Statistical Methods for Generalized Linear Models with Covariates Subject to Detection Limits

Arunajadai SG, Rauh VA (2012) Handling covariates subject to limits of detection in regression. Environ Ecol Stat 157:369–391

Austin PC, Brunner LJ (2003) Type I error inflation in the presence of a ceiling effect. Am Stat 57:97–104

Austin PC, Hoch JS (2004) Estimating linear regression models in the presence of a censored independent variable. Stat Med 23:411–429

Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:677–692

Firth D (1993) Bias reduction of maximum likelihood estimates. Biometrika 23:27–38

Giovanini J (2008) Generalized linear mixed models with censored covariates. PhD thesis, Oregon State University

Helsel DR (2012) Statistics for censored environmental data using minitab and R. Wiley, New York

Herring AH, Ibrahim JG (2001) Likelihood-based methods for missing covariates in the Cox proportional hazards model. J Am Stat Assoc 96:292–302

Herring AH, Ibrahim JG, Lipsitz SR (2004) Non-ignorable missing covariate data in survival analysis: a case-study of an international breast cancer study group trial. J R Stat Soc, Ser C, Appl Stat 53:293–310

Hofert M, Kojadinovic I, Maechler M, Yan J (2012) Copula: Multivariate dependence with copulas. R package version 0.999-5. http://CRAN.R-project.org/package=copula

Hornung RW, Reed LD (1990) Estimation of average concentration in the presence of nondetectable values. Appl Occup Environ Hyg 5:46–51

Hughes JP (1999) Mixed effects models with censored data with application to HIV RNA levels. Biometrics 55:625–629

Ibrahim JG, Chen MH, Lipsitz SR (2002) Bayesian methods for generalized linear models with covariates missing at random. Can J Stat 30:55–78

Ibrahim JG, Chen MH, Lipsitz SR, Herring AH (2005) Missing-data methods for generalized linear models: a comparative review. J Am Stat Assoc 100:332–346

Kellum JA, Kong L, Fink MP, Weissfeld LA, Yealy DM, Pinsky MR, Fine J, Krichevsky A, Delude R, Angus D (2007) Understanding the inflammatory cytokine response in pneumonia and sepsis. Arch Intern Med 167:1655–1663

Lee M, Kong L, Weissfeld L (2012) Multiple imputation for left-censored biomarker data based on Gibbs sampling method. Stat Med 31:1838–1848

Lipsitz SR, Ibrahim JG, Chen MH, Peterson H (1999) Non-ignorable missing covariates in generalized linear models. Stat Med 18:2435–2448

Little RJA (1992) Regression with missing x’s: a review. J Am Stat Assoc 87:1227–1237

Lubin JH, Colt JS, Camann D, Davis S, Cerhan JR, Severson RK, Bernstein L, Hartge P (2004) Epidemiologic evaluation of measurement data in the presence of detection limits. Environ Health Perspect 112:1691–1696

Lyles RH, Lyles CM, Taylor DJ (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, Appl Stat 49:485–497

Lyles RH, Fan D, Chauchoowon R (2001) Correlation coefficient estimation involving a left censored laboratory assay variable. Stat Med 20:2921–2933

Lynn HS (2001) Maximum likelihood inference for left-censored HIV RNA data. Stat Med 20:33–45

May RC, Ibrahim JG, Chu H (2011) Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits. Stat Med 30:2551–2561

Moulton LH, Halsey NA (1995) A mixture model with detection limits for regression analysis of antibody response to vaccine. Biometrics 51:1570–1578

Nan B, Kalbfleisch JD, Yu M (2009) Asymptotic theory for the semiparametric accelerated failure time model with missing data. Ann Stat 37:2351–2376

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 21S:S17–S24

Paxton WB, Coombs RW, McElrath MJ, Keefer MC, Hughes J, Sinagil F, Chernoff D, Demeter L, Williams B, Corey L (1997) Longitudinal analysis of quantitative virologic measures in human immunodeficiency virus-infected subjects with ≥400 cd4 lymphocytes: implications for applying measurements to individual patients. J Infect Dis 175:247–254

Pettitt AN (1986) Censored observations, repeated measures and mixed effects models—An approach using the em algorithm and normal errors. Biometrika 73:635–643

Piepho H-P, Thoni H, Müller H-M (2002) Estimating the product-moment correlation in samples with censoring on both variables. Biom J 44:657–670

Rigobon R, Stoker TM (2007) Estimation with censored regressors: basic issues. Int Econ Rev 48:1441–1467

Rigobon R, Stoker TM (2009) Bias from censored regressors. J Bus Econ Stat 27:340–353

Robins JM, Wang N (2000) Inference for imputation estimators. Biometrika 87:113–124

Rubin DB (1987) Multiple imputation for nonresponse. In: Surveys. Wiley, New York

Schaubel DE, Cai J (2006) Multiple imputation methods for recurrent event data with missing event category. Can J Stat 34:677–692

Thiebaut R, Jacqmin-Gadda H, Babiker A, Commenges D (The CASCADE Collaboration) (2005) Joint modelling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of cd4+ cell count and HIV RNA viral load in response to treatment of HIV infection. Stat Med 24:65–82

Tsiatis AA (2006) Semiparametric theory and missing data. Springer, Berlin

Tsimikas JV, Bantis LE, Georgiou SD (2012) Inference in generalized linear regression models with a censored covariate. Comput Stat Data Anal 56:1854–1868

Wang H, Feng X (2012) Multiple imputation for m-regression with censored covariates. J Am Stat Assoc 107:194–204

Wang H, Fygenson M (2009) Inference for censored quantile regression models in longitudinal studies. Ann Stat 37:756–781

Wang N, Robins JM (1998) Large-sample theory for parametric multiple imputation procedures. Biometrika 84:935–948

Wu H, Chen Q, Ware LB, Koyama T (2012) A Bayesian approach for generalized linear models with explanatory biomarker measurement variables subject to detection limit—An application to acute lung injury. Appl Stat 39:1733–1747

Wu L (2002) A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with applications to aids studies. J Am Stat Assoc 97:955–964