  Regression calibration is a popular approach for correcting biases in
estimated regression parameters when exposure variables are measured with
error. This approach involves building a calibration equation to estimate the
value of the unknown true exposure given the error-prone measurement and other
confounding covariates. The estimated, or calibrated, exposure is then
substituted for the true exposure in the health outcome regression model. When
used properly, regression calibration can greatly reduce the bias induced by
exposure measurement error. Here, we first provide an overview of the
statistical framework for regression calibration, specifically discussing how a
special type of error, called Berkson error, arises in the estimated exposure.
We then present practical issues to consider when applying regression
calibration, including: (1) how to develop the calibration equation and which
covariates to include; (2) valid ways to calculate standard errors (SE) of
estimated regression coefficients; and (3) problems arising if one of the
covariates in the calibration model is a mediator of the relationship between
the exposure and outcome. Throughout the paper, we provide illustrative
examples using data from the Hispanic Community Health Study/Study of Latinos
(HCHS/SOL) and simulations. We conclude with recommendations for how to perform
regression calibration.
