Table 1. Median “after-the-fact” power to detect defined differences in the proportions of events between two study groups and their corresponding effect sizes using Cohen’s h.
| Proportion of events in Group 2 | Cohen’s h | Median power in the 66 studies included |
|---|---|---|
| Baseline proportion of events in Group 1 = 10% | ||
| 20% | 0.28 (small effect) | 14% |
| 29.3% | 0.50 (medium effect) | 42% |
| 30% | 0.52 (medium effect) | 44% |
| 40% | 0.73 (medium effect) | 75% |
| 50% | 0.93 (large effect) | 93% |
| Baseline proportion of events in Group 1 = 30% | ||
| 10% | 0.52 (medium effect) | 44% |
| 20% | 0.23 (small effect) | 11% |
| 30% | 0 | 3% |
| 40% | 0.21 (small effect) | 10% |
| 50% | 0.41 (small effect) | 30% |
| 54.4% | 0.50 (medium effect) | 43% |
| 60% | 0.61 (medium effect) | 61% |
| 70% | 0.82 (large effect) | 87% |
Note:
A median power of 44% to detect an effect size of 0.52 with a baseline proportion of events of 10% means that retrospective power analysis was performed for each of the 66 studies on the assumption that 10% of the patients in arm 1 and 30% in arm 2 have the target event. The median power observed among the 66 studies was calculated and reported as shown above. The same assessment was done with a varying proportion of events in group 2 and with another baseline proportion of events (30%). A median power of 40% indicates a 40%, chance of obtaining a significant result with the sample sizes used in the 66 studies, assuming a true effect size of 0.52 (proportion of events 30% vs 10%).