The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under assumed data-generation processes that also define posterior distributions. Model misspecification can distort effect estimation and compromise control over operating characteristics. Generalized posterior distributions are defined using generalized likelihoods that characterize data generation under fewer assumptions, enhancing the robustness of Bayesian analysis and study design. However, widely applicable and computationally efficient design methodology with generalized posteriors is lacking. We propose an economical method to determine suitable sample sizes and decision criteria associated with generalized posteriors under the hybrid approach. Using theoretical results to model posterior summaries as functions of the sample size, we efficiently assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. While the benefits of the proposed methodology are emphasized by redesigning an adaptive clinical trial with time-to-event outcomes, we overview our framework's broader applicability to experiments involving Bayesian analogues to M-estimation.

翻译：混合实验设计方法旨在控制贝叶斯决策过程的频率学派操作特性。这些操作特性通过在后验分布所假定的数据生成过程下模拟后验汇总量的抽样分布来评估。模型误设可能导致效应估计失真并削弱对操作特性的控制。广义后验分布利用在较少假设下描述数据生成过程的广义似然函数进行定义，从而增强贝叶斯分析与研究设计的稳健性。然而，目前尚缺乏广泛适用且计算高效的基于广义后验的设计方法。本文提出一种经济性方法，用于确定混合方法框架下与广义后验分布相匹配的适宜样本量及决策准则。通过利用理论结果将后验汇总量建模为样本量的函数，我们仅需在两个样本量下进行模拟，即可高效评估整个样本量空间内的操作特性。通过重新设计一项基于时间至事件结局的自适应临床试验以凸显本方法优势的同时，我们也概述了该框架在涉及贝叶斯类比M估计的实验中的更广泛适用性。