Simulation-based sequential design

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.

Automated summary

In this paper, we review some simulation-based methods for implementing optimal decisions in sequential design problems that arise in clinical trial design. Using a simplified version of a dose-ranging design in the ASTIN trial as a motivating example, we characterize the approach as constrained backward induction. The constraint involves restricting decisions to a set of actions that are implicitly functions of the current history through a low-dimensional summary statistic.