A propensity score adjustment method for longitudinal time series models under nonignorable nonresponse

Analysis of data with nonignorable nonresponse is an important and challenging task. Although some methods have been developed for inference under nonignorable nonresponse, they are only available for independent data. In this paper, we develop a two-stage propensity score adjustment method to estimate longitudinal time series models with nonignorable missingness. In particular, the response probability or propensity score is first estimated via solving the mean score equation based on the observed sample. Then, the inverse propensity scores are employed to conduct weighting adjustment for a composite likelihood based estimation. The propensity scores weighted estimation equations are shown to yield consistent and asymptotic normal estimators. Simulation studies and application to AIDS Clinical Trial data are presented to evaluate the performance of the proposed method.