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Sequential decision making significantly speeds up research and is morecost-effective compared to fixed-n methods. We present a method for sequentialdecision making for stratified count data that retains Type-I error guaranteeor false discovery rate under optional stopping, using e-variables. We invertthe method to construct stratified anytime-valid confidence sequences, wherecross-talk between subpopulations in the data can be allowed during datacollection to improve power. Finally, we combine information collected inseparate subpopulations through pseudo-Bayesian averaging and switching tocreate effective estimates for the minimal, mean and maximal treatment effectsin the subpopulations.

Safe Sequential Testing and Effect Estimation in Stratified Count Data