The probability of success (POS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making.
To address this issue, we can consider conditional power in a Bayesian setting by considering the treatment effect parameter to be a random variable.
Traditional pilot trial design is typically done by controlling type I error rate and power for detecting a specific parameter value.
The first equation ensures that the PPOS is small such that not too many trials will be prevented entering next stage, to guard against false negatives.
The first equation also ensures that the PPOS is not too small such that not too many trials will enter the next stage, to guard against false positives.
The second equation also ensures that the PPOS credible interval is not too tight such that it won't demand too many resources.
In contrast probability of success has an intuitive interpretation and hence can facilitate communication with non-statistician colleagues.
Tang (2016)[3][4] proposes the use of the following criteria to support efficacy interim decision making: mCPOS>c1 lCPOS>c2 where mCPOS is the median of CPOS with respect to the distribution of the parameter and lCPOS is the lower bound of the credible interval of CPOS.