Thank you very much for your responses. I have also read the paper attached by @andrewgelman regarding multiple hypothesis comparisons, which I find to be very elegant; however, it is quite difficult to apply to hypotheses that measure very different things; for instance, in clinical trials, where a drug needs to present its efficacy and safety across a set of outcomes that differ from one another.
To put in context, FDA or EMA have always used methods to control the Family-Wise Error Rate (FWER), such as the Holm procedure or Bonferroni correction, in addition to requiring the presentation of a confidence interval for each hypothesis. However, I want to change this arbitrary criteria, and I am trying to introduce Bayesian knowledge into the approval of drugs (despite complicating my life). What would be the correct way to present the outcomes for approval? As I mentioned earlier, it feels [1] the Stan community is against presenting any 95% intervals. Reading BARG [2] from @JohnKruschke, seems that the alternative would be to present a Bayes factor, or the posterior probability that an outcome is greater than 0, right? And regarding multiple comparisons, these agencies do not understand that there is no need to correct for multiple hypotheses. Should a multilevel model be made for, say, 8 hypotheses, even if they measure very different things? e.g. how would this be done to multiple test two hypothesis that measure the impact on a biomarker and a satisfaction test? Is there any solid argument to convince them that there is no need for multiple correction? Thank you very much for all the interaction in this post.