Handling covariates subject to limits of detection in regression

Environmental and Ecological Statistics

Volumn 19, Issue 3, 2012, Pages 369-391

  Arunajadai, Srikesh G ^a   Rauh, Virginia A ^a  

^a Department of Biostatistics ^*  (United States)

Author keywords

Generalized gamma distribution; Limit of detection; Multiple imputation; Regression

Indexed keywords

COVARIANCE ANALYSIS; POLLUTION EXPOSURE; REGRESSION ANALYSIS;

EID: 84865755108     PISSN: 13528505     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10651-012-0191-6     Document Type: Article

References (33)

1. Baccarelli A, Pfeiffer R, Consonni D, Pesatori A, Bonzini M, Patterson D Jr, Bertazzi P, Landi M (2005) Handling of dioxin measurement data in the presence of non-detectable values: overview of available methods and their application in the Seveso chloracne study. Chemosphere 60(7): 898-906.
2. Carroll R, Ruppert D, Stefanski L, Crainiceanu C (2006) Measurement error in nonlinear models: a modern perspective. Chapman and Hall/CRC, Boca Raton.
3. Cox C, Chu H, Schneider M, Muñoz A (2007) Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat Med 26(23): 4352-4374.
4. Gillespie B, Chen Q, Reichert H, Franzblau A, Hedgeman E, Lepkowski J, Adriaens P, Demond A, Luksemburg W, Garabrant D (2010) Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21(4): S64.
5. Gilliom R, Helsel D (1986) Estimation of distributional parameters for censored trace level water quality data 1. estimation techniques. Water Resour Res. http://www. agu. org/pubs/crossref/1986/WR022i002p00135. shtml.
6. Gomes O, Combes C, Dussauchoy A (2008) Parameter estimation of the generalized gamma distribution. Math Comput Simul 79(4): 955-963.
7. Helsel D (1990) Less than obvious-statistical treatment of data below the detection limit. Environ Sci Technol. http://pubs. acs. org/doi/abs/10. 1021/es00082a001.
8. Helsel D (2005) Nondetects and data analysis: statistics for censored environmental data. Wiley-Blackwell, Hoboken.
9. Helsel D, Cohn T (1988) Estimation of descriptive statistics for multiply censored water quality data. Water Resour Res. http://www. agu. org/pubs/crossref/1988/WR024i012p01997. shtml.
10. Hughes J (1999) Mixed effects models with censored data with application to hiv rna levels. Biometrics. http://www3. interscience. wiley. com/journal/119061990/abstract.
11. Jacqmin-Gadda H, Thiebaut R, Chene G (2000) Analysis of left-censored longitudinal data with application to viral load in hiv infection. Biostatistics. http://biostatistics. oxfordjournals. org/cgi/content/abstract/1/4/355.
12. Jassal S, Kritz-Silverstein D, Barrett-Connor E (2010) A prospective study of albuminuria and cognitive function in older adults: the Rancho Bernardo Study. Am J Epidemiol 171: 277-286.
13. Leith K, Bowerman W, Wierda M, Best D, Grubb T, Sikarske J (2010) A comparison of techniques for assessing central tendency in left-censored data using PCB and p, p'DDE contaminant concentrations from Michigan's Bald Eagle Biosentinel Program. Chemosphere 80: 7-12.
14. Little R (1992) Regression with missing X's: a review. J Am Stat Assoc 87(420): 1227-1237.
15. Lubin J, Colt J, Camann D, Davis S, Cerhan J, Severson R, Bernstein L, Hartge P (2004) Epidemiologic evaluation of measurement data in the presence of detection limits. Environ Health Perspect 112(17): 1691.
16. Lyles R, Lyles C, Taylor D (2000) Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs. J R Stat Soc Ser C. http://www3. interscience. wiley. com/journal/119037970/abstract.
17. Lynn H (2001) Maximum likelihood inference for left-censored HIV RNA data. Stat Med 20(1): 33-45.
18. Nadarajah S, Kotz S (2006) R programs for computing truncated distributions. J Stat Softw 16: 273-278.
19. Navas-Acien A, Tellez-Plaza M, Guallar E, Muntner P, Silbergeld E, Jaar B, Weaver V (2009) Blood cadmium and lead and chronic kidney disease in US adults: a joint analysis. Am J Epidemiol 170: 1156-1164.
20. Neta G, von Ehrenstein O, Goldman L, Lum K, Sundaram R, Andrews W, Zhang J (2010) Umbilical cord serum cytokine levels and risks of small-for-gestational-age and preterm birth. Am J Epidemiol 171(8): 859.
21. Nie L, Chu H, Liu C, Cole SR, Vexler A, Schisterman EF (2010) Linear regression with an independent variable subject to a detection limit. Epidemiology 21: S17-S24. doi: 10. 1097/EDE. 0b013e3181ce97d8.
22. Prentice R (1974) A log gamma model and its maximum likelihood estimation. Biometrika 61(3): 539.
23. R Development Core Team (2010) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, http://www. R-project. org, ISBN 3-900051-07-0.
24. Raghunathan T, Lepkowski J, van Hoewyk J, Solenberger P (2001) A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodol 27(1): 85-96.
25. Richardson D, Ciampi A (2003) Effects of exposure measurement error when an exposure variable is constrained by a lower limit. Am J Epidemiol. http://aje. oxfordjournals. org/cgi/content/abstract/157/4/355.
26. Rubin D (2004) Multiple imputation for nonresponse in surveys. John Wiley and Sons Inc, Hoboken.
27. Schafer J (1999) Multiple imputation: a primer. Stat Methods Med Res 8(1): 3.
28. Schisterman E, Vexler A, Whitcomb B, Liu A (2006) The limitations due to exposure detection limits for regression models. Am J Epidemiol. 163: 374-383. http://aje. oxfordjournals. org/cgi/content/abstract/163/4/374.
29. Stacy E, Mihram G (1965) Parameter estimation for a generalized gamma distribution. Technometrics 7(3): 349-358.
30. Stein C, Savitz D, Dougan M (2009) Serum levels of perfluorooctanoic acid and perfluorooctane sulfonate and pregnancy outcome. Am J Epidemiol 170(7): 837.
31. Sutton-Tyrrell K, Zhao X, Santoro N, Lasley B, Sowers M, Johnston J, Mackey R, Matthews K (2010) Reproductive hormones and obesity: 9 years of observation from the study of women's health across the nation. Am J Epidemiol 171: 1203-1213.
32. Waller L, Turnbull B (1992) Probability plotting with censored data. Am Stat 46: 5-12.
33. Wannemuehler K, Lyles R (2005) A unified model for covariate measurement error adjustment in an occupational health study while accounting for non-detectable exposures. J R Stat Soc Ser C Appl Stat 54(1): 259-271. http://www. jstor. org/stable/3592611.