Title | Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits. |
Publication Type | Journal Article |
Year of Publication | 2011 |
Authors | May, Ryan C., Joseph G. Ibrahim, and Haitao Chu |
Journal | Stat Med |
Volume | 30 |
Issue | 20 |
Pagination | 2551-61 |
Date Published | 2011 Sep 10 |
ISSN | 1097-0258 |
Keywords | Algorithms, Computer Simulation, Humans, Likelihood Functions, Limit of Detection, Linear Models, Male, Metals, Heavy, Monte Carlo Method, Neoplasms |
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. |
DOI | 10.1002/sim.4280 |
Alternate Journal | Stat Med |
Original Publication | Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits. |
PubMed ID | 21710558 |
PubMed Central ID | PMC3375355 |
Grant List | R01 CA074015-11A1 / CA / NCI NIH HHS / United States R01 GM070335-13A1 / GM / NIGMS NIH HHS / United States CA 74015 / CA / NCI NIH HHS / United States R01 GM070335 / GM / NIGMS NIH HHS / United States GM 70335 / GM / NIGMS NIH HHS / United States T32 CA106209 / CA / NCI NIH HHS / United States P01 CA142538 / CA / NCI NIH HHS / United States R01 CA074015 / CA / NCI NIH HHS / United States |
Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits.
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