Table 8 Well-approximated type I error rates and power with miss-specification of the prior distribution for \(p_0\)
From: Practical basket design for binary outcomes with control of family-wise error rate
| Â | Â | Â | Subpopulation j | |||
|---|---|---|---|---|---|---|
Scenario | Method | \(p_0\) | 1 | 2 | 3 | 4 |
1 | Independent | Beta(0.1,0.9) | 0% | 0% | 0% | 0% |
Beta(0.2,0.8) | 0% | 0% | 0% | 0% | ||
BHM-weak | Beta(0.1,0.9) | 0% | 1% | 1% | 1% | |
Beta(0.2,0.8) | 0% | 1% | 1% | 1% | ||
BHM-strong | Beta(0.1,0.9) | 1% | 1% | 1% | 1% | |
Beta(0.2,0.8) | 1% | 1% | 1% | 1% | ||
2 | Independent | Beta(0.1,0.9) | 0% | 0% | 0% | 54% |
Beta(0.2,0.8) | 0% | 0% | 0% | 54% | ||
BHM-weak | Beta(0.1,0.9) | 1% | 1% | 1% | 61% | |
Beta(0.2,0.8) | 1% | 1% | 1% | 62% | ||
BHM-strong | Beta(0.1,0.9) | 2% | 3% | 3% | 65% | |
Beta(0.2,0.8) | 2% | 2% | 3% | 65% | ||
3 | Independent | Beta(0.1,0.9) | 0% | 0% | 61% | 54% |
Beta(0.2,0.8) | 0% | 0% | 61% | 54% | ||
BHM-weak | Beta(0.1,0.9) | 1% | 1% | 72% | 65% | |
Beta(0.2,0.8) | 1% | 1% | 72% | 65% | ||
BHM-strong | Beta(0.1,0.9) | 5% | 7% | 83% | 76% | |
Beta(0.2,0.8) | 5% | 7% | 83% | 76% | ||
4 | Independent | Beta(0.1,0.9) | 0% | 57% | 61% | 53% |
Beta(0.2,0.8) | 0% | 57% | 61% | 53% | ||
BHM-weak | Beta(0.1,0.9) | 1% | 70% | 76% | 68% | |
Beta(0.2,0.8) | 1% | 70% | 75% | 68% | ||
BHM-strong | Beta(0.1,0.9) | 10% | 85% | 91% | 84% | |
Beta(0.2,0.8) | 10% | 85% | 91% | 84% | ||
5 | Independent | Beta(0.1,0.9) | 57% | 57% | 61% | 53% |
Beta(0.2,0.8) | 57% | 57% | 61% | 53% | ||
BHM-weak | Beta(0.1,0.9) | 75% | 73% | 78% | 71% | |
Beta(0.2,0.8) | 74% | 73% | 78% | 71% | ||
BHM-strong | Beta(0.1,0.9) | 91% | 90% | 95% | 90% | |
Beta(0.2,0.9) | 91% | 90% | 95% | 90% | ||