Intrigued by Effect sizes for power and evidence for effectiveness, I have been reading Frank’s Introduction to Bayes for Evaluation of Treatments, and find the following heading §2.1
Utility functions are extremely difficult to specify in latephase drug development. Even though we seldom provide this function we need to provide the inputs (posterior probability distribution) to decisions that will be based on an informal utility function.
This section also sent me to Spiegelhalter (1986) [1] and thence to Box (1980) [2]. Box emphasizes Bayes as a technology for estimation from a given model “conditional on its truth”, which at once necessitates and enables an attendant process of model criticism — the model might not be true! — via sampling theory. (Cf. BDA3 § 4.4 ‘Frequency evaluations of Bayesian inferences’.)
Talking about scientific modelbuilding, Box says [emphasis mine]:
In any such enterprise many subjective choices are made, conscious or unconscious, good or bad. They determine for instance which plots, displays and checks of data and residuals are looked at; and what treatments and variables are included at which levels, over what experimental region, in which transformation, in what design, to illuminate which models. The wisdom of these choices over successive stages of development is the major determinant of how fast the iteration will converge or of whether it converges at all, and distinguishes good scientists and statisticians from bad. It is in this context that theories of inference need be considered. While it is comforting to remember that a good scientific iteration is likely to share the property of a good numerical iteration—that mistakes often are selfcorrecting, this also implies that the investigator must worry particularly about mistakes which are likely not to be selfcorrecting.
So now here is a challenge: if we are leaving utilities implicit in adaptive Bayesian trial designs, then to produce robust regulatory decisions we may wish to find methods for recovering these utilities (at least approximately) so that we can subject them to criticism.
I recognize of course that this is an illposed inverse problem, but has this sort of thing been attempted previously? (I have undertaken efforts in this vein, relative to the implicit priors in certain trial designs [3].)

Spiegelhalter DJ. Probabilistic prediction in patient management and clinical trials. Statistics in Medicine. 1986;5(5):421433. doi:10.1002/sim.4780050506

Box GEP. Sampling and Bayes’ Inference in Scientific Modelling and Robustness. Journal of the Royal Statistical Society Series A (General). 1980;143(4):383. doi:10.2307/2982063

Norris DC. What Were They Thinking? Pharmacologic priors implicit in a choice of 3+3 doseescalation design. arXiv:201205301 [statME]. Published online December 24, 2020. Accessed December 25, 2020. https://arxiv.org/abs/2012.05301