Measurement error models with interactions.

Author(s): Midthune D,  Carroll RJ,  Freedman LS,  Kipnis V

Journal: Biostatistics

Date: 2016 Apr

Major Program(s) or Research Group(s): BRG

PubMed ID: 26530858

PMC ID: PMC4834948

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.