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Table 4 Proposed optimal adaptive designs for π a =π u +0.15 at α=0.05. Simon’s minimax design (r1/n1,r/n), and the minimax that stops for futility and efficacy ((r1,r2)/n1,r/n), are provided as reference

From: Minimax and admissible adaptive two-stage designs in phase II clinical trials

Power=80 %

Power=90 %

S

n2(S)

n(S)

r(S)

S

n2(S)

n(S)

r(S)

π u =0.1

Simon: (2/22,7/40)

Simon: (3/31,9/55)

Minimax-EF: ((4,6)/33,7/38)

Minimax-EF: ((6,8)/47,9/53)

New: n1=18

New: n1=33

≤1

0

18

0

≤3

0

33

0

2

20

38

7

4

20

53

8

3

20

38

7

5

20

53

9

4

19

37

6

6

20

53

9

5

19

37

6

7

18

51

8

6

18

36

6

8

17

50

8

≥7

0

18

0

≥9

0

33

0

π u =0.2

Simon: (6/31,15/53)

Simon: (8/42,21/77)

Minimax-EF: ((6,13)/31,15/53)

Minimax-EF: ((13,18)/62,21/76)

New: n1=31

New: n1=47

≤6

0

31

0

≤9

0

47

0

7

22

53

15

10

27

74

20

8

22

53

15

11

27

74

20

9

22

53

15

12

27

74

20

10

22

53

15

13

27

74

20

11

22

53

15

14

26

73

20

12

21

52

15

15

26

73

20

≥13

0

31

0

16

26

73

20

    

17

25

72

20

    

18

14

61

18

    

≥19

0

47

0

π u =0.3

Simon: (16/46,25/65)

Simon: (27/77,33/88)

Minimax-EF: ((13,19)/43,25/64)

Minimax-EF: ((27,33)/77,33/88)

New: n1=32

New: n1=51

≤9

0

32

0

≤15

0

51

0

10

32

64

24

16

37

88

33

11

32

64

25

17

37

88

33

12

32

64

25

18

37

88

33

13

32

64

25

19

37

88

33

14

32

64

25

20

37

88

33

15

31

63

24

21

37

88

33

16

30

62

24

22

37

88

33

17

29

61

24

23

37

88

33

18

24

56

22

24

37

88

34

≥19

0

32

0

25

36

87

33

    

26

34

85

33

    

27

34

85

33

    

≥28

0

51

0

π u =0.4

Simon: (28/59,34/70)

Simon: (24/62,45/94)

Minimax-EF: ((16,23)/41,34/69)

Minimax-EF: ((21,31)/55,45/94)

New: n1=37

New: n1=52

≤15

0

37

0

≤20

0

52

0

16

32

69

33

21

42

94

44

17

32

69

34

22

42

94

45

18

32

69

34

23

42

94

45

19

32

69

34

24

42

94

45

20

32

69

34

25

42

94

45

21

31

68

33

26

42

94

45

22

31

68

33

27

42

94

45

23

31

68

33

28

42

94

45

24

21

58

29

29

42

94

45

≥25

0

37

0

30

42

94

45

    

31

39

91

43

    

≥32

0

52

0

π u =0.5

Simon: (39/66,40/68)

Simon: (28/57,54/93)

Minimax-EF: ((39,40)/66,40/68)

Minimax-EF: ((30,38)/59,54/93)

New: n1=54

New: n1=55

≤28

0

54

0

≤28

0

55

0

29

13

67

39

29

38

93

54

30

13

67

40

30

38

93

54

31

13

67

40

31

38

93

54

32

13

67

40

32

38

93

54

33

13

67

40

33

38

93

54

34

13

67

39

34

38

93

54

35

13

67

39

35

38

93

53

36

13

67

39

36

38

93

54

37

9

63

38

37

38

93

53

≥38

0

54

0

≥38

0

55

0

π u =0.6

Simon: (18/30,43/62)

Simon: (48/72,57/84)

Minimax-EF: ((16,22)/27,43/62)

Minimax-EF: ((48,53)/72,57/84)

New: n1=32

New: n1=58

≤19

0

32

0

≤37

0

58

0

20

29

61

42

38

26

84

57

21

29

61

42

39

26

84

57

22

29

61

42

40

26

84

57

23

28

60

42

41

26

84

57

24

28

60

42

42

25

83

57

25

28

60

42

43

25

83

57

26

27

59

41

44

23

81

56

27

27

59

41

≥45

0

58

0

28

15

47

34

    

≥29

0

32

0

    

π u =0.7

Simon: (16/23,39/49)

Simon: (33/44,53/68)

Minimax-EF: ((16,21)/23,39/49)

Minimax-EF: ((29,35)/41,51/65)

New: n1=25

New: n1=37

≤18

0

25

0

≤26

0

37

0

19

24

49

39

27

28

65

51

20

24

49

39

28

28

65

51

21

24

49

39

29

28

65

51

22

23

48

38

30

28

65

51

23

8

33

26

31

27

64

50

≥24

0

25

0

32

27

64

50

    

33

24

61

48

    

≥34

0

37

0