Dimension reduction in survival regressions with censored data via an imputed spline approach

A Bayesian Approach for Imputation of Censored Survival Data

A common feature of much survival data is censoring due to incompletely observed lifetimes. Survival analysis methods and models have been designed to take account of this and provide appropriate relevant summaries, such as the Kaplan–Meier plot and the commonly quoted median survival time of the group under consideration. 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, and the Kaplan–Meier plot can be difficult for the patient to understand and also is often mis-interpreted, even by some physicians. This paper considers an alternative approach of treating the censored data as a form of missing, incomplete data and proposes an imputation scheme to construct a completed dataset. This allows the use of standard descriptive statistics and graphical displays to convey both typical outcomes and the associated variability. We propose a Bayesian approach to impute any censored observations, making use of other information in the dataset, and provide a completed dataset. This can then be used for standard displays, summaries, and even, in theory, analysis and model fitting. We particularly focus on the data visualisation advantages of the completed data, allowing displays such as density plots, boxplots, etc, to complement the usual Kaplan–Meier display of the original dataset. We study the performance of this approach through a simulation study and consider its application to two clinical examples.