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Two-stage longitudinal studies are common in the treatment of mental diseases, such as chronic forms of major depressive disorders. Outcomes in such studies often consist of repeated measurements of scores, such as the 24-item Hamilton Rating Scale for Depression, throughout the duration of therapy. Two issues that make the analysis of data from such two-stage studies different from standard longitudinal data are: (1) the randomization in the second stage for patients who fail to respond in the first stage; and (2) the drop-out of patients which sometimes occurs before the second stage. In this article, we show how the weighted generalized estimating equations can be used to draw inference for treatment regimes from two-stage studies. Specifically, we show how to construct weights and use them in the generalized estimating equations to derive consistent estimators of regime effects, and compare them. Large-sample properties of the proposed estimators are derived analytically, and examined through simulations. We demonstrate our methods by applying them to a depression dataset.

Weighted generalized estimating equations for response-adaptive treatment regimes in two-stage longitudinal studies