Time Series Analysis for Longitudinal Survey Data under Informative Sampling and Nonignorable Missingness

The analysis of longitudinal survey data is often complicated when informative sampling or non-ignorable missing data exists. Existing methods that can handle both informative sampling and nonignorable missing data are only limited to the situation of no time dependence in the data. In this paper, we develop a sample likelihood based approach for estimation of time series model in longitudinal survey data under informative sampling and nonignorable missingness. In particular, some informative sampling models and a response model are proposed to describe the mechanisms of informative sampling and nonignorable missingness. A sample likelihood is derived based on the conditional distribution of the observed measurements. Also, an effective computation algorithm is developed to compute the sample likelihood. Simulation studies are carried out to investigate the performance of the proposed estimator. A real data example based on data from AIDS Clinical Trial Group 193A Study is presented to illustrate the proposed method.