Bayesian sensitivity models for missing covariates in the analysis of survival data

Abstract

This paper presents a Bayesian approach using WinBUGS for analysing survival data in which observations have missing information on some covariates. Modelling the joint density of the survival time and the covariates allows for the missing covariate data to be missing at random (MAR), as opposed to the more restrictive assumptions imposed by a complete case analysis. Here, the survival times are modelled by the accelerated failure time model and the joint covariate density is factorized as a series of conditional densities, each modelled by logistic regression. We propose a class of models to examine MAR assumption by using Bayesian informative priors or auxiliary data. In the example considered, the complete case analysis underestimates the proportion of severely impaired cases. Furthermore, models evaluating sensitivity to the MAR assumption suggest that median life expectancies could be increased. Gains in precision are small in the application considered, possibly a reflection of extra uncertainty because of the inclusion of all cases, including those of unknown severity. Through simple Bayesian models, more realistic assumptions concerning the nature of the missing data can be made. Implementation in WinBUGS means that this model is accessible to practicing statisticians.