Semiparametric Likelihood Estimation for Cox Regression with Subject-specific Measurement Error

Abstract

Observations from diet and disease studies are often used to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity of the additive measurement error assumption for self-report nutrient data. Recently, some study designs using more reliable biomarker data have been considered, in which the additive measurement error assumption is more likely to hold. Biomarker data are often available for a small sample, while self- reported data can be obtained from a large study cohort. Self-report data often encounter with various serious biases. Complications arise primarily because the magnitude of measurement errors is often associated with some characteristics of a study subject. A more general measurement error model has been developed for self-report data. In this paper, a semiparametric maximum likelihood estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors. This method is consistent under very general conditions. Simulation studies are presented to compare it with other naive estimation procedures.