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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. 

Randomized clinical trials have been the mainstay of clinical research, but are prohibitively expensive and subject to increasingly difficult patient recruitment. Recently, there is a movement to use real-world data (RWD) from electronic health records, patient registries, claims data and other sources in lieu of or supplementing controlled clinical trials. This process of combining information from diverse sources calls for inference under a Bayesian paradigm. We review some of the currently used methods and a novel non-parametric Bayesian (BNP) method. Carrying out the desired adjustment for differences in patient populations is naturally done with BNP priors that facilitate understanding of and adjustment for population heterogeneities across different data sources. We discuss the particular problem of using RWD to create a synthetic control arm to supplement single-arm treatment only studies. At the core of the proposed approach is the model-based adjustment to achieve equivalent patient populations in the current study and the (adjusted) RWD. This is implemented using common atoms mixture models. The structure of such models greatly simplifies inference. The adjustment for differences in the populations can be reduced to ratios of weights in such mixtures. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.