title: Measurement error models with interactions.
abstract: An important use of measurement error models is to correct regression models for bias due to covariate measurement error. Most measurement error models assume that the observed error-prone covariate (WW ) is a linear function of the unobserved true covariate (X) plus other covariates (Z) in the regression model. In this paper, we consider models for W that include interactions between X and Z. We derive the conditional distribution of X given W and Z and use it to extend the method of regression calibration to this class of measurement error models. We apply the model to dietary data and test whether self-reported dietary intake includes an interaction between true intake and body mass index. We also perform simulations to compare the model to simpler approximate calibration models.
authors.affiliation: Biometry Research Group, Division of Cancer Prevention, National Cancer Institute, 9609 Medical Center Drive, Room 5E122, Bethesda, MD 20892, USA midthund@mail.nih.gov.
authors.forename: Douglas
authors.initials: D
authors.lastname: Midthune
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA and School of Mathematical Sciences, University of Technology, Sydney, Broadway, NSW 2007, Australia.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
authors.affiliation: Gertner Institute for Epidemiology and Health Policy Research, Sheba Medical Center, Tel Hashomer 52161, Israel.
authors.forename: Laurence S
authors.initials: LS
authors.lastname: Freedman
authors.affiliation: Biometry Research Group, Division of Cancer Prevention, National Cancer Institute, 9609 Medical Center Drive, Room 5E118, Bethesda, MD 20892, USA.
authors.forename: Victor
authors.initials: V
authors.lastname: Kipnis
mesh_terms: D000328:Adult; D015992:Body Mass Index; D002138:Calibration; D003198:Computer Simulation; D004032:Diet; D005260:Female; D006801:Humans; D008297:Male; D015233:Models, Statistical; D012044:Regression Analysis; D012107:Research Design
keywords: Interactions; Measurement error; Mixed models; Nonlinear mixed models; Nutritional epidemiology