Simulation‐based sequential design

• Published in: Pharmaceutical statistics : the journal of the pharmaceutical industry Vol. 21; no. 4; pp. 729 - 739
• Main Authors: Müller, Peter, Duan, Yunshan, Garcia Tec, Mauricio
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Inc 01.07.2022; Wiley Subscription Services, Inc
• Subjects: backward induction; decision problem; reinforcement learning; sequential design
• ISSN: 1539-1604; 1539-1612
• DOI: 10.1002/pst.2216

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.