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Summary We propose several Bayesian models for modelling time-to-event data. We consider a piecewise exponential model, a fully parametric cure rate model and a semiparametric cure rate model. For each model, we derive the likelihood function and examine some of its properties for carrying out Bayesian inference with non-informative priors. We also examine model identifiability issues and give conditions which guarantee identifiability. Also, for each model, we construct a class of informative prior distributions based on historical data, i.e. data from similar previous studies. These priors, called power priors, prove to be quite useful in this context. We examine the properties of the power priors for Bayesian inference and, in particular, we study their effect on the current analysis. Tools for model comparison and model assessment are also proposed. A detailed case-study of a recently completed melanoma clinical trial conducted by the Eastern Cooperative Oncology Group is presented and the methodology proposed is demonstrated in detail.
Chen et al. (Wed,) studied this question.