Linear Transformation Models for Failure Time Data With Covariate Measurement Error

Abstract

In medical studies, patients' biological parameters are often imprecisely measured due to the measuring mechanism or the biological variability. In the presence of covariate measurement error, survival analysis using the Cox model with the observed covariate may yield a biased estimate for the regression parameter. Existing research on this topic has focused on adapting the Cox model to covariates with measurement errors. In this article we generalize linear transformation models to accommodate covariate measurement error. We derive inference procedures for the regression coefficients of examining the covariate effects on survival times under a generalized estimating equation framework. Our method relaxes the normality assumption on the unobserved true covariates and the measurement errors and can be easily adopted to conduct sensitivity analyses when the magnitude of the measurement error variance is unknown. The extra variation owing to the measurement error corrections is accounted for through an asymptotic U statistic expression of the estimator for the measurement error model parameter. We illustrate the numerical performance of our estimator with an example, and investigate it through simulation studies.

KEY WORDS:

• Generalized estimating equation
• Martingale
• Semiparametric model
• U statistic