title: Regression calibration for models with two predictor variables measured with error and their interaction, using instrumental variables and longitudinal data.
abstract: Regression calibration provides a way to obtain unbiased estimators of fixed effects in regression models when one or more predictors are measured with error. Recent development of measurement error methods has focused on models that include interaction terms between measured-with-error predictors, and separately, methods for estimation in models that account for correlated data. In this work, we derive explicit and novel forms of regression calibration estimators and associated asymptotic variances for longitudinal models that include interaction terms, when data from instrumental and unbiased surrogate variables are available but not the actual predictors of interest. The longitudinal data are fit using linear mixed models that contain random intercepts and account for serial correlation and unequally spaced observations. The motivating application involves a longitudinal study of exposure to two pollutants (predictors) - outdoor fine particulate matter and cigarette smoke - and their association in interactive form with levels of a biomarker of inflammation, leukotriene E4 (LTE 4 , outcome) in asthmatic children. Because the exposure concentrations could not be directly observed, we used measurements from a fixed outdoor monitor and urinary cotinine concentrations as instrumental variables, and we used concentrations of fine ambient particulate matter and cigarette smoke measured with error by personal monitors as unbiased surrogate variables. We applied the derived regression calibration methods to estimate coefficients of the unobserved predictors and their interaction, allowing for direct comparison of toxicity of the different pollutants. We used simulations to verify accuracy of inferential methods based on asymptotic theory.
authors.affiliation: Division of Biostatistics & Bioinformatics, National Jewish Health, Denver, CO, U.S.A.; Department of Biostatistics & Informatics, Colorado School of Public Health, University of Colorado Denver, Denver, CO, U.S.A.
authors.forename: Matthew
authors.initials: M
authors.lastname: Strand
authors.forename: Stefan
authors.initials: S
authors.lastname: Sillau
authors.forename: Gary K
authors.initials: GK
authors.lastname: Grunwald
authors.forename: Nathan
authors.initials: N
authors.lastname: Rabinovitch
mesh_terms: D001249:Asthma / Q000209:etiology; D002648:Child; D003198:Computer Simulation; D004784:Environmental Monitoring / Q000379:methods*; D006801:Humans; D017999:Leukotriene E4 / Q000652:urine; D008137:Longitudinal Studies; D015233:Models, Statistical; D009010:Monte Carlo Method; D052638:Particulate Matter / Q000009:adverse effects / Q000032:analysis; D012044:Regression Analysis; D014028:Tobacco Smoke Pollution / Q000009:adverse effects / Q000032:analysis
chemical_list: D052638:Particulate Matter; D014028:Tobacco Smoke Pollution; D017999:Leukotriene E4
keywords: LTE 4; PM2.5; cotinine; errors in variables; measurement error; surrogate
references.citation: Stat Med. 1997 Oct 30;16(20):2349-80
references.pmid: 9351170
references.citation: J Expo Anal Environ Epidemiol. 2001 Mar-Apr;11(2):103-15
references.pmid: 11409003
references.citation: Biometrics. 2000 Jun;56(2):368-75
references.pmid: 10877291
references.citation: Stat Med. 2007 Oct 15;26(23):4293-310
references.pmid: 17340676
references.citation: J Expo Sci Environ Epidemiol. 2006 Jan;16(1):30-8
references.pmid: 16007115
references.citation: Am J Respir Crit Care Med. 2011 Dec 15;184(12):1350-7
references.pmid: 21868505
references.citation: J Expo Sci Environ Epidemiol. 2007 Sep;17(6):549-58
references.pmid: 17505504
references.citation: Stat Med. 2009 Nov 10;28(25):3158-78
references.pmid: 19777493
references.citation: Multivariate Behav Res. 2004 Jan 1;39(1):37-67
references.pmid: 26759934
references.citation: Biometrics. 2009 Dec;65(4):1003-10
references.pmid: 19302405
references.citation: Stat Med. 2004 Mar 30;23(6):987-98
references.pmid: 15027084