Non-parametric Maximum Likelihood Estimation for Cox Regression with Subject-Specific Measurement Error

• Published in: Scandinavian journal of statistics Vol. 35; no. 4; pp. 613 - 628
• Main Author: WANG, C. Y.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.12.2008; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Applications; Biological markers; biomarker data; Biomarkers; Calibration; calibration sample; Consistent estimators; corrected score; Data sampling; Estimation bias; Estimators; Exact sciences and technology; General topics; Linear inference, regression; Mathematics; measurement error; Medical sciences; Parametric inference; Probability and statistics; Questionnaires; Sampling bias; Sciences and techniques of general use; Self reports; Statistical variance; Statistics; Biometrics; Parameter estimation; Error estimation; Non parametric estimation; Multivariate analysis; Covariate; Epidemiology; biomarker data; Parametric method; Hypothesis test; Statistical test; Medical science; Measurement error; Chronic disease; Statistical association; Parametric estimation; Statistical method; Statistical regression; Experimental design; Maximum likelihood; corrected score; calibration sample; EM algorithm; Application; Biased estimation
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2008.00605.x

Many epidemiological studies have been conducted 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 in a subcohort. Self-report data often encounter with a variety of 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 non-parametric maximum likelihood (NPML) estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors.