You can view a typical power calculation not as guess work, but as an estimate of the unknown fixed true power. This means you can also perform inference on power by constructing a confidence interval for it using parameter estimates and standard error estimates from historical studies. In the example below the point estimate of power is above 90% but the inference cannot rule out that the true power might be considerably lower.
Example: A phase 2 and 3 development plan is being created for an asset to treat an immuno-inflammation disorder. Phase 3 is planned as a non-inferiority study using a difference in proportions on a binary responder index. The non-inferiority margin is set by the regulatory agency at –0.12, as is the one-sided significance level of 0.025. Phase 2 is a dose finding study on a continuous endpoint. This study also collects data on the responder index and includes a control arm to estimate the difference in proportions planned for phase 3. A stricter non-inferiority margin of –0.05 is considered in phase 2, but since the sample size in phase 2 is typically smaller than in phase 3, a larger one-sided significance level of 0.20 is tolerated. Based on a literature review the estimated response proportion for the comparator is 0.43 with N=1200.
The power curve shows the long-run probability of succeeding in phase 3 as a function of the unknown true difference in proportions based on N=365 subjects per arm when testing Ho: Difference in Proportions ≤ –0.12 at the one-sided 0.025 significance level using a likelihood ratio test. This long-run probability forms the level of confidence in the next experimental outcome. If one is satisfied with the inference on phase 3 power given minimal success in phase 2, one would be satisfied for any other successful phase 2 result. The confidence curve above depicts one-sided p-values and confidence intervals of all levels by inverting a likelihood ratio test, showing what minimal success would look like at the end of phase 2. This is based on N=90 subjects per arm, a 0.43 response rate estimate in the control arm, and an estimated difference in proportions of 0.01 (minimum detectable effect) testing Ho: Difference in Proportions ≤ –0.05. This produces a one-sided p-value of 0.20. A nearly identical confidence curve can be produced by inverting a Wald test using an identity link function. The p-value depicts the ex-post sampling probability of the observed phase 2 result or something more extreme if the hypothesis for the difference in proportions is true. This long-run probability represents the plausibility of the hypothesis given the data.
The figure above shows that minimal success in phase 2 produces inference around high values of phase 3 power, but still assumes some risk. While the maximum likelihood estimate of phase 3 power is 95.9%, one can claim with only 80% confidence that the power of the phase 3 study is no less than 50% given minimal success in phase 2 (p-value = 0.2 testing Ho: Phase 3 Power ≤ 0.50). The phase 2 null hypothesis Ho: Difference in Proportions ≤ –0.05 was chosen as the value at which phase 3 power is 50%.
In my view ensuring phase 3 power is no worse than a coin toss conditional on passing phase 2 is a good rule of thumb. If stronger inference on phase 3 power is desired given minimal success in phase 2, one could simply increase the phase 3 sample size. This will steepen the phase 3 power curve relative to the phase 3 null hypothesis by lowering the phase 3 minimum detectable effect. Alternatively, one could adjust the phase 2 significance level and null hypothesis, and select the phase 2 sample size based on an acceptable phase 2 minimum detectable effect. Once the phase 2 study results are available, two-sided confidence limits for phase 3 power can be provided along side the maximum likelihood point estimate. These point and interval estimates can even be plotted as a function of the phase 3 sample size.
Here is a paper that discusses performing inference on power and compares this to Bayesian probability of success. Here is a related LinkedIn article.