  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.
