Bayesian analysis of Birnbaum-Saunders survival model with cure fraction under a variety of activation mechanism

In this paper we propose a new cure rate survival model. Our approach enables different underlying activation mechanisms which lead to the event of interest. The number of competing causes which may be responsible for the occurrence of the event of interest is assumed to follow a geometric distribution while the time to event is assumed to follow a Birnbaum-Saunders distribution. As an advantage our approach may scan all underlying activation mechanisms from the first to last one based on order statistics. 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. In particular, case deletion influence diagnostics are developed for the joint posterior distribution based on the ψ-divergence, which includes the Kullback-Leibler (K-L), J-distance, L1 norm and χ2-square divergence measures as particular cases. Simulation studies are performed for study frequentist properties of the Bayesian estimates. The methodology is illustrated on a real malignant melanoma data.