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 ($W$) 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.
Bibliographical noteFunding Information:
R.J.C.'s research was supported by a grant from the National Cancer Institute (U01-CA057030).
© 2015 Published by Oxford University Press 2015.
- Measurement error
- Mixed models
- Nonlinear mixed models
- Nutritional epidemiology