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.

在本文中，我们开发了一种在纵向调查的拟合时间序列模型中处理不可忽略的缺失数据的方法。我们假设响应概率不仅取决于辅助变量，还取决于当前和过去的结果，这些结果可能会丢失。在不可忽略的缺失机制下，提出了一种基于观测样本分布和响应概率的观测似然估计方法。同样，我们推导了所观察到的似然函数中积分的级数展开近似。仿真研究的结果表明了所提出方法的有效性。提供了一个基于AIDS临床试验小组193A研究数据的经验示例，以说明所提出的方法。