Modelling the distribution of grouped survival data via dependant neutral-to-the-right priors

Abstract

With each update of its browser, Firefox receives reports of the time of discovery of a large number of bugs associated with that update. This process yields survival data which is separated by update into groups and often exhibits much commonality. We propose a model which, rather than treating each group separately, allows for borrowing of information across the entire dataset. To this end, we use superposed completely random measures to construct a vector of dependent neutral-to-the-right priors. The model is completed by accounting for an unobserved number of right-censored data points per group. An explicit characterisation of the posterior distribution of the defined vector of dependent neutral-to-the-right priors is derived and, in turn, used to devise an efficient marginal Markov chain Monte Carlo sampler for posterior inference. A simulation study is carried out to assess the performance of the model. While motivated by the Firefox data, our approach could potentially be useful across a wide range of applications of survival analysis.