The SAS System

The SEQDESIGN Procedure
Design: ErrorSpend

Design Information
Statistic Distribution | Normal
Boundary Scale | Standardized Z
Alternative Hypothesis | Two-Sided
Alternative Reference | 0.693147
Number of Stages | 1
Alpha | 0.05
Beta | 0.1
Power | 0.9
Max Information (Percent of Fixed Sample) | 100
Max Information | 21.86982
Null Ref ASN (Percent of Fixed Sample) | 100
Alt Ref ASN (Percent of Fixed Sample) | 100
Adj Design Alpha | 0.05
Adj Design Beta | 0.1
Adj Design Power | 0.9
Adj Design Max Information (Percent of Fixed Sample) | 100
Adj Design Max Information | 21.86982
Adj Design Null Ref ASN (Percent of Fixed Sample) | 100
Adj Design Alt Ref ASN (Percent of Fixed Sample) | 100

Method Information
Boundary | Alpha | Beta | Alternative Reference | Drift
--- | --- | --- | --- | ---
Upper Alpha | 0.02500 | 0.10000 | 0.693147 | 3.241516
Lower Alpha | 0.02500 | 0.10000 | -0.69315 | -3.24152

Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 1.0000 | 21.86982 | 87.4793 | -3.24152 | 3.24152 | -1.95996 | 1.95996

Sample Size Summary
Test | Two-Sample Survival
Null Hazard Rate | 0.03466
Hazard Rate (Group A) | 0.01733
Hazard Rate (Group B) | 0.03466
Hazard Ratio | 0.5
log(Hazard Ratio) | -0.69315
Reference Hazards | Alt Ref
Accrual | Uniform
Accrual Rate | 8.213132
Accrual Time | 24
Follow-up Time | 12
Total Time | 36
Max Number of Events | 87.4793
Max Sample Size | 197.1152
Expected Sample Size (Null Ref) | 197.1152
Expected Sample Size (Alt Ref) | 197.1152
Follow-up Time (Ceiling Time) | 12
Total Time (Ceiling Time) | 36

Numbers of Events (D) and Sample Sizes (N) Two-Sample Log-Rank Test
_Stage_ | Fractional Time | Ceiling Time
--- | --- | ---
D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information | D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information
1 | 87.48 | 33.07 | 54.41 | 36.0000 | 197.12 | 98.56 | 98.56 | 21.8698 | 87.48 | 33.07 | 54.41 | 36 | 197.12 | 98.56 | 98.56 | 21.8698

Ceiling-Adjusted Design Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 1.0000 | 21.86982 | 87.4793 | -3.24152 | 3.24152 | -1.95996 | 1.95996

The SAS System

The SEQDESIGN Procedure
Design: ErrorSpend

Design Information
Statistic Distribution | Normal
Boundary Scale | Standardized Z
Alternative Hypothesis | Two-Sided
Alternative Reference | 0.693147
Number of Stages | 1
Alpha | 0.05
Beta | 0.1
Power | 0.9
Max Information (Percent of Fixed Sample) | 100
Max Information | 21.86982
Null Ref ASN (Percent of Fixed Sample) | 100
Alt Ref ASN (Percent of Fixed Sample) | 100
Adj Design Alpha | 0.05
Adj Design Beta | 0.0954
Adj Design Power | 0.9046
Adj Design Max Information (Percent of Fixed Sample) | 100
Adj Design Max Information | 22.23082
Adj Design Null Ref ASN (Percent of Fixed Sample) | 100
Adj Design Alt Ref ASN (Percent of Fixed Sample) | 100

Method Information
Boundary | Alpha | Beta | Alternative Reference | Drift
--- | --- | --- | --- | ---
Upper Alpha | 0.02500 | 0.10000 | 0.693147 | 3.241516
Lower Alpha | 0.02500 | 0.10000 | -0.69315 | -3.24152

Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 1.0000 | 21.86982 | 87.4793 | -3.24152 | 3.24152 | -1.95996 | 1.95996

Sample Size Summary
Test | Two-Sample Survival
Null Hazard Rate | 0.03466
Hazard Rate (Group A) | 0.01733
Hazard Rate (Group B) | 0.03466
Hazard Ratio | 0.5
log(Hazard Ratio) | -0.69315
Reference Hazards | Alt Ref
Accrual | Uniform
Accrual Rate | 6
Accrual Time | 30.36265
Follow-up Time | 12
Total Time | 42.36265
Max Number of Events | 87.4793
Max Sample Size | 182.1759
Expected Sample Size (Null Ref) | 182.1759
Expected Sample Size (Alt Ref) | 182.1759
Follow-up Time (Ceiling Time) | 12.63735
Total Time (Ceiling Time) | 43

Numbers of Events (D) and Sample Sizes (N) Two-Sample Log-Rank Test
_Stage_ | Fractional Time | Ceiling Time
--- | --- | ---
D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information | D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information
1 | 87.48 | 33.56 | 53.92 | 42.3627 | 182.18 | 91.09 | 91.09 | 21.8698 | 88.92 | 34.19 | 54.73 | 43 | 182.18 | 91.09 | 91.09 | 22.2308

Ceiling-Adjusted Design Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 1.0000 | 22.23082 | 88.92328 | -3.26816 | 3.26816 | -1.95996 | 1.95996

The SAS System

The SEQDESIGN Procedure
Design: ErrorSpend

Design Information
Statistic Distribution | Normal
Boundary Scale | Standardized Z
Alternative Hypothesis | Two-Sided
Early Stop | Reject Null
Method | Error Spending
Boundary Key | Both
Alternative Reference | 0.693147
Number of Stages | 4
Alpha | 0.05
Beta | 0.1
Power | 0.9
Max Information (Percent of Fixed Sample) | 101.8279
Max Information | 22.26962
Null Ref ASN (Percent of Fixed Sample) | 101.2586
Alt Ref ASN (Percent of Fixed Sample) | 77.73131
Adj Design Alpha | 0.05
Adj Design Beta | 0.10044
Adj Design Power | 0.89956
Adj Design Max Information (Percent of Fixed Sample) | 101.9868
Adj Design Max Information | 22.26962
Adj Design Null Ref ASN (Percent of Fixed Sample) | 101.3918
Adj Design Alt Ref ASN (Percent of Fixed Sample) | 77.50332

Method Information
Boundary | Method | Alpha | Beta | Error Spending | Alternative Reference | Drift
--- | --- | --- | --- | --- | --- | ---
Function
Upper Alpha | Error Spending | 0.02500 | 0.10000 | Approx O'Brien-Fleming | 0.693147 | 3.27101
Lower Alpha | Error Spending | 0.02500 | 0.10000 | Approx O'Brien-Fleming | -0.69315 | -3.27101

Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 0.2500 | 5.567405 | 22.26962 | -1.63550 | 1.63550 | -4.33263 | 4.33263
2 | 0.5000 | 11.13481 | 44.53924 | -2.31295 | 2.31295 | -2.96333 | 2.96333
3 | 0.7500 | 16.70221 | 66.80886 | -2.83278 | 2.83278 | -2.35902 | 2.35902
4 | 1.0000 | 22.26962 | 89.07847 | -3.27101 | 3.27101 | -2.01409 | 2.01409

Sample Size Summary
Test | Two-Sample Survival
Null Hazard Rate | 0.03466
Hazard Rate (Group A) | 0.01733
Hazard Rate (Group B) | 0.03466
Hazard Ratio | 0.5
log(Hazard Ratio) | -0.69315
Reference Hazards | Alt Ref
Accrual | Uniform
Accrual Rate | 28.26166
Accrual Time | 10
Follow-up Time | 10
Total Time | 20
Max Number of Events | 89.07847
Max Sample Size | 282.6166
Expected Sample Size (Null Ref) | 282.6158
Expected Sample Size (Alt Ref) | 282.4276
Follow-up Time (Ceiling Time) | 10
Total Time (Ceiling Time) | 20

Numbers of Events (D) and Sample Sizes (N) Two-Sample Log-Rank Test
_Stage_ | Fractional Time | Ceiling Time
--- | --- | ---
D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information | D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information
1 | 22.27 | 7.65 | 14.62 | 8.0879 | 228.58 | 114.29 | 114.29 | 5.5674 | 27.35 | 9.42 | 17.92 | 9 | 254.35 | 127.18 | 127.18 | 6.8366
2 | 44.54 | 15.51 | 29.03 | 11.7797 | 282.62 | 141.31 | 141.31 | 11.1348 | 45.87 | 15.99 | 29.89 | 12 | 282.62 | 141.31 | 141.31 | 11.4682
3 | 66.81 | 23.67 | 43.14 | 15.6525 | 282.62 | 141.31 | 141.31 | 16.7022 | 68.69 | 24.38 | 44.31 | 16 | 282.62 | 141.31 | 141.31 | 17.1726
4 | 89.08 | 32.21 | 56.87 | 20.0000 | 282.62 | 141.31 | 141.31 | 22.2696 | 89.08 | 32.21 | 56.87 | 20 | 282.62 | 141.31 | 141.31 | 22.2696

Ceiling-Adjusted Design Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 0.3070 | 6.83661 | 27.34644 | -1.81237 | 1.81237 | -3.87992 | 3.87992
2 | 0.5150 | 11.4682 | 45.8728 | -2.34732 | 2.34732 | -2.91658 | 2.91658
3 | 0.7711 | 17.17259 | 68.69037 | -2.87239 | 2.87239 | -2.32174 | 2.32174
4 | 1.0000 | 22.26962 | 89.07847 | -3.27101 | 3.27101 | -2.02011 | 2.02011

The SAS System

The SEQDESIGN Procedure
Design: ErrorSpend

Design Information
Statistic Distribution | Normal
Boundary Scale | Standardized Z
Alternative Hypothesis | Two-Sided
Early Stop | Reject Null
Method | Error Spending
Boundary Key | Both
Alternative Reference | 0.693147
Number of Stages | 4
Alpha | 0.05
Beta | 0.1
Power | 0.9
Max Information (Percent of Fixed Sample) | 101.8279
Max Information | 22.26962
Null Ref ASN (Percent of Fixed Sample) | 101.2586
Alt Ref ASN (Percent of Fixed Sample) | 77.73131
Adj Design Alpha | 0.05
Adj Design Beta | 0.09901
Adj Design Power | 0.90099
Adj Design Max Information (Percent of Fixed Sample) | 101.8836
Adj Design Max Information | 22.36004
Adj Design Null Ref ASN (Percent of Fixed Sample) | 101.2966
Adj Design Alt Ref ASN (Percent of Fixed Sample) | 77.24425

Method Information
Boundary | Method | Alpha | Beta | Error Spending | Alternative Reference | Drift
--- | --- | --- | --- | --- | --- | ---
Function
Upper Alpha | Error Spending | 0.02500 | 0.10000 | Approx O'Brien-Fleming | 0.693147 | 3.27101
Lower Alpha | Error Spending | 0.02500 | 0.10000 | Approx O'Brien-Fleming | -0.69315 | -3.27101

Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 0.2500 | 5.567405 | 22.26962 | -1.63550 | 1.63550 | -4.33263 | 4.33263
2 | 0.5000 | 11.13481 | 44.53924 | -2.31295 | 2.31295 | -2.96333 | 2.96333
3 | 0.7500 | 16.70222 | 66.80886 | -2.83278 | 2.83278 | -2.35902 | 2.35902
4 | 1.0000 | 22.26962 | 89.07848 | -3.27101 | 3.27101 | -2.01409 | 2.01409

Sample Size Summary
Test | Two-Sample Survival
Null Hazard Rate | 0.034657
Hazard Rate (Group A) | 0.017329
Hazard Rate (Group B) | 0.034657
Hazard Ratio | 0.5
log(Hazard Ratio) | -0.69315
Reference Hazards | Alt Ref
Accrual | Uniform
Accrual Rate | 6
Accrual Time | 25
Follow-up Time | 24.74524
Total Time | 49.74524
Max Number of Events | 89.07848
Max Sample Size | 150
Expected Sample Size (Null Ref) | 149.9994
Expected Sample Size (Alt Ref) | 149.861
Follow-up Time (Ceiling Time) | 25
Total Time (Ceiling Time) | 50

Numbers of Events (D) and Sample Sizes (N) Two-Sample Log-Rank Test
_Stage_ | Fractional Time | Ceiling Time
--- | --- | ---
D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information | D | D(Grp 1) | D(Grp 2) | Time | N | N(Grp 1) | N(Grp 2) | Information
1 | 22.27 | 7.92 | 14.35 | 18.3766 | 110.26 | 55.13 | 55.13 | 5.5674 | 23.68 | 8.43 | 15.25 | 19 | 114.00 | 57.00 | 57.00 | 5.9196
2 | 44.54 | 16.26 | 28.28 | 27.0531 | 150.00 | 75.00 | 75.00 | 11.1348 | 47.00 | 17.22 | 29.79 | 28 | 150.00 | 75.00 | 75.00 | 11.7509
3 | 66.81 | 25.28 | 41.53 | 36.6750 | 150.00 | 75.00 | 75.00 | 16.7022 | 67.46 | 25.56 | 41.90 | 37 | 150.00 | 75.00 | 75.00 | 16.8657
4 | 89.08 | 35.36 | 53.72 | 49.7452 | 150.00 | 75.00 | 75.00 | 22.2696 | 89.44 | 35.53 | 53.91 | 50 | 150.00 | 75.00 | 75.00 | 22.3600

Ceiling-Adjusted Design Boundary Information (Standardized Z Scale) Null Reference = 0
_Stage_ |  | Alternative | Boundary Values
--- | --- | --- | ---
Information Level | Reference | Lower | Upper
Proportion | Actual | Events | Lower | Upper | Alpha | Alpha
1 | 0.2647 | 5.919645 | 23.67858 | -1.68645 | 1.68645 | -4.20191 | 4.20191
2 | 0.5255 | 11.7509 | 47.00359 | -2.37608 | 2.37608 | -2.88074 | 2.88074
3 | 0.7543 | 16.86574 | 67.46295 | -2.84661 | 2.84661 | -2.35628 | 2.35628
4 | 1.0000 | 22.36004 | 89.44017 | -3.27764 | 3.27764 | -2.01576 | 2.01576