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Bayesian Sequential Analysis For Multiple-arm Clinical Trials

机译：多臂临床试验的贝叶斯序列分析

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摘要

Use of full Bayesian decision-theoretic approaches to obtain optimal stopping rules for clinical trial designs typically requires the use of Backward Induction. However, the implementation of Backward Induction, apart from simple trial designs, is generally impossible due to analytical and computational difficulties. In this paper we present a numerical approximation of Backward Induction in a multiple-arm clinical trial design comparing k experimental treatments with a standard treatment where patient response is binary. We propose a novel stopping rule, denoted by τ~P as an approximation of the optimal stopping rule, using the optimal stopping rule of a single-arm clinical trial obtained by Backward Induction. We then present an example of a double-arm (k = 2) clinical trial where we use a simulation-based algorithm together with τ~P to estimate the expected utility of continuing and compare our estimates with exact values obtained by an implementation of Backward Induction. For trials with more than two treatment arms, we evaluate τ~P by studying its operating characteristics in a three-arm trial example. Results from these examples show that our approximate trial design has attractive properties and hence offers a relevant solution to the problem posed by Backward Induction.
机译：使用完整的贝叶斯决策理论方法来获得临床试验设计的最佳停止规则通常需要使用向后归纳法。但是，由于分析和计算上的困难，除了简单的试验设计之外，通常都不可能实施向后归纳法。在本文中，我们提供了多臂临床试验设计中反向诱导的数值近似，将k种实验治疗与标准治疗（其中患者反应为二进制）进行了比较。我们提出了一种新颖的停止规则，用Backward Induction获得的单臂临床试验的最佳停止规则，将其表示为最佳停止规则的近似值。然后，我们提供一个双臂（k = 2）临床试验的示例，在该示例中，我们将基于模拟的算法与τ〜P一起使用，以估计继续进行的预期效用，并将我们的估计值与通过实施Backward获得的准确值进行比较感应。对于具有两个以上治疗臂的试验，我们通过在三臂试验示例中研究τ〜P的操作特性来评估τ〜P。这些示例的结果表明，我们的近似试验设计具有吸引人的特性，因此可以为反向归纳法带来的问题提供相关的解决方案。

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