Table 3.
Sample size (power) under mis-specification of the Weibull shape parameter κ for the three tests with 90% nominal power and 5% type I error (two-sided test).
| Mis-specification rate of κ | |||||||
|---|---|---|---|---|---|---|---|
|
| |||||||
| Δ | κ | Test | 1 | 0.7 | 0.8 | 1.2 | 1.3 |
| 1.5 | 0.5 | Schoenfeld | 189 (90) | 213 (93) | 204 (92) | 176 (88) | 170 (87) |
| Sprott | 188 (90) | 211 (93) | 203 (93) | 175 (88) | 170 (88) | ||
| Log-rank | 187 (90) | 210 (93) | 202 (92) | 174 (87) | 169 (87) | ||
|
| |||||||
| 1 | Schoenfeld | 145 (90) | 165 (94) | 157 (92) | 138 (89) | 136 (88) | |
| Sprott | 145 (90) | 165 (94) | 156 (92) | 138 (89) | 136 (88) | ||
| Log-rank | 144 (89) | 164 (93) | 156 (92) | 138 (89) | 135 (88) | ||
|
| |||||||
| 2 | Schoenfeld | 130 (90) | 134 (91) | 132 (91) | 129 (90) | 129 (90) | |
| Sprott | 130 (90) | 135 (91) | 132 (91) | 130 (90) | 129 (90) | ||
| Log-rank | 129 (89) | 134 (91) | 132 (90) | 129 (89) | 129 (89) | ||
|
| |||||||
| 2.0 | 0.5 | Schoenfeld | 72 (91) | 82 (94) | 79 (93) | 67 (89) | 64 (88) |
| Sprott | 70 (91) | 80 (94) | 77 (93) | 65 (88) | 63 (87) | ||
| Log-rank | 69 (90) | 79 (93) | 75 (92) | 64 (87) | 62 (86) | ||
|
| |||||||
| 1 | Schoenfeld | 53 (91) | 62 (94) | 58 (93) | 49 (89) | 48 (88) | |
| Sprott | 53 (91) | 61 (95) | 58 (93) | 50 (89) | 49 (89) | ||
| Log-rank | 52 (90) | 60 (94) | 57 (92) | 49 (88) | 48 (87) | ||
|
| |||||||
| 2 | Schoenfeld | 45 (90) | 47 (92) | 46 (91) | 45 (90) | 44 (90) | |
| Sprott | 46 (91) | 48 (92) | 47 (92) | 45 (90) | 45 (90) | ||
| Log-rank | 45 (89) | 47 (91) | 46 (90) | 45 (89) | 44 (88) | ||
|
| |||||||
| 2.5 | 0.5 | Schoenfeld | 46 (92) | 53 (95) | 50 (94) | 42 (90) | 40 (88) |
| Sprott | 44 (91) | 50 (94) | 48 (93) | 40 (88) | 39 (88) | ||
| Log-rank | 42 (90) | 48 (93) | 46 (92) | 39 (88) | 38 (87) | ||
|
| |||||||
| 1 | Schoenfeld | 32 (91) | 39 (96) | 36 (94) | 30 (90) | 29 (89) | |
| Sprott | 32 (91) | 38 (95) | 35 (94) | 30 (90) | 29 (90) | ||
| Log-rank | 31 (89) | 37 (94) | 35 (93) | 29 (88) | 29 (88) | ||
|
| |||||||
| 2 | Schoenfeld | 26 (90) | 28 (92) | 27 (92) | 26 (90) | 26 (90) | |
| Sprott | 27 (91) | 29 (93) | 28 (92) | 27 (91) | 27 (91) | ||
| Log-rank | 26 (88) | 28 (90) | 27 (89) | 26 (88) | 26 (88) | ||
Sample sizes are calculated under mis-specified value of κ. Empirical powers (in brackets) are calculated for the corresponding sample sizes under the true value of κ based on 20,000 simulated runs.