Bayesian imputation of right censored data in time-to-event studies

Abstract

In time-to-event studies subjects are followed until the event of interest has happened. Subjects who do not experience the event are referred to as censored. Due to censoring, methods of plotting individual survival time, such as density plots, are invalid. The graphical displays of time-to-event data usually take the form of a Kaplan-Meier survival plot. However, using a Kaplan-Meier survival plot might not be the most informative way to present the data to answer the typical questions of interest. The median survival is often used as a summary of the survival experience of a patients' population and it is easily read of the Kaplan-Meier plot. It is unlikely however that the median is a relevant summary at the patient level and a density plot of the data is perhaps more informative for communication than a single summary statistic. A fundamental idea in this thesis is to consider censored data as a form of missing, incomplete, data and use approaches from the missing data literature to handle this issue. In particular, we will use the idea of imputing the censored observations, based on the other information in the dataset and some form of assumed model. By imputing values for the censored observations and combining the original complete and imputed incomplete data, it is possible to plot the density of the full data to complement the information given by Kaplan-Meier plots. In this thesis, we consider using parametric Bayesian and non-parametric Bayesian methods to impute right censored survival data to achieve this aim. The imputation of censored observations not only allows more interpretable graphics to be produced for a wider general audience (physicians and patients), but it opens up the possibility of the use of standard formal methods of analysis for continuous responses.