A Latent Promotion Time Cure Rate Model using Dependent Tail-Free Mixtures
Li Li, Ji‐Hyun Lee · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2016
Summary The paper extends the latent promotion time cure rate marker model of Kim, Xi and Chen for right-censored survival data. Instead of modelling the cure rate parameter as a deterministic function of risk factors, they assumed that the cure rate parameter of a targeted population is distributed over a number of ordinal levels according to the probabilities governed by the risk factors. We propose to use a mixture of linear dependent tail-free processes as the prior for the distribution of the cure rate parameter, resulting in a latent promotion time cure rate model. This approach provides an immediate answer to perhaps one of the most pressing questions ‘what is the probability that a targeted population has high proportions (e.g. greater than 70%) of being cured?’. The approach proposed can accommodate a rich class of distributions for the cure rate parameter, while centred at gamma densities. The algorithms that are developed in this work allow the fitting of latent promotion time cure rate models with several survival models for metastatic tumour cells.