Some thoughts on stat power. First, we compute
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First, we compute p-values under the assumption the drug has zero effect.
Computing power requires stating an alternative: i.e. 80% odds of detecting a signal (i.e. p=<.05 under the no drug effect assumption) if in the larger population the effect size is "X."
So the results come in statistically significant - there is still a CI on X, and the boundary could be close to no benefit. And, yes, lower powered trials will have wider CIs.
To me, someone saying a stat significant trial is "underpowered" is just saying the effect size isn't well determined, may well be close to zero, and conveying that they internally are running the tests with a small, but positive required minimum drug effect for adoption - perhaps weighing clinical significance.
Appreciate thoughts / relevant computations to the contrary.