. Author manuscript; available in PMC: 2019 Aug 23.

Published in final edited form as: Biometrics. 2019 Apr 3;75(2):371–381. doi: 10.1111/biom.12994

Table 6.

Robustness simulation results. α = probability of a type I error or concluding that an inferior version of A is better than C under the null. γ₁ = generalized power at $x_{S}^{opt}$ under the alternative hypothesis (probability of selecting the best dose $x_{S}^{opt}$ and declaring $A (x_{S}^{opt})$ superior to C). γ₂ = generalized power (probability of selecting any superior dose and declaring $A ({\hat{x}}_{S}^{opt})$ superior to C). $\bar{W}$ is the mean improvement in survival time under the alternative hypothesis. $\bar{Dur}$ and $\bar{N}$ are the mean trial duration and sample size, respectively.

Scenario

Distribution

Phase I-II → phase III

Phase I-II/III Design

\bar{W}

γ₁

γ₂

\bar{W}

γ₁

γ₂

Lognormal, σ = .5

7.72

.30

.02

14.56

.80

.03

Lognormal, σ = 1

6.18

.30

.02

14.88

.85

.03

Weibull Increasing

6.37

.30

.02

12.00

.77

.03

Weibull Decreasing

1.96

.13

.02

4.14

.32

.02

Gamma

5.02

.30

.02

11.72

.89

.04

Lognormal, σ = .5

12.18

.73

.05

15.14

.91

.05

Lognormal, σ = 1

11.70

.70

.06

13.78

.82

.03

Weibull Increasing

9.08

.73

.06

11.20

.90

.06

Weibull Decreasing

3.98

.32

.05

4.75

.38

.03

Gamma

9.11

.73

.06

11.30

.90

.03

Lognormal, σ = .5

2.17

.06

< .01

13.91

.85

.04

Lognormal, σ = 1

2.02

.06

< .01

12.91

.81

.03

Weibull Increasing

2.14

.06

< .01

13.63

.84

.03

Weibull Decreasing

.90

.03

< .01

4.94

.32

.03

Gamma

2.07

.06

< .01

13.23

.86

.03

Lognormal, σ = .5

4.50

.32

.05

7.23

.52

.05

Lognormal, σ = 1

3.86

.28

.05

5.61

.40

.06

Weibull Increasing

4.67

.33

.04

6.61

.47

.04

Weibull Decreasing

4.14

.28

.06

6.21

.42

.07

Gamma

4.62

.31

.04

6.93

.47

.04

Lognormal, σ = .5

6.63

.21

.25

.01

18.19

.76

.96

.03

Lognormal, σ = 1

5.74

.21

.25

.01

16.78

.69

.87

.03

Weibull Increasing

7.41

.21

.25

.01

15.88

.64

.77

.03

Weibull Decreasing

4.00

.16

.18

.01

12.27

.48

.63

.03

Gamma

6.73

.21

.25

.01

18.73

.80

.92

.03

Lognormal, σ = .5

11.92

.34

.52

.04

15.56

.58

.83

.06

Lognormal, σ = 1

11.50

.34

.52

.02

15.66

.60

.80

.04

Weibull Increasing

10.29

.34

.52

.04

12.76

.54

.77

.05

Weibull Decreasing

5.46

.21

.31

.02

6.63

.32

.38

.03

Gamma

10.90

.34

.52

.02

14.80

.59

.83

.04