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.

翻译：贝叶斯推断以及使用后验概率或后验预测概率进行决策在临床试验中日益流行。当前贝叶斯临床试验的实践依赖于一种混合贝叶斯-频率学派方法，其中设计标准和决策准则通过频率学派操作特征（如给定参数集条件下的检验功效和第一类错误率）进行评估。这些操作特征通常通过模拟研究获得。近期研究已证明，贝叶斯度量（例如“保证度”）通过在估计试验中各种决策概率时纳入模型参数的不确定性而具有实用性。然而，计算负担仍是更广泛应用此类准则的主要障碍。本文提出一种方法，利用后验分布的大样本理论来定义用于决策的后验汇总抽样分布的参数模型。这些模型的参数通过少量模拟场景进行估计，从而优化模型以捕捉小至中等样本量下的抽样分布。所提出的方法用于评估条件性和边际性操作特征及确定样本量，可视为"模拟辅助型"而非"模拟驱动型"。该方法通过设计先验正式纳入试验假设的不确定性，并显著降低了贝叶斯试验设计的计算负担。