Sequential decision making significantly speeds up research and is more cost-effective compared to fixed-n methods. We present a method for sequential decision making for stratified count data that retains Type-I error guarantee or false discovery rate under optional stopping, using e-variables. We invert the method to construct stratified anytime-valid confidence sequences, where cross-talk between subpopulations in the data can be allowed during data collection to improve power. Finally, we combine information collected in separate subpopulations through pseudo-Bayesian averaging and switching to create effective estimates for the minimal, mean and maximal treatment effects in the subpopulations.

翻译：序贯决策相比固定样本量方法能显著加速研究进程并更具成本效益。本文针对分层计数数据提出了一种序贯决策方法，该方法在允许可选停时情形下，利用e变量保持I型错误保证或错误发现率控制。我们通过反演该方法构建了分层任意有效置信序列，在数据收集过程中允许子种群间的信息交叉以提升统计功效。最后，我们通过伪贝叶斯平均与切换整合各子种群的收集信息，为子种群中的最小、平均及最大处理效应构建有效估计。