Abstract
Inference for parameters associated with optimal dynamic treatment regimes is challenging as these estimators are nonregular when there are non-responders to treatments. In this discussion, we comment on three aspects of alleviating this nonregularity. We first discuss an alternative approach for smoothing the quality functions. We then discuss some further details on our existing work to identify non-responders through penalization. Third, we propose a clinically meaningful value assessment whose estimator does not suffer from nonregularity.
Highlights
The authors are to be congratulated for their excellent and thoughtful paper on statistical inference for dynamic treatment regimens
We discuss replacing the nonsmooth objective functions via a SoftMax Q-learning approach, which directly addresses the trade-off between bias and variance of the maximum operation in the local asymptotic framework
We briefly describe the SoftMax Q-learning algorithm, and present some theoretical and simulation results
Summary
The authors are to be congratulated for their excellent and thoughtful paper on statistical inference for dynamic treatment regimens. They have addressed several important and long-standing issues in this area. As discussed by the authors, nonsmoothness of the problem in some of the parameters of interest leads to estimators that are not smooth in the data. Nonregularity of the estimators for the parameters associated with the optimal treatment regimes is mainly due to the existence of non-responders to treatments. It would be useful and important if we could identify these non-responders. We claim that this alternative value function is clinically meaningful and does not suffer from nonregularity
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