Table 6 The mean and standard deviation (in parenthesis) of type I error and power.
From: A simulation study for comparing testing statistics in response-adaptive randomization
| Â | Â | Type I error of test statistics | Â | ||||
|---|---|---|---|---|---|---|---|
Target | Method | T MW | T RISK | T MO | T MC | T ML | Row Mean |
| Â | SMLE | 4.4(1.1) | 4.6(4.1) | 2.0(1.4) | 5.0(0.6) | 6.8(0.9) | 4.6(2.4) |
| Â | DBCD | 4.3(1.4) | 5.1(5.1) | 1.7(1.7) | 4.8(1.2) | 7.2(0.8) | 4.6(2.9) |
R Wald | SEU | 4.0(0.9) | 3.4(2.4) | 2.3(1.2) | 4.8(0.2) | 5.6(0.6) | 4.0(1.7) |
| Â | GDL | 4.4(0.8) | 3.7(3.1) | 2.1(1.6) | 5.2(0.4) | 6.6(1.0) | 4.4(2.2) |
| Â | Mean | 4.3(1.0) | 4.2(3.6) | 2.0(1.4) | 5.0(0.7) | 6.5(1.0) | 4.4(2.3) |
| Â | SMLE | 4.4(1.4) | 8.6(3.5) | 2.4(1.8) | 5.5(1.4) | 6.0(1.0) | 5.4(2.8) |
| Â | DBCD | 4.6(2.0) | 10.2(4.4) | 2.6(2.3) | 5.7(2.2) | 6.5(1.4) | 5.9(3.5) |
R Risk | SEU | 3.7(0.8) | 7.6(2.3) | 2.1(0.8) | 5.4(1.3) | 5.1(0.4) | 4.8(2.2) |
| Â | GDL | 4.2(1.3) | 7.9(2.4) | 2.4(1.9) | 5.4(1.6) | 5.8(1.4) | 5.1(2.5) |
| Â | Mean | 4.2(1.3) | 8.6(3.1) | 2.4(1.7) | 5.5(1.5) | 5.9(1.2) | 5.3(2.8) |
| Â | SMLE | 3.7(0.6) | 2.4(0.5) | 2.9(0.5) | 4.8(0.4) | 4.5(0.4) | 3.7(1.0) |
| Â | DBCD | 3.6(0.7) | 2.1(0.8) | 3.1(0.7) | 4.7(0.3) | 4.1(0.2) | 3.5(1.1) |
R Odds | SEU | 3.6(0.5) | 3.6(0.8) | 2.3(0.7) | 4.7(0.3) | 4.9(0.7) | 3.8(1.1) |
| Â | GDL | 3.7(0.8) | 3.4(0.8) | 3.0(1.1) | 5.1(0.4) | 4.5(0.4) | 3.9(1.0) |
| Â | Mean | 3.7(0.6) | 2.9(0.9) | 2.8(0.8) | 4.9(0.4) | 4.5(0.5) | 3.7(1.1) |
| Â | SMLE | 4.0(0.6) | 2.7(1.2) | 2.7(1.0) | 5.0(0.2) | 5.2(0.6) | 3.9(1.3) |
| Â | DBCD | 4.2(0.8) | 3.3(2.6) | 2.4(1.5) | 5.0(0.4) | 6.1(0.8) | 4.2(1.9) |
R LLR | SEU | 4.0(0.6) | 2.8(1.6) | 2.4(1.0) | 4.9(0.2) | 5.4(0.8) | 3.9(1.5) |
| Â | GDL | 3.7(0.5) | 2.5(1.3) | 2.7(1.2) | 4.9(0.4) | 5.4(0.9) | 3.8(1.5) |
| Â | Mean | 3.9(0.6) | 2.8(1.6) | 2.5(1.1) | 5.0(0.3) | 5.6(0.8) | 4.0(1.5) |
| Â | SMLE | 4.2(1.1) | 6.2(4.0) | 2.3(1.5) | 5.2(0.8) | 6.1(0.7) | 4.8(2.4) |
| Â | DBCD | 4.3(1.5) | 6.9(5.2) | 2.0(1.6) | 5.2(1.3) | 6.5(1.1) | 5.0(3.0) |
R RSIHR | SEU | 3.9(0.8) | 4.8(3.4) | 2.3(1.0) | 4.8(0.4) | 5.5(0.5) | 4.3(1.9) |
| Â | GDL | 4.3(0.9) | 4.7(3.0) | 2.2(1.6) | 5.1(0.6) | 6.1(0.9) | 4.5(2.0) |
| Â | Mean | 4.2(1.0) | 5.7(3.8) | 2.2(1.3) | 5.1(0.8) | 6.1(0.8) | 4.6(2.3) |
| Â | RPW | 4.2(0.8) | 6.2(0.5) | 2.5(1.6) | 5.5(1.4) | 5.4(0.8) | 4.8(1.7) |
| Â | DL | 4.3(0.8) | 4.8(1.0) | 2.6(1.7) | 5.3(0.9) | 5.3(0.4) | 4.5(1.4) |
| Â | SMLE | 4.2(0.9) | 6.5(0.6) | 2.8(1.8) | 5.4(1.6) | 5.1(0.8) | 4.8(1.7) |
R RPW | DBCD | 4.3(0.9) | 6.7(1.0) | 2.9(2.1) | 5.7(1.8) | 4.8(1.0) | 4.9(1.9) |
| Â | SEU | 3.8(0.6) | 5.7(1.3) | 2.2(0.6) | 5.4(0.8) | 5.1(0.6) | 4.5(1.5) |
| Â | GDL | 4.0(0.8) | 5.1(0.6) | 2.7(1.6) | 5.2(0.7) | 5.0(0.8) | 4.4(1.3) |
| Â | Mean | 4.1(0.8) | 5.8(1.1) | 2.6(1.5) | 5.4(1.2) | 5.1(0.7) | 4.6(1.6) |
Equal Allocation | 4.0(0.5) | 2.9(1.7) | 2.4(1.0) | 5.0(0.2) | 5.6(0.8) | 4.0(1.5) | |
| Â | Â | Power of test statistics | |||||
Target | Method | T MW | T RISK | T MO | T MC | T ML | Row Mean |
| Â | SMLE | 56.6(34.1) | 48.6(35.2) | 48.5(36.8) | 57.6(33.4) | 59.4(31.9) | 54.2(33.2) |
| Â | DBCD | 56.9(34.4) | 49.5(35.9) | 48.0(37.6) | 57.7(33.9) | 60.2(31.8) | 54.5(33.7) |
R Wald | SEU | 56.0(34.0) | 47.7(34.8) | 49.6(36.1) | 57.5(33.0) | 58.4(32.3) | 53.8(32.9) |
| Â | GDL | 57.3(34.0) | 50.0(36.2) | 50.6(36.9) | 58.4(33.2) | 60.0(32.0) | 55.3(33.3) |
| Â | Mean | 56.7(32.8) | 49.0(34.2) | 49.2(35.4) | 57.8(32.1) | 59.5(30.7) | 54.4(33.0) |
| Â | SMLE | 53.4(33.2) | 57.9(31.5) | 45.4(35.2) | 56.2(32.7) | 55.1(31.1) | 53.6(31.7) |
| Â | DBCD | 53.3(33.4) | 60.0(30.5) | 43.7(36.0) | 56.5(32.9) | 55.0(31.1) | 53.7(31.9) |
R Risk | SEU | 52.5(32.8) | 55.3(32.2) | 45.9(34.1) | 55.2(32.1) | 54.2(31.2) | 52.6(31.3) |
| Â | GDL | 53.2(33.3) | 58.1(31.6) | 45.8(35.8) | 56.5(32.6) | 55.2(31.7) | 53.8(31.9) |
| Â | Mean | 53.1(31.9) | 57.8(30.3) | 45.2(33.9) | 56.1(31.3) | 54.9(30.1) | 53.4(31.5) |
| Â | SMLE | 54.6(33.9) | 47.1(34.3) | 52.1(34.9) | 57.6(32.6) | 56.4(32.9) | 53.6(32.5) |
| Â | DBCD | 54.8(34.2) | 47.3(35.2) | 53.4(34.5) | 57.8(32.7) | 56.5(33.4) | 53.9(32.8) |
R Odds | SEU | 54.8(33.5) | 50.8(33.8) | 50.4(34.8) | 57.5(32.5) | 56.6(32.2) | 54.0(32.1) |
| Â | GDL | 54.6(34.2) | 53.0(34.6) | 52.5(35.0) | 58.1(32.7) | 56.8(33.0) | 55.0(32.5) |
| Â | Mean | 54.7(32.6) | 49.5(33.2) | 52.1(33.4) | 57.8(31.4) | 56.6(31.6) | 54.1(32.3) |
| Â | SMLE | 55.9(33.9) | 48.4(35.0) | 51.6(35.6) | 58.0(32.8) | 58.0(32.6) | 54.4(32.8) |
| Â | DBCD | 57.2(34.0) | 49.9(35.9) | 51.4(36.6) | 58.6(33.1) | 60.0(32.2) | 55.4(33.2) |
R LLR | SEU | 56.1(33.9) | 48.5(34.8) | 51.2(35.7) | 58.1(32.8) | 58.2(32.5) | 54.4(32.8) |
| Â | GDL | 56.4(34.1) | 50.4(35.8) | 53.1(35.9) | 58.9(33.1) | 59.5(32.5) | 55.7(33.1) |
| Â | Mean | 56.4(32.6) | 49.3(34.0) | 51.8(34.6) | 58.4(31.7) | 58.9(31.2) | 55.0(32.7) |
| Â | SMLE | 56.0(33.9) | 54.8(33.7) | 48.7(36.4) | 57.5(33.2) | 58.4(32.0) | 55.1(32.6) |
| Â | DBCD | 56.8(34.0) | 56.3(33.4) | 48.2(37.0) | 58.2(33.2) | 59.4(31.8) | 55.7(32.8) |
R RSIHR | SEU | 54.5(33.8) | 50.5(34.5) | 48.6(35.8) | 56.4(33.0) | 56.6(32.4) | 53.3(32.7) |
| Â | GDL | 57.4(33.7) | 54.4(34.5) | 50.6(36.6) | 58.7(33.0) | 59.7(32.1) | 56.2(32.8) |
| Â | Mean | 56.2(32.6) | 54.0(32.8) | 49.0(35.0) | 57.7(31.8) | 58.5(30.8) | 55.1(32.5) |
| Â | RPW | 52.4(32.3) | 55.9(32.1) | 46.3(34.1) | 55.8(32.1) | 52.9(30.1) | 52.7(31.0) |
| Â | DL | 56.0(33.5) | 55.9(33.4) | 50.0(36.1) | 58.2(32.6) | 57.4(32.5) | 55.5(32.4) |
| Â | SMLE | 51.7(32.3) | 56.2(31.8) | 46.7(33.7) | 55.7(31.9) | 51.7(30.2) | 52.4(30.9) |
R RPW | DBCD | 51.2(31.8) | 57.3(31.2) | 47.0(34.1) | 56.0(31.5) | 48.3(29.2) | 52.0(30.6) |
| Â | SEU | 54.0(33.1) | 54.0(32.7) | 48.3(34.4) | 56.7(32.1) | 55.9(31.7) | 53.8(31.6) |
| Â | GDL | 54.6(33.5) | 56.0(33.0) | 50.2(35.3) | 57.8(32.4) | 56.4(32.3) | 55.0(32.0) |
| Â | Mean | 53.3(31.4) | 55.9(31.0) | 48.1(33.2) | 56.7(30.7) | 53.8(29.8) | 53.5(31.2) |
Equal Allocation | 56.2(33.9) | 48.5(35.0) | 50.9(35.9) | 58.1(32.9) | 58.4(32.4) | 54.4(32.9) | |