  This article focuses on measurement error in covariates in regression
analyses in which the aim is to estimate the association between one or more
covariates and an outcome, adjusting for confounding. Error in covariate
measurements, if ignored, results in biased estimates of parameters
representing the associations of interest. Studies with variables measured with
error can be considered as studies in which the true variable is missing, for
either some or all study participants. We make the link between measurement
error and missing data and describe methods for correcting for bias due to
covariate measurement error with reference to this link, including regression
calibration (conditional mean imputation), maximum likelihood and Bayesian
methods, and multiple imputation. The methods are illustrated using data from
the Third National Health and Nutrition Examination Survey (NHANES III) to
investigate the association between the error-prone covariate systolic blood
pressure and the hazard of death due to cardiovascular disease, adjusted for
several other variables including those subject to missing data. We use
multiple imputation and Bayesian approaches that can address both measurement
error and missing data simultaneously. Example data and R code are provided in
supplementary materials.
