Analysis of longitudinal data with covariate measurement error and missing responses: An improved unbiased estimating equation

Because of the data collection process, measurement error and missing responses are common in longitudinal data, and correctly addressing these scenarios becomes one of main challenges in longitudinal data analysis. First, an unbiased estimating equation is proposed to improve the efficiency of parameter estimations for the marginal mean model for longitudinal data with covariate measurement error. The proposed unbiased estimating equation is asymptotically more efficient than the method in Qin et al. (2016a). Second, the proposed method can be extended to handle more complicated scenarios. Specifically, robust estimation for partially linear models with missing responses and covariate measurement error is considered. The proposed robust estimation does not require specifying the distribution of the covariate or the measurement error and is computationally easy to implement. Simulation studies are conducted to evaluate the improvement of the proposed method over existing methods (Qin et al., 2016b), and a sketch of the proof of its asymptotic property is provided. Finally, the proposed method is applied to the data from the Lifestyle Education for Activity and Nutrition (LEAN) study.