Additive Hazards Regression with Covariate Measurement Error

Abstract

The additive hazards model specifies that the hazard function conditional on a set of covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates. This article deals with the analysis of this semiparametric regression model with censored failure time data when covariates are subject to measurement error. We assume that the true covariate is measured on a randomly chosen validation set, whereas a Surrogate covariate (i.e., an error-prone version of the true covariate) is measured on all study subjects. The Surrogate covariate is modeled as a linear function of the true covariate plus a random error. Only moment conditions are imposed on the measurement error distribution. We develop a class of estimating functions for the regression parameters that involve weighted combinations of the contributions from the validation and nonvalidation sets. The optimal weight can be selected by an adaptive procedure. The resulting estimators are consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use. Illustration with a real medical study is provided.

Key Words:

• Censoring
• Corrected score
• Error in variables
• Failure time
• Surrogate covariate.