I have been trying to unpick the source of my misunderstanding. I am more familiar with the concept of asking individual patients about what outcome(s) they fear from a diagnosis (e.g. premature death within y years). The severity of the disease postulated by the diagnosis has an important bearing on the probabilities of these outcomes of course. I therefore consider estimates of the probability of the outcome conditional on disease severity with and without treatment (e.g., see Figures 1 and 2 in https://discourse.datamethods.org/t/risk-based-treatment-and-the-validity-of-scales-of-effect/6649?u=huwllewelyn ).
I then discuss at what probability difference the patient would accept the treatment. Initially this would be in the absence of cost and adverse effects to be discussed later, perhaps in an informal decision analysis. If the patient’s choice was 0.22-0.1 = 0.12 (e.g. at a score level of 100 in Figures 1 and 2 above), then this difference could be regarded as the minimum clinically important probability difference (MICIpD for that particular patient. The corresponding score of 100 would be regarded as the minimum clinically important difference (MCID) in the diagnostic test result (e.g. BP) or multivariate score. .
There will be a range of MICpDs and corresponding MICDs for different patients making up a distribution of probabilities and scores. with upper and lower 2 SDs of the score on the X axis on which the probabilities are conditioned. The lower 2SD could be regarded as a the upper end of a reference range that replaces the current ‘normal’ range. This lower 2SD could chosen as the MCID for a population with the diagnosis for RCT planning. For the sake of argument I used such an (unsubstantiated and imaginary) BP difference from zero as an example MCID in my sensitivity analysis. I am aware that there are many different ways of choosing MCIDs of course.
In my ‘power calculations for replication’ I estimate subjectively what I think the probability distribution of a study would be by estimating the BP difference and SD (without considering a MCID). I then calculate the sample size to get a power of replication in the second replicating study. If this estimate was a huge number and unrealistic I might reconsider the RCT design or not do it! The sample size should be triple the conventional Frequentist estimate for the first study. Once some interim results of the first study become known then these can be used to estimate the probability of replication in the second study by using the observed difference and SD so far in that first study and applying twice its variance. Some stopping rule can be applied based on the probability of replication as suggested in the paper flagged by @R_cubed (Power Calculations for Replication Studies (projecteuclid.org) ). The original estimated prior distribution could be combined in a Bayesian manner with the result of the first study to estimate the mean and CI of a posterior distribution. However if I did the same for estimating the probability of replication in the second study, I might over-estimate it. I would be grateful for advice about this.