Fitting time series models for longitudinal surveys with nonignorable missing data

In this paper, we develop a method for handling nonignorable missing data in fitting time series models for longitudinal surveys. We assume that the response probability not only depends on auxiliary variables but also the current and past outcomes which are subject to missingness. Under a nonignorable missing mechanism, an observed likelihood estimation approach is proposed based on the distribution of the observed sample and the response probability. Also, we derive a series expansion approximation for an integral in the observed likelihood function. Results from simulation studies are presented to show the usefulness of the proposed methodology. An empirical example based on data from the AIDS Clinical Trial Group 193A Study is provided to illustrate the proposed method. (C) 2021 Elsevier B.V. All rights reserved.