Bias correction for multiple covariate analysis using empirical bayesian estimation in mixed-effects models for longitudinal data

Abstract

The naïve empirical Bayes method has been widely used as an ad hoc tool in fitting linear mixed-effect models, which is much computationally efficient than the maximum likelihood estimation method. However, the shrinkage effect of the empirical Bayes method causes bias in the estimates of the fixed effects. Bias-correction has been proposed for the mixed-effects model when only one covariate is present. In this paper, we derive the shrinkage factor of the empirical Bayes predictors of the random effects and the variance-covariance matrix of the corrected estimates when the model has more than one covariate. The empirical Bayes estimates and test statistics are then corrected using the derived factor. Theoretical derivations, simulation studies and a real data application demonstrate the validity of the proposed method in that the corrected estimates are unbiased and the corrected tests have correct p-values.