Accelerated failure time models with covariates subject to measurement error

Abstract

It has been well known that ignoring measurement error may result in substantially biased estimates in many contexts including linear and nonlinear regressions. For survival data with measurement error in covariates there has been extensive discussion in the literature with the focus being on the Cox proportional hazards models. However, the impact of measurement error on accelerated failure time (AFT) models has received little attention, though AFT models are very useful in survival data analysis. In this paper, we discuss AFT models with error-prone covariates and study the bias induced by the naive approach of ignoring measurement error in covariates. To adjust for such a bias, we describe a simulation and extrapolation method. This method is appealing because it is simple to implement and it does not require modelling the true but error-prone covariate process that is often not observable. Asymptotic normality for the resulting estimators is established. Simulation studies are carried out to evaluate the performance of the proposed method as well as the impact of ignoring measurement error in covariates. The proposed method is applied to analyse a data set arising from the Busselton Health study (Australian J. Public Health 1994; 18:129-135).