Bias analysis of generalized estimating equations under measurement error and practical bias correction

A correctly specified working correlation structure ensures the efficiency in inferences for marginal regressions based on estimating equations. When there are measurement errors in covariates, however, correct specification of the working correlation structure may lead to more severe bias and higher mean squared error than working independence. We report this lesser known phenomenon and explain it in a bias analysis. The bias can be corrected using a functional approach with efficiency improved through the generalized method of moments, which works well only for large samples. For practical purposes, we further address two computational issues and correct the variance estimator for small samples. The proposed approaches are validated in simulation studies and illustrated in an example. The methods are publicly available in an R package eiv.