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

Statistics in Medicine

Volumn 30, Issue 20, 2011, Pages 2551-2561

  May, Ryan C ^a   Ibrahim, Joseph G ^a   Chu, Haitao ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

EM algorithm; Gibbs sampling; Logistic regression; Maximum likelihood estimation; Monte Carlo EM; NHANES

Indexed keywords

HEAVY METAL;

ALGORITHM; ANALYTIC METHOD; ARTICLE; COVARIANCE; DATA ANALYSIS; LIMIT OF DETECTION; LINEAR REGRESSION ANALYSIS; LOGISTIC REGRESSION ANALYSIS; MAXIMUM LIKELIHOOD METHOD; MONTE CARLO METHOD; SIMULATION; STATISTICAL MODEL; URINE LEVEL; COMPUTER SIMULATION; HUMAN; MALE; NEOPLASM; URINE;

ALGORITHMS; COMPUTER SIMULATION; HUMANS; LIKELIHOOD FUNCTIONS; LIMIT OF DETECTION; LINEAR MODELS; MALE; METALS, HEAVY; MONTE CARLO METHOD; NEOPLASMS;

EID: 80051796418     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.4280     Document Type: Article

References (22)

1. Centers for Disease Control and Prevention (CDC). National Health and Nutrition Examination Survey Data. 2005-2006.
2. Rigobon R, Stoker TM. Estimation with censored regressors: basic issues. International Economic Review 2007; 48(4):1441-1467.
3. D'Angelo G, Weissfeld L. An index approach for the Cox model with left censored covariates. Statistics in Medicine 2008; 27:4502-4514.
4. Nie L, Chu H, Liu C, Cole SR, Vexler A, Schisterman EF. Linear regression with an independent variable subject to a detection limit. Epidemiology 2010; 21(4):S17-S24.
5. Helsel DR. Nondetects and Data Analysis: Statistics for Censored Environmental Data: New York, 2004.
6. Lynn H. Maximum likelihood inference for left-censored HIV RNA data. Statistics in Medicine 2001; 20:33-45.
7. Helsel DR. Fabricating data: how substituting values for nondetects can ruin results, and what can be done about it. Chemosphere 2006; 65:2434-2439.
8. Lubin JH, Colt JS, Camann D, Davis S, Cerhan JR, Severson RK, Bernstein L, Hartge P. Epidemiologic evaluation of measurement data in the presence of detection limits. Environmental Health Perspectives 2004; 112(17):1691-1696.
9. Singh A, Nocerino J. Chemometrics and Intelligent Laboratory Systems, Vol. 60, 2002.
10. Thompson M, Nelson KP. Linear regression with Type I interval- and left-censored response data. Environmental and Ecological Statistics 2003; 10:221-230.
11. Richardson DB, Ciampi A. Effects of exposure measurement error when an exposure variable is constrained by a lower limit. American Journal of Epidemiology 2003; 157(4):355-363.
12. Schisterman E, Vexler A, Whitcomb B, Liu A. The limitations due to exposure detection limits for regression models. American Journal of Epidemiology 2006; 163(4):374-383.
13. Cole SR, Chu H, Nie L, Schisterman EF. Estimating the odds ratio when exposure has a limit of detection.International Journal of Epidemiology 2009; 38:1674-1680.
14. Tobin J. Estimation of relationships for limited dependent variables. Econometrica 1958; 26:24-36.
15. Ibrahim JG. Incomplete data in generalized linear models. Journal of the American Statistical Association 1990; 85:765-769.
16. Lipsitz SR, Ibrahim JG. A conditional model for incomplete covariates in parametric regression models. Biometrika 1996; 72:916-922.
17. Ibrahim JG, Lipsitz SR, Chen M. Missing covariates in generalized linear models when the missing data mechanism is non-ignorable. Journal of the Royal Statistical Society, Series B 1999; 61:173-190.
18. Wei GC, Tanner MA. A Monte Carlo implementation of the EM algorithm and the poor dan's data augmentation algorithms. Journal of the American Statistical Association 1990; 85:699-704.
19. Gilks WR, Best NG, Tan KKC. Adaptive rejection metropolis sampling within Gibbs sampling. Applied Statistics 1995; 44:455-472.
20. Gilks WR, Wild P. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 1992; 41:337-348.
21. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics 1953; 21:1087-1092.
22. Louis T. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 1982; 44:226-233.