover, some discussions on the model selection to compare the fitted models are given, as well as case deletion influence diagnostics are developed for the joint posterior distribution based on the -divergence, which has several divergence measures as particular cases, such as the Kullback-Leibler (K-L), J-distance, L-1 norm, and (2)-square divergence measures. Simulation studies are performed and experimental results are illustrated based on a real malignant melanoma data.