Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits

• Published in: Statistics in medicine Vol. 30; no. 20; pp. 2551 - 2561
• Main Authors: May, Ryan C., Ibrahim, Joseph G., Chu, Haitao
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.09.2011; Wiley Subscription Services, Inc
• Subjects: Algorithms; Computer Simulation; Data analysis; EM algorithm; Gibbs sampling; Humans; Likelihood Functions; Limit of Detection; Linear Models; logistic regression; Male; maximum likelihood estimation; Maximum likelihood method; Medical statistics; Metals, Heavy - urine; Monte Carlo EM; Monte Carlo Method; Monte Carlo simulation; Neoplasms - urine; NHANES; Urology; NHANES; Gibbs sampling; logistic regression; EM algorithm; maximum likelihood estimation; Monte Carlo EM
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.4280

The analysis of data subject to detection limits is becoming increasingly necessary in many environmental and laboratory studies. Covariates subject to detection limits are often left censored because of a measurement device having a minimal lower limit of detection. In this paper, we propose a Monte Carlo version of the expectation–maximization algorithm to handle large number of covariates subject to detection limits in generalized linear models. We model the covariate distribution via a sequence of one‐dimensional conditional distributions, and sample the covariate values using an adaptive rejection metropolis algorithm. Parameter estimation is obtained by maximization via the Monte Carlo M‐step. This procedure is applied to a real dataset from the National Health and Nutrition Examination Survey, in which values of urinary heavy metals are subject to a limit of detection. Through simulation studies, we show that the proposed approach can lead to a significant reduction in variance for parameter estimates in these models, improving the power of such studies. Copyright © 2011 John Wiley & Sons, Ltd.