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

Mathematics

Journal of Biometrics & Biostatistics

Author(s): May RC, Ibrahim JG, Chu H

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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. Copyright © 2011 John Wiley & Sons, Ltd.
This article was published in Stat Med and referenced in Journal of Biometrics & Biostatistics

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