Dynamic treatment regimes are of growing interest across the clinicalsciences as these regimes provide one way to operationalize and thus informsequential personalized clinical decision making. A dynamic treatment regime isa sequence of decision rules, with a decision rule per stage of clinicalintervention; each decision rule maps up-to-date patient information to arecommended treatment. We briefly review a variety of approaches for using datato construct the decision rules. We then review an interesting challenge, thatof nonregularity that often arises in this area. By nonregularity, we mean theparameters indexing the optimal dynamic treatment regime are nonsmoothfunctionals of the underlying generative distribution. A consequence is that no regular or asymptotically unbiased estimator ofthese parameters exists. Nonregularity arises in inference for parameters inthe optimal dynamic treatment regime; we illustrate the effect of nonregularityon asymptotic bias and via sensitivity of asymptotic, limiting, distributionsto local perturbations. We propose and evaluate a locally consistent AdaptiveConfidence Interval (ACI) for the parameters of the optimal dynamic treatmentregime. We use data from the Adaptive Interventions for Children with ADHDstudy as an illustrative example. We conclude by highlighting and discussingemerging theoretical problems in this area.
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