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Abstract We consider a decision maker who faces a binary treatment choice when their welfare is only partially identified from data. We contribute to the literature by anchoring our finite-sample analysis on mean square regret, a decision criterion advocated by Kitagawa et al. in (2022) Treatment Choice with Nonlinear Regret . We find that optimal rules are always fractional, irrespective of the width of the identified set and precision of its estimate. The optimal treatment fraction is a simple logistic transformation of the commonly used t-statistic multiplied by a factor calculated by a simple constrained optimization. This treatment fraction gets closer to 0.5 as the width of the identified set becomes wider, implying the decision maker becomes more cautious against the adversarial Nature.
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Simulation‐based sequential design
Abstract We review some simulation‐based methods to implement optimal decisions in sequential design problems as they naturally arise in clinical trial design. As a motivating example we use a stylized version of a dose‐ranging design in the ASTIN trial. The approach can be characterized as constrained backward induction. The nature of the constraint is a restriction of the decisions to a set of actions that are functions of the current history only implicitly through a low‐dimensional summary statistic. In addition, the action set is restricted to time‐invariant policies. Time‐dependence is only introduced indirectly through the change of the chosen summary statistic over time. This restriction allows computationally efficient solutions to the sequential decision problem. A further simplification is achieved by restricting optimal actions to be described by decision boundaries on the space of such summary statistics.
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- Award ID(s):
- 1952679
- PAR ID:
- 10368910
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Pharmaceutical Statistics
- Volume:
- 21
- Issue:
- 4
- ISSN:
- 1539-1604
- Page Range / eLocation ID:
- p. 729-739
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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