Background
Methods
PowerSwtichingTrial overview
Two main functions of PowerSwtichingTrial
Results
A scenario from a real clinical trial
s.dist = “gamma” | s.dist = “indepExp” | |||||
---|---|---|---|---|---|---|
rho (correlation of s with T1) | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | 0 |
Power at the significance level of 0.01 with n= 232 and r = 1 | 0.024 | 0.060 | 0.093 | 0.104 | 0.099 | 0.074 |
Required sample sizes (n) to attain the power of 0.9 at the significance level of 0.01 | > 10,000 | 3339 | 2276 | 2034 | 2084 | 2828 |
Simulation scenarios
Effect of the relative effectiveness on power and sample sizes estimation
p | no switching | switching s.dist = “beta” | switching s.dist = “gamma” | switching s.dist = “unif” | switching s.dist = “indepExp” | |
---|---|---|---|---|---|---|
m2/m1 = 1.5 | ||||||
0.2 | n | 130 | 166 | 165 | 168 | 169 |
E1 | 104.0 | 130.8 | 130.1 | 132.5 | 132.8 | |
E2 | 89.2 | 113.8 | 113.2 | 115.1 | 115.8 | |
Powera | 0.80 | 0.70 | 0.70 | 0.70 | 0.69 | |
ns/nno − s | – | 1.28 | 1.27 | 1.29 | 1.30 | |
0.4 | n | 130 | 215 | 219 | 217 | 235 |
E1 | 104.0 | 167.0 | 169.9 | 168.5 | 180.9 | |
E2 | 89.2 | 147.6 | 150.2 | 148.9 | 161.1 | |
Powera | 0.80 | 0.57 | 0.58 | 0.57 | 0.54 | |
ns/nno − s | – | 1.65 | 1.68 | 1.67 | 1.81 | |
0.6 | n | 130 | 294 | 301 | 297 | 344 |
E1 | 104.0 | 225.0 | 230.0 | 227.1 | 259.4 | |
E2 | 89.2 | 201.7 | 206.4 | 203.9 | 236.0 | |
Powera | 0.80 | 0.47 | 0.45 | 0.48 | 0.40 | |
ns/nno − s | – | 2.26 | 2.32 | 2.28 | 2.65 | |
0.8 | n | 130 | 418 | 437 | 416 | 534 |
E1 | 104.0 | 314.7 | 328.5 | 313.3 | 394.8 | |
E2 | 89.2 | 286.4 | 299.6 | 285.2 | 366.4 | |
Powera | 0.80 | 0.35 | 0.33 | 0.35 | 0.29 | |
ns/nno − s | – | 3.22 | 3.36 | 3.20 | 4.11 | |
1.0 | n | 130 | 627 | 782 | 657 | 937 |
E1 | 104.0 | 464.9 | 578.1 | 487.2 | 678.4 | |
E2 | 89.2 | 430.3 | 536.3 | 450.7 | 642.2 | |
Powera | 0.80 | 0.24 | 0.23 | 0.24 | 0.18 | |
ns/nno − s | – | 4.82 | 6.02 | 5.05 | 7.21 | |
m2/m1 = 2 | ||||||
0.2 | n | 48 | 64 | 63 | 62 | 64 |
E1 | 38.4 | 49.9 | 48.9 | 48.2 | 49.4 | |
E2 | 28.4 | 38.1 | 37.4 | 36.9 | 38.0 | |
Powera | 0.80 | 0.69 | 0.69 | 0.69 | 0.68 | |
ns/nno − s | – | 1.33 | 1.31 | 1.29 | 1.33 | |
0.4 | n | 48 | 87 | 84 | 84 | 88 |
E1 | 38.4 | 65.8 | 63.5 | 63.7 | 65.7 | |
E2 | 28.4 | 51.8 | 49.9 | 49.9 | 52.2 | |
Powera | 0.80 | 0.56 | 0.57 | 0.56 | 0.53 | |
ns/nno − s | – | 1.81 | 1.75 | 1.75 | 1.83 | |
0.6 | n | 48 | 114 | 124 | 116 | 127 |
E1 | 38.4 | 83.8 | 90.7 | 85.1 | 92.1 | |
E2 | 28.4 | 67.5 | 73.5 | 69.0 | 76.0 | |
Powera | 0.80 | 0.44 | 0.42 | 0.45 | 0.40 | |
ns/nno − s | – | 2.38 | 2.58 | 2.42 | 2.65 | |
0.8 | n | 48 | 167 | 182 | 167 | 202 |
E1 | 38.4 | 119.0 | 129.0 | 118.9 | 140.0 | |
E2 | 28.4 | 99.1 | 108.1 | 99.0 | 119.8 | |
Powera | 0.80 | 0.32 | 0.31 | 0.31 | 0.27 | |
ns/nno − s | – | 3.48 | 3.79 | 3.48 | 4.21 | |
1.0 | n | 48 | 265 | 296 | 269 | 355 |
E1 | 38.4 | 182.7 | 203.3 | 185.7 | 236.2 | |
E2 | 28.4 | 157.4 | 175.7 | 159.4 | 210.7 | |
Powera | 0.80 | 0.23 | 0.22 | 0.23 | 0.19 | |
ns/nno − s | – | 5.52 | 6.17 | 5.60 | 7.40 |
Effect of the switching probability on power and sample sizes estimation
Effect of the switching time on power and sample sizes estimation
m2/m1 = 1.5 | m2/m1 = 2 | ||||||
---|---|---|---|---|---|---|---|
p | no switching | switching s = 0.5/log(2) | switching s = 1.0/log(2) | no switching | switching s = 0.5/log(2) | switching s = 1.0/log(2) | |
0.2 | n | 130 | 165 | 144 | 48 | 63 | 55 |
E1 | 104.0 | 129.7 | 114.1 | 38.4 | 48.9 | 43.2 | |
E2 | 89.2 | 113.2 | 98.7 | 28.4 | 37.4 | 32.7 | |
Powera | 0.80 | 0.71 | 0.76 | 0.80 | 0.70 | 0.76 | |
ns/nno − s | – | 1.27 | 1.11 | – | 1.31 | 1.15 | |
0.4 | n | 130 | 217 | 165 | 48 | 83 | 63 |
E1 | 104.0 | 167.4 | 129.3 | 38.4 | 62.3 | 48.7 | |
E2 | 89.2 | 148.9 | 113.2 | 28.4 | 49.2 | 37.4 | |
Powera | 0.80 | 0.59 | 0.71 | 0.80 | 0.57 | 0.70 | |
ns/nno − s | – | 1.67 | 1.27 | – | 1.73 | 1.31 | |
0.6 | n | 130 | 290 | 187 | 48 | 113 | 71 |
E1 | 104.0 | 219.8 | 145.1 | 38.4 | 82.8 | 53.9 | |
E2 | 89.2 | 198.7 | 128.3 | 28.4 | 67.8 | 42.2 | |
Powera | 0.80 | 0.47 | 0.65 | 0.80 | 0.46 | 0.65 | |
ns/nno − s | – | 2.23 | 1.44 | – | 2.35 | 1.48 | |
0.8 | n | 130 | 427 | 214 | 48 | 164 | 81 |
E1 | 104.0 | 317.4 | 164.4 | 38.4 | 115.2 | 60.4 | |
E2 | 89.2 | 292.8 | 146.8 | 28.4 | 97.4 | 48.1 | |
Powera | 0.80 | 0.36 | 0.59 | 0.80 | 0.35 | 0.59 | |
ns/nno − s | – | 3.28 | 1.65 | – | 3.42 | 1.69 | |
1.0 | n | 130 | 628 | 248 | 48 | 247 | 93 |
E1 | 104.0 | 458.1 | 188.3 | 38.4 | 167.1 | 68.1 | |
E2 | 89.2 | 430.8 | 170.0 | 28.4 | 146.7 | 55.2 | |
Powera | 0.80 | 0.26 | 0.53 | 0.80 | 0.25 | 0.53 | |
ns/nno − s | – | 4.83 | 1.91 | – | 5.15 | 1.94 |
Power estimation when true distributions deviate from the assumed distributions
shape | no switching | switching s.dist = “beta” | switching s.dist = “gamma” | switching s.dist = “unif” | switching s.dist = “indepExp” | |
---|---|---|---|---|---|---|
Switching probability p = 0.2 | ||||||
n | 130 | 166 | 165 | 168 | 169 | |
1.0 | Power | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
E1 | 104.0 | 130.8 | 130.1 | 132.5 | 132.8 | |
E2 | 89.2 | 113.8 | 113.2 | 115.1 | 115.8 | |
0.5 | Power | 0.24 | 0.26 | 0.27 | 0.25 | 0.25 |
E1 | 96.2 | 108.7 | 108.1 | 110.1 | 110.3 | |
E2 | 77.0 | 98.4 | 97.5 | 99.4 | 99.9 | |
0.75 | Power | 0.53 | 0.53 | 0.54 | 0.53 | 0.53 |
E1 | 96.1 | 121.0 | 120.2 | 122.4 | 122.6 | |
E2 | 83.3 | 106.2 | 105.5 | 107.5 | 108.1 | |
1.25 | Power | 0.95 | 0.94 | 0.95 | 0.95 | 0.95 |
E1 | 109.5 | 137.9 | 140.0 | 139.5 | 139.7 | |
E2 | 94.4 | 120.6 | 119.7 | 122.0 | 122.7 | |
Switching probability p = 0.6 | ||||||
n | 130 | 294 | 301 | 297 | 344 | |
1.0 | Power | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
E1 | 104.0 | 225.0 | 230.0 | 227.1 | 259.4 | |
E2 | 89.2 | 201.7 | 206.4 | 203.9 | 236.0 | |
0.5 | Power | 0.24 | 0.26 | 0.25 | 0.26 | 0.27 |
E1 | 96.2 | 188.1 | 192.2 | 190.2 | 218.0 | |
E2 | 77.0 | 173.8 | 178.2 | 175.8 | 203.5 | |
0.75 | Power | 0.53 | 0.54 | 0.52 | 0.53 | 0.55 |
E1 | 96.1 | 208.0 | 212.7 | 210.3 | 240.4 | |
E2 | 83.3 | 188.2 | 192.8 | 190.2 | 220.1 | |
1.25 | Power | 0.95 | 0.95 | 0.94 | 0.95 | 0.94 |
E1 | 109.5 | 237.3 | 242.8 | 239.8 | 274.4 | |
E2 | 94.4 | 213.4 | 218.6 | 215.6 | 249.7 |