Robust analysis of longitudinal data with nonignorable missing responses

We encounter missing data in many longitudinal studies. When the missing data are nonignorable, it is important to analyze the data by incorporating the missing data mechanism into the observed data likelihood function. The classical maximum likelihood (ML) method for analyzing longitudinal missing data has been extensively studied in the literature. However, it is well-known that the ordinary ML estimators are sensitive to extreme observations or outliers in the data. In this paper, we propose and explore a robust method, which is developed in the framework of the ML method, and is useful for downweighting any influential observations in the data when estimating the model parameters. We study the empirical properties of the robust estimators in small simulations. We also illustrate the robust method using incomplete longitudinal data on CD4 counts from clinical trials of HIV-infected patients.