Predictive probability of success (PPOS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making.
In clinical trials, PPOS is the probability of observing a success in the future based on existing data.
A Bayesian means by which the PPOS can be determined is through integrating the data's likelihood over possible future responses (posterior distribution).
[1] Conditional power is the probability of observing a statistically significance assuming the parameter equals to a specific value.
For example, health authorities often require the magnitude of treatment effect to be bigger than statistical significance to support a registration decision.
To address this issue, Tang[5] introduced PPOS credible interval to quantify the amount of its uncertainty.
Tang advocates to use both PPOS point estimate and credible interval in applications such as decision making and clinical trial designs.
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 negative.
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 positive.
The second equation also ensures that the PPOS credible interval is not too tight such that it won't demand too much resource.
[1] Futility is when a clinical trial does not show signs of reaching its objective (i.e. providing enough to make a conclusion about the null).