General discussions on Phase II clinical trials are presented in
PhaseII.php and not repeated here
This page provides explanations, calculations, and sample size tables for Phase II trials using Gehan's procedure.
Gehan's is for a preliminary study (phase II) of a new treatment, to test whether the proportion of success from the treatment
satisfies the level required to warrant further detailed study in a Phase III trial. The procedure is in two stages
- Stage 1 :
- Sample size for stage 1 (s1) is the number of cases to be used in stage 1. This depends on
- The proportion of success required (p) is defined, a value between 0 (0%) and 1 (100%)
- The power required, the ability to detect that proportion if it is there. Mathematically power = 1-β,
where β is the probability of error in rejecting the new treatment
- At the end of stage 1, after s1 cases are included, k = the number of successes found
- If k=0 or k< a critical value where reaching the required proportion of success is unlikely, the treatment
is rejected without proceeding to stage 2
- If k> a critical value where reaching the required proportion of success is likely, the treatment
is accepted without proceeding to stage 2
- Otherwise, stage 2 of the procedure is required for decision making.
- Stage 2 :
- The sample size in stage 2 is the number of additional cases to be used in stage 2 This depends on
- The number of cases already used in stage 1 (s1)
- The number of successes (k) found in stage 1
- The acceptable probability of error for a decision to accept the treatment (ε, conceptually similar to Type I Error α)
- The total number of successes is the number of successes in stage 1 (k) + number of successes in stage 2 .
- The required total number of successes for a decision to accept the treatment is n = p(s1+s2)
- if the total number of successes reached n, then the trial can be terminated, with a decision to accept the treatment for further study (phase III)
- If at the end of stage 2, the total number of successes had not reached n, then a decision to reject the treatment is made.
Gehan's procedure therefore has advantages over
Fleming's procedure in that a smaller sample size is required to reject a new treatment with inadequate success rate, and a much simpler protocol than
Simon's Procedure.
Example
A new drug is developed to treat cancer which looks promising, and we wish to conduct a Phase II trial. We decided that
if the new drug can achieve the survival rate of survival to 40% in a phase II trial, then it is worth the expense
of develop this drug and test it in a large phase III trial (acceptance of the treatment). Otherwise this new drug should be rejected from further development (rejection of the treatment).
The required success rate is set to 40% (0.4), the Type I Error α is set to 0.05, and the power set to 0.8
- The sample size for stage 1 (ss1) = 4
- If no success was observed in the 4 cases, then the new treatment is considered inadequate, and rejected from further evaluation
- If all 4 cases are successful, then the treatment can be accepted for further evaluation (phase III) and no stage 2 is required.
- If 1 cases is successful in stage 1, then
- 40 successes (stage 1 and 2) are required for the drug to be accepted for further evaluation (phase III)
- If less than 40 successes are observed with a maximum 96 cases (stage 1 and 2), then the new treatment is considered inadequate and rejected from further evaluation
- If 2 cases are successful in stage 1, then
- 30 successes (stage 1 and 2) are required for the drug to be accepted for further evaluation (phase III)
- If less than 30 successes are observed with a maximum 70 cases (stage 1 and 2), then the new treatment is considered inadequate and rejected from further evaluation
- If 3 cases are successful in stage 1, then
- 11 successes (stage 1 and 2) are required for the drug to be accepted for further evaluation (phase III)
- If less than 11 successes are observed with a maximum 22 cases (stage 1 and 2), then the new treatment is considered inadequate and rejected from further evaluation
References
Gehan E A (1961) The determination of the number of patients required in a preliminary and a follow-up trial of a
new chemotherapeutic agent Journal of Chronic Diseases. 13:4, Pages 346-353
Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for
Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 255-256
Power(1-β) = 0.8
Power=0.8, π=proportion of success required, ε=Error of accepting treatment
Stage 1 : s1=sample size for stage 1 r=numbers success in stage 1
Stagte 2 [cells] : sample size for stage 2 + (total number of successes required to accept treatment, stage 1 + 2)
R = Reject and A = Accept treatment for further studies at the end of stage 1
| | Error (ε) = 0.1 | Error (ε) = 0.05 |
π | s1 | r=1 | r=2 | r=3 | r=4 | r=5 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=7 | r=8 | r=9 |
0.03 | 53 | R | A | A | A | A | R | A | A | A | A | A | A | A | A |
---|
0.04 | 40 | R | A | A | A | A | R | A | A | A | A | A | A | A | A |
---|
0.05 | 32 | R | A | A | A | A | R | 10(3) | A | A | A | A | A | A | A |
---|
0.06 | 27 | R | A | A | A | A | 8(3) | 22(3) | 33(4) | 43(5) | A | A | A | A | A |
---|
0.07 | 23 | R | A | A | A | A | 18(3) | 32(4) | 44(5) | 54(6) | 62(6) | 69(7) | A | A | A |
---|
0.08 | 20 | R | A | A | A | A | 25(4) | 41(5) | 54(6) | 64(7) | 71(8) | 76(8) | 80(8) | A | A |
---|
0.09 | 18 | R | A | A | A | A | 31(5) | 48(6) | 61(8) | 70(8) | 77(9) | 81(9) | 82(9) | 81(9) | A |
---|
0.10 | 16 | R | A | A | A | A | 38(6) | 55(8) | 68(9) | 77(10) | 82(10) | 84(10) | 83(10) | 79(10) | A |
---|
0.11 | 14 | 1(2) | 6(3) | A | A | A | 46(7) | 64(9) | 76(10) | 83(11) | 86(11) | 85(11) | 81(11) | 72(10) | A |
---|
0.12 | 13 | 3(2) | 8(3) | A | A | A | 50(8) | 68(10) | 80(12) | 86(12) | 87(12) | 84(12) | 77(11) | 66(10) | A |
---|
0.13 | 12 | 5(3) | 10(3) | 12(4) | A | A | 55(9) | 73(12) | 84(13) | 88(13) | 87(13) | 81(13) | 71(11) | 56(9) | A |
---|
0.14 | 11 | 7(3) | 11(4) | 14(4) | A | A | 60(10) | 77(13) | 87(14) | 89(14) | 86(14) | 76(13) | 62(11) | A | A |
---|
0.15 | 10 | 9(3) | 13(4) | 15(4) | A | A | 65(12) | 82(14) | 90(15) | 89(15) | 82(14) | 68(12) | 48(9) | A | A |
---|
0.16 | 10 | 9(4) | 13(4) | 15(4) | A | A | 65(12) | 82(15) | 90(16) | 89(16) | 82(15) | 68(13) | 48(10) | A | A |
---|
0.17 | 9 | 11(4) | 15(5) | 16(5) | 15(5) | A | 71(14) | 87(17) | 91(17) | 87(17) | 74(15) | 54(11) | A | A | A |
---|
0.18 | 9 | 11(4) | 15(5) | 16(5) | 15(5) | A | 71(15) | 87(18) | 91(19) | 87(18) | 74(15) | 54(12) | 30(8) | A | A |
---|
0.19 | 8 | 14(5) | 17(5) | 17(5) | 15(5) | A | 77(17) | 91(19) | 91(19) | 81(17) | 61(14) | 35(9) | A | A | |
---|
0.20 | 8 | 14(5) | 17(5) | 17(5) | 15(5) | A | 77(17) | 91(20) | 91(20) | 81(18) | 61(14) | 35(9) | A | A | |
---|
0.22 | 7 | 16(6) | 18(6) | 17(6) | 12(5) | A | 83(20) | 93(22) | 88(21) | 69(17) | 41(11) | A | A | | |
---|
0.24 | 6 | 18(6) | 19(6) | 15(6) | A | A | 90(24) | 93(24) | 78(21) | 49(14) | A | A | | | |
---|
0.26 | 6 | 18(7) | 19(7) | 15(6) | A | A | 90(25) | 93(26) | 78(22) | 49(15) | A | A | | | |
---|
0.28 | 5 | 20(8) | 19(7) | 11(5) | A | A | 95(29) | 88(27) | 58(18) | 17(7) | A | | | | |
---|
0.30 | 5 | 20(8) | 19(8) | 11(5) | A | A | 95(30) | 88(28) | 58(19) | 17(7) | A | | | | |
---|
0.35 | 4 | 21(9) | 15(7) | A | A | | 96(35) | 70(26) | 22(10) | A | | | | | |
---|
0.40 | 4 | 21(10) | 15(8) | A | A | | 96(40) | 70(30) | 22(11) | A | | | | | |
---|
0.45 | 3 | 19(10) | 6(5) | A | | | 85(40) | 31(16) | A | | | | | | |
---|
0.50 | 3 | 19(11) | 6(5) | A | | | 85(44) | 31(17) | A | | | | | | |
---|
0.50 | 3 | 19(11) | 6(5) | A | | | 85(44) | 31(17) | A | | | | | | |
---|
0.60 | 2 | 10(8) | A | | | | 45(29) | A | | | | | | | |
---|
0.70 | 2 | 10(9) | A | | | | 45(33) | A | | | | | | | |
---|
0.80 | 2 | 10(10) | A | | | | 45(38) | A | | | | | | | |
---|
0.90 | 1 | A | | | | | A | | | | | | | | |
---|
Power(1-β) = 0.9
Power=0.9, π=proportion of success required, ε=Error of accepting treatment
Stage 1 : s1=sample size for stage 1 r=numbers success in stage 1
Stagte 2 [cells] : sample size for stage 2 + (total number of successes required to accept treatment, stage 1 + 2)
R = Reject and A = Accept treatment for further studies at the end of stage 1
| | Error (ε) = 0.1 | Error (ε) = 0.05 |
π | s1 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=7 | r=8 | r=9 | r=10 | r=11 |
0.03 | 76 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A |
---|
0.04 | 57 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A |
---|
0.05 | 45 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A |
---|
0.06 | 38 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A |
---|
0.07 | 32 | R | R | A | A | A | A | R | 10(3) | 21(4) | 30(5) | A | A | A | A | A | A | A |
---|
0.08 | 28 | R | R | A | A | A | A | 6(3) | 19(4) | 30(5) | 40(6) | 48(7) | 55(7) | 61(8) | A | A | A | A |
---|
0.09 | 25 | R | R | A | A | A | A | 13(4) | 27(5) | 38(6) | 48(7) | 57(8) | 63(8) | 68(9) | 72(9) | A | A | A |
---|
0.10 | 22 | R | R | A | A | A | A | 20(5) | 35(6) | 47(7) | 57(8) | 65(9) | 71(10) | 75(10) | 78(10) | 78(10) | A | A |
---|
0.11 | 20 | R | R | A | A | A | A | 25(5) | 41(7) | 54(9) | 64(10) | 71(11) | 76(11) | 80(11) | 80(11) | 80(11) | 77(11) | A |
---|
0.12 | 19 | R | R | A | A | A | A | 28(6) | 45(8) | 57(10) | 67(11) | 74(12) | 79(12) | 81(12) | 81(12) | 79(12) | 75(12) | A |
---|
0.13 | 17 | R | 1(3) | A | A | A | A | 35(7) | 52(9) | 65(11) | 74(12) | 80(13) | 83(13) | 83(13) | 81(13) | 76(13) | 69(12) | A |
---|
0.14 | 16 | R | 2(3) | A | A | A | A | 38(8) | 55(10) | 68(12) | 77(14) | 82(14) | 84(14) | 83(14) | 79(14) | 73(13) | 64(12) | A |
---|
0.15 | 15 | R | 4(3) | 7(4) | A | A | A | 42(9) | 59(12) | 72(14) | 80(15) | 85(15) | 85(15) | 83(15) | 77(14) | 68(13) | 56(11) | A |
---|
0.16 | 14 | R | 6(4) | 9(4) | A | A | A | 46(10) | 64(13) | 76(15) | 83(16) | 86(16) | 85(16) | 81(16) | 72(14) | 61(12) | A | A |
---|
0.17 | 13 | 3(3) | 8(4) | 11(5) | 12(5) | A | A | 50(11) | 68(14) | 80(16) | 86(17) | 87(17) | 84(17) | 77(16) | 66(14) | 51(11) | A | A |
---|
0.18 | 12 | 5(4) | 10(4) | 12(5) | 13(5) | A | A | 55(13) | 73(16) | 84(18) | 88(19) | 87(18) | 81(17) | 71(15) | 56(13) | 38(10) | A | A |
---|
0.19 | 11 | 7(4) | 11(5) | 14(5) | 14(5) | A | A | 60(14) | 77(17) | 87(19) | 89(20) | 86(19) | 76(17) | 62(14) | 43(11) | A | A | A |
---|
0.20 | 11 | 7(4) | 11(5) | 14(5) | 14(5) | A | A | 60(15) | 77(18) | 87(20) | 89(20) | 86(20) | 76(18) | 62(15) | 43(11) | A | A | A |
---|
0.22 | 10 | 9(5) | 13(6) | 15(6) | 15(6) | 13(6) | A | 65(17) | 82(21) | 90(22) | 89(22) | 82(21) | 68(18) | 48(13) | A | A | A | |
---|
0.24 | 9 | 11(5) | 15(6) | 16(6) | 15(6) | 12(6) | A | 71(20) | 87(24) | 91(24) | 87(24) | 74(20) | 54(16) | 30(10) | A | A | | |
---|
0.26 | 8 | 14(6) | 17(7) | 17(7) | 15(6) | A | A | 77(23) | 91(26) | 91(26) | 81(24) | 61(18) | 35(12) | A | A | | | |
---|
0.28 | 8 | 14(7) | 17(8) | 17(8) | 15(7) | 10(6) | A | 77(24) | 91(28) | 91(28) | 81(25) | 61(20) | 35(13) | A | A | | | |
---|
0.30 | 7 | 16(7) | 18(8) | 17(8) | 12(6) | A | A | 83(27) | 93(30) | 88(29) | 69(23) | 41(15) | A | A | | | | |
---|
0.35 | 6 | 18(9) | 19(9) | 15(8) | 8(5) | A | A | 90(34) | 93(35) | 78(30) | 49(20) | 12(7) | A | | | | | |
---|
0.40 | 5 | 20(10) | 19(10) | 11(7) | A | A | | 95(40) | 88(38) | 58(26) | 17(9) | A | | | | | | |
---|
0.45 | 4 | 21(12) | 15(9) | 3(4) | A | | | 96(45) | 70(34) | 22(12) | A | | | | | | | |
---|
0.50 | 4 | 21(13) | 15(10) | 3(4) | A | | | 96(50) | 70(37) | 22(13) | A | | | | | | | |
---|
0.50 | 4 | 21(13) | 15(10) | 3(4) | A | | | 96(50) | 70(37) | 22(13) | A | | | | | | | |
---|
0.60 | 3 | 19(14) | 6(6) | A | | | | 85(53) | 31(21) | A | | | | | | | | |
---|
0.70 | 2 | 10(9) | A | | | | | 45(33) | A | | | | | | | | | |
---|
0.80 | 2 | 10(10) | A | | | | | 45(38) | A | | | | | | | | | |
---|
0.90 | 2 | 10(11) | A | | | | | 45(43) | A | | | | | | | | | |
---|
Power(1-β) = 0.95
Power=0.95, π=proportion of success required, ε=Error of accepting treatment
Stage 1 : s1=sample size for stage 1 r=numbers success in stage 1
Stagte 2 [cells] : sample size for stage 2 + (total number of successes required to accept treatment, stage 1 + 2)
R = Reject and A = Accept treatment for further studies at the end of stage 1
| | Error (ε) = 0.1 | Error (ε) = 0.05 |
π | s1 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=7 | r=8 | r=9 | r=10 | r=11 | r=12 | r=13 |
0.03 | 99 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A | A | A |
---|
0.04 | 74 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A | A | A |
---|
0.05 | 59 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A | A | A |
---|
0.06 | 49 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A | A | A |
---|
0.07 | 42 | R | R | A | A | A | A | R | R | A | A | A | A | A | A | A | A | A | A | A |
---|
0.08 | 36 | R | R | A | A | A | A | R | 2(4) | 12(4) | 21(5) | 28(6) | A | A | A | A | A | A | A | A |
---|
0.09 | 32 | R | R | A | A | A | A | R | 10(4) | 21(5) | 30(6) | 38(7) | 45(7) | 51(8) | A | A | A | A | A | A |
---|
0.10 | 29 | R | R | A | A | A | A | 4(4) | 17(5) | 28(6) | 37(7) | 46(8) | 52(9) | 58(9) | 63(10) | 67(10) | A | A | A | A |
---|
0.11 | 26 | R | R | A | A | A | A | 11(5) | 24(6) | 36(7) | 46(8) | 54(9) | 60(10) | 66(11) | 70(11) | 73(11) | 74(11) | A | A | A |
---|
0.12 | 24 | R | R | A | A | A | A | 15(5) | 29(7) | 41(8) | 51(9) | 59(10) | 66(11) | 71(12) | 74(12) | 76(12) | 76(12) | 76(12) | A | A |
---|
0.13 | 22 | R | R | A | A | A | A | 20(6) | 35(8) | 47(9) | 57(11) | 65(12) | 71(13) | 75(13) | 78(13) | 78(13) | 78(13) | 75(13) | 71(13) | A |
---|
0.14 | 20 | R | R | A | A | A | A | 25(7) | 41(9) | 54(11) | 64(12) | 71(13) | 76(14) | 80(14) | 80(14) | 80(14) | 77(14) | 72(13) | 66(13) | A |
---|
0.15 | 19 | R | R | A | A | A | A | 28(8) | 45(10) | 57(12) | 67(13) | 74(14) | 79(15) | 81(15) | 81(15) | 79(15) | 75(15) | 69(14) | A | A |
---|
0.16 | 18 | R | R | 2(4) | A | A | A | 31(8) | 48(11) | 61(13) | 70(15) | 77(16) | 81(16) | 82(16) | 81(16) | 78(16) | 73(15) | 65(14) | A | A |
---|
0.17 | 17 | R | R | 4(4) | A | A | A | 35(9) | 52(12) | 65(14) | 74(16) | 80(17) | 83(17) | 83(17) | 81(17) | 76(16) | 69(15) | 59(13) | A | A |
---|
0.18 | 16 | R | 2(4) | 5(4) | 8(5) | A | A | 38(10) | 55(13) | 68(16) | 77(17) | 82(18) | 84(19) | 83(18) | 79(18) | 73(17) | 64(15) | 52(13) | A | A |
---|
0.19 | 15 | R | 4(4) | 7(5) | 9(5) | A | A | 42(11) | 59(15) | 72(17) | 80(19) | 85(20) | 85(20) | 83(19) | 77(18) | 68(16) | 56(14) | A | A | A |
---|
0.20 | 14 | R | 6(4) | 9(5) | 11(5) | A | A | 46(12) | 64(16) | 76(18) | 83(20) | 86(20) | 85(20) | 81(19) | 72(18) | 61(15) | 47(13) | A | A | A |
---|
0.22 | 13 | 3(4) | 8(5) | 11(6) | 12(6) | 12(6) | A | 50(14) | 68(18) | 80(21) | 86(22) | 87(22) | 84(22) | 77(20) | 66(18) | 51(15) | 34(11) | A | A | A |
---|
0.24 | 11 | 7(5) | 11(6) | 14(6) | 14(6) | 14(6) | A | 60(18) | 77(22) | 87(24) | 89(24) | 86(24) | 76(21) | 62(18) | 43(13) | A | A | A | | |
---|
0.26 | 10 | 9(5) | 13(6) | 15(7) | 15(7) | 13(6) | A | 65(20) | 82(24) | 90(26) | 89(26) | 82(24) | 68(21) | 48(16) | 25(10) | A | A | | | |
---|
0.28 | 10 | 9(6) | 13(7) | 15(8) | 15(8) | 13(7) | A | 65(22) | 82(26) | 90(29) | 89(28) | 82(26) | 68(22) | 48(17) | 25(10) | A | A | | | |
---|
0.30 | 9 | 11(6) | 15(8) | 16(8) | 15(8) | 12(7) | A | 71(24) | 87(29) | 91(30) | 87(29) | 74(25) | 54(19) | 30(12) | A | A | | | | |
---|
0.35 | 7 | 16(9) | 18(9) | 17(9) | 12(7) | A | A | 83(32) | 93(35) | 88(34) | 69(27) | 41(17) | A | A | | | | | | |
---|
0.40 | 6 | 18(10) | 19(10) | 15(9) | 8(6) | A | A | 90(39) | 93(40) | 78(34) | 49(22) | 12(8) | A | | | | | | | |
---|
0.45 | 6 | 18(11) | 19(12) | 15(10) | 8(7) | A | A | 90(44) | 93(45) | 78(38) | 49(25) | 12(9) | A | | | | | | | |
---|
0.50 | 5 | 20(13) | 19(12) | 11(8) | A | A | | 95(50) | 88(47) | 58(32) | 17(11) | A | | | | | | | | |
---|
0.50 | 5 | 20(13) | 19(12) | 11(8) | A | A | | 95(50) | 88(47) | 58(32) | 17(11) | A | | | | | | | | |
---|
0.60 | 4 | 21(15) | 15(12) | 3(5) | A | | | 96(60) | 70(45) | 22(16) | A | | | | | | | | | |
---|
0.70 | 3 | 19(16) | 6(7) | A | | | | 85(62) | 31(24) | A | | | | | | | | | | |
---|
0.80 | 2 | 10(10) | A | | | | | 45(38) | A | | | | | | | | | | | |
---|
0.90 | 2 | 10(11) | A | | | | | 45(43) | A | | | | | | | | | | | |
---|
The following is the code for Gehan's two stage procedure for Phase II studies. I have adapted the formulae as described in the text book by Machin et. el.. Those interested can copy, use, and modify these codes
# Data
errorI = 0.05 # alpha Type I Error
power = 0.8 # power 1-beta
pa = 0.4 # success rate above which treatment is accepted
# Sample Size for Stage 1
ssiz1 = ceiling(log(1 - power) / log( 1 - pa))
# Functions for Stage 2
FindGX <- function(n, r, m)
{
x = 0
for(s in 0 : r)
{
f = choose(n, s)
p = n - s
x = x + f * m^s * (1 - m)^p
}
x
}
FindGMu <- function(n, r) #iterations to find the correct mu
{
mL = 0.0001;
mR = 0.9999;
m = 0.5;
xL = FindGX(n, r, mL) - 0.25
x = FindGX(n, r, m) - 0.25
xR = FindGX(n, r, mR) - 0.25;
if((xL * x)>0 & (xR * x)<0)
{
mL = m
}
else
{
if((xL * x)<0 & (xR * x)>0)
{
mR = m;
}
else
{
return(0)
}
}
while(abs(x)>0.0001)
{
m = (mL + mR) / 2
xL = FindGX(n, r, mL) - 0.25
x = FindGX(n, r, m) - 0.25
if((xL * x)>0)
{
mL = m
}
else
{
mR = m
}
}
m
}
# Main Program for Stage 2
# Create vectors to contain results
r1 <- 0 : ssiz1 # number of successes in stage 1
ssiz2 <- 0 : ssiz1 # maximum samples size for stage 2
minSuc <- 0 : ssiz1 # minimum number of successes for tmt to be accepted
ssiz2[1] = "Reject" # r1=0 treatment rejected no stage 2
minSuc[1] = "Reject"
ssiz2[ssiz1 + 1] = "Accept" # r1=all treatment accepted no stage 2
minSuc[ssiz1 + 1] = "Accept"
for(i in 2 : ssiz1-1)
{
mu = FindGMu(s1, i)
s2 = ceiling(mu * (1 - mu) / errorI^2 - s1)
tot = s1 + s2
ns = ceiling(pa * tot)
ssiz2[i+1] = s2
minSuc[i+1] = ns
}
# Result display
# Sample Size Sate 1
ssiz1
# Stage 2 : r1=number of successes in stage 1
# ssiz2 = sample size in stage 2
# minSuc = minimum number of successes required in stage 2 for tmt to be accepted
outDF <- data.frame(r1,ssiz2,minSuc)
outDF
Results produced are
> # Result display
>
> # Sample Size Sate 1
> #s1
> ssiz1
[1] 4
> # Stage 2 : r1=number of successes in stage 1
> # ssiz2 = sample size in stage 2
> # minSuc = minimum number of successes required in stage 2 for tmt to be accepted
>
> outDF <- data.frame(r1,ssiz2,minSuc)
> outDF
r1 ssiz2 minSuc
1 0 Reject Reject
2 1 96 40
3 2 70 30
4 3 22 11
5 4 Accept Accept
>