Applying Linear Mixed-Effects Models to the Problem of Measurement Error in Epidemiologic Studies

Abstract

Although studies of the relationship between risk factors measured at baseline and a binary outcome are common problems occurring in statistical analyses of epidemiologic studies, little has been written about what constitutes a good measure of the true baseline value of a risk factor. This paper considers different schemes of providing for baseline risk factor data and proposes and compares methods for correcting estimates of relative risks for bias due to measurement error. Repeated measurements taken at baseline appear to allow for a correction in the estimate of risk that is comparable to the correction based on repeated measurements over a number of visits close to baseline. The procedures proposed are regression calibration/imputation type methods that involve estimating the covariates with less error and using these estimates in the standard model for the risk factor analysis. Shrinkage estimates from a linear mixed-effects model for multiple measurements at baseline are proposed as a method for estimating the true level of a risk factor at baseline. A simulation study shows that these shrinkage estimates give estimates of the risk of the outcome which have a smaller mean square error and confidence interval coverage proportions much closer to the nominal level than would be obtained using the observed data. This new imputation method is compared to the measurement error correction method earlier proposed by Rosner et al. (Rosner, B., Spiegelman, D., Willett, W. C. (1992). Correction of logistic regression relative risk estimates and confidence intervals for random within-person measurement error. American Journal of Epidemiology 136:1400–1413). In addition, the standard errors from the new method are compared to a nonparametric bootstrap estimate of the standard errors as well as to the asymptotic standard errors obtained using a method proposed by Carroll and Stefanski (Carroll, R. J., Stefanski, L. A. (1990). Approximate Quasi-likelihood Estimation in Models With Surrogate Predictors. Journal of the American Statistical Association 85:652–663).