Johnson Valen E, Cook John D
Department of Biostatistics, M.D. Anderson Cancer Center, Houston, TX 77030, USA.
Clin Trials. 2009 Jun;6(3):217-26. doi: 10.1177/1740774509105221.
Bayesian designs are increasingly used to conduct phase II clinical trials. However, stopping boundaries in most Bayesian designs are defined from posterior credible intervals. The use of designs based on posterior credible intervals results in a loss of efficiency when compared to formal stopping rules based on Bayesian hypothesis tests. Such designs also introduce an unnecessary element of subjectivity in the interpretation of trial results.
We derive a new class of Bayesian designs based on formal hypothesis tests. The prior densities used to define the alternative hypotheses in these tests assign no mass to parameter values that are consistent with the null hypotheses and are called nonlocal alternative prior densities.
We show that Bayesian designs based on hypothesis tests and nonlocal alternative prior densities are more efficient than common Bayesian designs based on posterior credible intervals and common frequentist designs. In contrast to trial designs based on Bayesian credible intervals, we demonstrate that the mis-specification of the prior densities used to describe the anticipated effect of the experimental treatment in designs based on hypothesis tests cannot increase the expected weight of evidence in favor of the trial agent.
Extension of test-based designs to phase I-II designs and randomized phase II designs remains an open research question.
Phase II single-arm trials designed using Bayesian hypothesis tests with nonlocal alternatives provide better operating characteristics, use fewer patients per correct decision, and provide more directly interpretable results than other commonly used Bayesian and frequentist designs. Because the mis-specification of the prior density on the effect of the experimental agent decreases the expected weight of evidence that is collected in favor of the experimental treatment, the use of Bayesian hypothesis tests to design clinical trials also eliminates a potential source of bias often associated with trials designed using posterior credible intervals.
贝叶斯设计越来越多地用于进行II期临床试验。然而，大多数贝叶斯设计中的停止边界是根据后验可信区间定义的。与基于贝叶斯假设检验的正式停止规则相比，使用基于后验可信区间的设计会导致效率损失。此类设计在试验结果的解释中还引入了不必要的主观性因素。
我们基于正式的假设检验推导了一类新的贝叶斯设计。在这些检验中用于定义备择假设的先验密度不对与原假设一致的参数值赋予概率，这些先验密度被称为非局部备择先验密度。
我们表明，基于假设检验和非局部备择先验密度的贝叶斯设计比基于后验可信区间的常见贝叶斯设计和常见频率主义设计更有效。与基于贝叶斯可信区间的试验设计不同，我们证明，在基于假设检验的设计中，用于描述实验性治疗预期效果的先验密度的错误设定不会增加支持试验药物的预期证据权重。
将基于检验的设计扩展到I-II期设计和随机II期设计仍然是一个开放的研究问题。
使用带有非局部备择假设的贝叶斯假设检验设计的II期单臂试验具有更好的操作特性，每次正确决策使用的患者更少，并且比其他常用的贝叶斯和频率主义设计提供更直接可解释的结果。由于对实验药物效果的先验密度的错误设定会降低为支持实验性治疗而收集的预期证据权重，因此使用贝叶斯假设检验来设计临床试验也消除了通常与使用后验可信区间设计的试验相关的潜在偏差来源。
