I am having trouble with interpretation of a prospective superiority randomised controlled trial. Study characteristics:
- Alpha value = 0.05
- 1-beta = 0.8
- Predicted effect size =0.15 [P1 = 0.65, P2 = 0.5]
- Numbers needed = 492
Effect size = 0.09 [P1 = 0.50, P2 = 0.41]
Numbers enrolled = 502
statistically significant P value -> P = 0.03
null hypothesis is rejected.
My impression is that the trial underestimated the effect size. If I use the observed results to calculate a sample size that would take into the effect size (same alpha and beta), I get a numbers needed of 900+ patients. This would suggest that the trial is actually under powered. And potentially, the result we see is a false positive result.