Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers

Measurement errors and outliers commonly arise during the process of longitudinal data collection and ignoring them in data analysis can lead to large deviations in estimates. Therefore, it is important to take into account the effect of measurement errors and outliers in longitudinal data analysis. In this paper, a robust estimating equation method for analyzing longitudinal data with covariate measurement errors and outliers is proposed. Specifically, the biases caused by measurement errors are reduced via using the independence between replicate measurements and the biases caused by outliers are corrected via centralizing the observed covariate matrix. The proposed method does not require specifying the distributions of the true covariates, response and measurement errors. In practice, it can be easily implemented via the standard generalized estimating equations algorithms. The asymptotic normality of the proposed estimator is established under regularity conditions. Extensive simulation studies show that the proposed method performs better in handling measurement errors and outliers than several existing methods. For illustration, the proposed method is applied to a data set from the Lifestyle Education for Activity and Nutrition (LEAN) study.