A new Bayesian model for survival data with a surviving fraction

We consider Bayesian methods for right-censored survival data for populatio ns with a surviving (cure) fraction. We propose a model that is quite diffe rent from the standard mixture model for cure rates. We provide a natural m otivation and interpretation of the model and derive several novel properti es of it. First, we show that the model has a proportional hazards structur e, with the covariates depending naturally on the cure rate. Second, we der ive several properties of the hazard function for the proposed model and es tablish mathematical relationships with the mixture model for cure rates. P rior elicitation is discussed in detail, and classes of noninformative and informative prior distributions are proposed. Several theoretical propertie s of the proposed priors and resulting posteriors are derived, and comparis ons are made to the standard mixture model. A real dataset from a melanoma clinical trial is discussed in detail.