Measurement error as a missing data problem
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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.
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