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Abstract:
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We consider sequential adaptive designs for learning an optimal treatment rule. In particular, we consider group sequential adaptive designs in which the randomization probabilities for assigning treatment are learned from the completed data on previously recruited subjects. We demonstrate a targeted minimum loss estimator (TMLE) of the mean outcome under the optimal rule or the estimated optimal rule, with inference. We then consider a generalization to adaptive designs that adapt in continuous time so that randomization probabilities are learned from all the data available at that time, including incomplete data. We demonstrate that such adaptive designs can deal with long-term clinical outcomes by learning the treatment effect on surrogate outcomes. Again, we demonstrate a TMLE with robust inference. Finally, we consider adaptive designs within a single time-series that learn the best treatment decision from the past time-series for the sake of optimizing a short-term outcome. The asymptotic theory for the TMLE relies on martingale central limit theorem and asymptotic equicontinuity of martingale processes. We demonstrate the finite sample performance with simulations.
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