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Abstract:
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Percentile-finding sequential designs aim to concentrate treatment allocation around the target percentile $Q_p$, as quickly and efficiently as possible. The 'Up-and-Down' (U&D) algorithm utilizes the Markov property, to converge with a geometric rate to a stationary treatment distribution peaked near $Q_p$. The Bayesian CRM approach, developed in the context of Phase I clinical trials, utilizes a parametric model to achieve better asymptotic allocation concentration than U&D. However, CRM's rate of convergence is $\sqrt{n}$ at best. We propose to combine the two approaches within a Bayesian framework. The U&D transition rule is used as a default, to be overridden only when the CRM transition promises improvement with acceptable posterior credibility. Simulation results demonstrate the potential of this approach for Phase I and other percentile-finding applications.
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