Parametric and Non-parametric Bayesian Imputation for Right Censored Survival Data

A common feature of much survival data is censoring due to incompletely observed lifetimes. Survival analysis methods have been designed to take account of this and provide appropriate relevant summaries, such as the Kaplan-Meier plot and the median is easily read off this plot. However, a single summary is not really a relevant quantity for communication to an individual patient, as it conveys no notion of variability and uncertainty. The aim of this paper is to consider censored data as a form of missing data and impute them using Bayesian methods. We introduce two novel parametric and non-parametric Bayesian approaches for imputing right censored observations to be used as a complement to formal inferential methods and to allow more interpretable displays to be made for physicians and patients.