Semiparametric Bayesian analysis of censored linear regression with errors-in-covariates

The accelerated failure time (AFT) model is a well-known alternative to the Cox proportional hazard model for analyzing time-to-event data. In this paper we consider fitting an AFT model to right censored data when a predictor variable is subject to measurement errors. First, without measurement errors, estimation of the model parameters in the AFT model is a challenging task due to the presence of censoring, especially when no specific assumption is made regarding the distribution of the logarithm of the time-to-event. The model complexity increases when a predictor is measured with error. We propose a non-parametric Bayesian method for analyzing such data. The novel component of our approach is to model (1) the distribution of the time-to-event, (2) the distribution of the unobserved true predictor, and (3) the distribution of the measurement errors all non-parametrically using mixtures of the Dirichlet process priors. Along with the parameter estimation we also prescribe how to estimate survival probabilities of the time-to-event. Some operating characteristics of the proposed approach are judged via finite sample simulation studies. We illustrate the proposed method by analyzing a data set from an AIDS clinical trial study.