Nonignorable missing data occur frequently in longitudinal studies and can cause biased estimations. Refreshment samples which draw new subjects randomly in subsequent waves from the original population could mitigate the bias. In this paper, we introduce a mixed-effects estimating equation approach that enables one to incorporate refreshment samples and recover informative missing information from the measurement process. We show that the proposed method achieves consistency and asymptotic normality for fixed-effect estimation under shared-parameter models, and we extend it to a more general nonignorable-missing framework. Our finite sample simulation studies show the effectiveness and robustness of the proposed method under different missing mechanisms. In addition, we apply our method to election poll longitudinal survey data with refreshment samples from the 2007-2008 Associated Press-Yahoo! News.
Bibliographical noteFunding Information:
by the National Science Foundation
This research was partially supported by the National Science Foundation (DMS-1308227). The authors thank the Editor, An associate editor, and two reviewers for helpful comments and suggestions.
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- Missing not at random
- Non-monotone missing pattern
- Quadratic inference function
- Shared-parameter model
- Survey data