title: Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits.
abstract: 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.
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA. ryanmay@unc.edu.
authors.forename: Ryan C
authors.initials: RC
authors.lastname: May
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D057230:Limit of Detection; D016014:Linear Models; D008297:Male; D019216:Metals, Heavy / Q000652:urine; D009010:Monte Carlo Method; D009369:Neoplasms / Q000652:urine
chemical_list: D019216:Metals, Heavy