The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials and animal experiments, where early stopping for efficacy or futility is desirable. However, designing such studies is challenging because computing design characteristics, such as the probability of obtaining conclusive evidence or the expected sample size, typically requires computationally intensive Monte Carlo simulations, as no closed-form or efficient numerical methods exist. To address this issue, we extend results from classical group sequential design theory to sequential Bayes factor designs. The key idea is to derive Bayes factor stopping regions in terms of the z-statistic and use the known distribution of the cumulative z-statistics to compute stopping probabilities through multivariate normal integration. The resulting method is fast, accurate, and simulation-free. We illustrate it with examples from clinical trials, animal experiments, and psychological studies. We also provide an open-source implementation in the bfpwr R package. Our method makes exploring sequential Bayes factor designs as straightforward as classical group sequential designs, enabling experiments to rapidly design informative and efficient experiments.

翻译：贝叶斯因子作为从先验比到后验比的数据驱动更新因子，是衡量两个竞争假设相对证据的原则性指标。它天然适用于临床试验和动物实验等场景中的序贯数据分析，这些场景通常期望能基于有效性或无效性提前终止试验。然而，此类研究的设计具有挑战性，因为计算设计特征（例如获得决定性证据的概率或期望样本量）通常需要计算密集的蒙特卡洛模拟，目前尚无闭式解或高效数值方法可用。为解决这一问题，我们将经典成组序贯设计理论的结果推广至序贯贝叶斯因子设计。其核心思想在于基于z统计量推导贝叶斯因子停止域，并利用累积z统计量的已知分布通过多元正态积分计算停止概率。所得方法快速、准确且无需模拟。我们通过临床试验、动物实验和心理学研究的案例进行演示，并在开源R包bfpwr中提供了实现。本方法使得探索序贯贝叶斯因子设计如同经典成组序贯设计般直接，助力研究者快速设计信息丰富且高效的实验方案。