Sequential designs drive innovation in clinical, industrial, and corporate settings. Early stopping for failure in sequential designs conserves experimental resources, whereas early stopping for success accelerates access to improved interventions. Bayesian decision procedures provide a formal and intuitive framework for early stopping using posterior and posterior predictive probabilities. Design parameters including decision thresholds and sample sizes are chosen to control the error rates associated with the sequential decision process. These choices are routinely made based on estimating the sampling distribution of posterior summaries via intensive Monte Carlo simulation for each sample size and design scenario considered. In this paper, we propose an efficient method to assess error rates and determine optimal sample sizes and decision thresholds for Bayesian sequential designs. We prove theoretical results that enable posterior and posterior predictive probabilities to be modeled as a function of the sample size. Using these functions, we assess error rates at a range of sample sizes given simulations conducted at only two sample sizes. The effectiveness of our methodology is highlighted using two substantive examples.

翻译：序贯设计在临床、工业和商业环境中推动着创新。序贯设计中因失败而提前终止可节省实验资源，而因成功而提前终止则能加速获得改进的干预措施。贝叶斯决策程序为利用后验概率和后验预测概率进行提前终止提供了形式化且直观的框架。通过选择包括决策阈值和样本量在内的设计参数，可以控制与序贯决策过程相关的错误率。这些选择通常基于对每个考虑的样本量和设计场景，通过密集的蒙特卡洛模拟来估计后验摘要的抽样分布。本文提出了一种高效的方法，用于评估贝叶斯序贯设计的错误率并确定最优样本量与决策阈值。我们证明了可将后验概率与后验预测概率建模为样本量函数的理论结果。利用这些函数，我们仅基于在两个样本量下进行的模拟，即可评估一系列样本量下的错误率。我们通过两个实质性案例突显了该方法的有效性。