贝叶斯临床试验中后验决策摘要的抽样分布估计
Estimating the Sampling Distribution of Posterior Decision Summaries in Bayesian Clinical Trials
AI总结：
本文提出利用后验分布大样本理论建立后验决策摘要抽样分布的参数模型，通过少量模拟场景估计参数，从而在纳入试验假设不确定性的同时显著降低贝叶斯临床试验设计的计算负担。
摘要：
贝叶斯推断以及使用后验或后验预测概率进行决策在临床试验中变得越来越流行。当前贝叶斯临床试验的实践依赖于一种混合的贝叶斯-频率主义方法，其中设计和决策标准通过频率主义操作特性（如功效和I类错误率）来评估，并以给定的一组参数为条件。这些操作特性通常通过模拟研究获得。最近已有研究证明了贝叶斯度量（如“保证度”）的实用性，这些度量在估计试验中各种决策的概率时纳入了关于模型参数的不确定性。然而，计算负担仍然是更广泛使用此类标准的障碍。在本文中，我们提出了一种方法，利用后验分布的大样本理论来定义用于决策的后验摘要抽样分布的参数模型。这些模型的参数使用少量模拟场景进行估计，从而改进这些模型以捕捉小到中等样本量下的抽样分布。所提出的评估条件和边际操作特性以及确定样本量的方法可被视为模拟辅助而非基于模拟的。它通过设计先验正式纳入了关于试验假设的不确定性，并显著减少了一般贝叶斯试验设计的计算负担。
英文摘要：
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate conditioning on a given set of parameters. These operating characteristics are commonly obtained via simulation studies. The utility of Bayesian measures, such as ``assurance", that incorporate uncertainty about model parameters in estimating the probabilities of various decisions in trials has been demonstrated recently. However, the computational burden remains an obstacle toward wider use of such criteria. In this article, we propose methodology which utilizes large sample theory of the posterior distribution to define parametric models for the sampling distribution of the posterior summaries used for decision making. The parameters of these models are estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward the assessment of conditional and marginal operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based. It enables formal incorporation of uncertainty about the trial assumptions via a design prior and significantly reduces the computational burden for the design of Bayesian trials in general.
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