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

Boundary Plot

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

Boundary Plot

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

Boundary Plot

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

Boundary Plot

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