c:\ian\git\artbin\package\artbin.ado
*!version 2.1.0 IW     04jan2024
c:\ian\git\artbin\package\art2bin.ado
*!version 1.01  09june2022

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.100 (two-sided)
                                        (taken as .05 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         78

Sample size per group (calculated)     39 39
Expected total number of events        7.8
Expected number of events per group    3.9 3.9
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.300  0.300 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         3532

Sample size per group (calculated)     1766 1766
Expected total number of events        1059.6
Expected number of events per group    529.8 529.8
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15

Anticipated event probabilities        0.150  0.150 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         240

Sample size per group (calculated)     120 120
Expected total number of events        36
Expected number of events per group    18 18
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1

Anticipated event probabilities        0.200  0.200 

Alpha                                  0.200 (two-sided)
                                        (taken as .1 one-sided)
Power (designed)                       0.800

Total sample size (calculated)         290

Sample size per group (calculated)     145 145
Expected total number of events        58
Expected number of events per group    29 29
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         1514

Sample size per group (calculated)     757 757
Expected total number of events        151.4
Expected number of events per group    75.7 75.7
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2

Anticipated event probabilities        0.250  0.250 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         198

Sample size per group (calculated)     99 99
Expected total number of events        49.5
Expected number of events per group    24.75 24.75
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15

Anticipated event probabilities        0.200  0.200 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         300

Sample size per group (calculated)     150 150
Expected total number of events        60
Expected number of events per group    30 30
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.150  0.150 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         2144

Sample size per group (calculated)     1072 1072
Expected total number of events        321.6
Expected number of events per group    160.8 160.8
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.9000
         alpha = 0.0500 (one-sided)
            pi = 0.0500
         delta = 0.0500
         estimated required sample size (per group) = 326

The total estimated sample size is 652

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.050  0.050 

Alpha                                  0.100 (two-sided)
                                        (taken as .05 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         652

Sample size per group (calculated)     326 326
Expected total number of events        32.6
Expected number of events per group    16.3 16.3
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.8000
         alpha = 0.0500 (one-sided)
            pi = 0.2000
         delta = 0.1000
         estimated required sample size (per group) = 198

The total estimated sample size is 396

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1

Anticipated event probabilities        0.200  0.200 

Alpha                                  0.100 (two-sided)
                                        (taken as .05 one-sided)
Power (designed)                       0.800

Total sample size (calculated)         396

Sample size per group (calculated)     198 198
Expected total number of events        79.2
Expected number of events per group    39.6 39.6
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.7000
         alpha = 0.0250 (one-sided)
            pi = 0.3000
         delta = 0.1000
         estimated required sample size (per group) = 260

The total estimated sample size is 520

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1

Anticipated event probabilities        0.300  0.300 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.700

Total sample size (calculated)         520

Sample size per group (calculated)     260 260
Expected total number of events        156
Expected number of events per group    78 78
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.9000
         alpha = 0.0250 (one-sided)
            pi = 0.5000
         delta = 0.3000
         estimated required sample size (per group) = 59

The total estimated sample size is 118

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .3
Alternative hypothesis                 H1: pi2 - pi1 < .3

Anticipated event probabilities        0.500  0.500 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.900

Total sample size (calculated)         118

Sample size per group (calculated)     59 59
Expected total number of events        59
Expected number of events per group    29.5 29.5
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.8000
         alpha = 0.0500 (one-sided)
            pi = 0.6000
         delta = 0.0500
         estimated required sample size (per group) = 1188

The total estimated sample size is 2376

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.600  0.600 

Alpha                                  0.100 (two-sided)
                                        (taken as .05 one-sided)
Power (designed)                       0.800

Total sample size (calculated)         2376

Sample size per group (calculated)     1188 1188
Expected total number of events        1425.6
Expected number of events per group    712.8 712.8
------------------------------------------------------------------------------

Estimated sample size for two-sample comparison of proportions (non-inferiority)

Null hypothesis: p2 - p1 ³ delta (inferior), where:
                               pi (entered in command) is the overall proportion of participants
                               expected to experience the outcome if the treatments
                               are non-inferior, and delta is the smallest change in
                               proportions between groups (p2 - p1) which would still
                               be clinically important.

Alternative hypothesis: p2 - p1 < delta (non-inferior)

Note: a non-inferiority analysis is one-sided.

Assumptions:
         power = 0.7000
         alpha = 0.0250 (one-sided)
            pi = 0.8000
         delta = 0.1000
         estimated required sample size (per group) = 198

The total estimated sample size is 396

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1

Anticipated event probabilities        0.800  0.800 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.700

Total sample size (calculated)         396

Sample size per group (calculated)     198 198
Expected total number of events        316.8
Expected number of events per group    158.4 158.4
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.100 (two-sided)
                                        (taken as .05 one-sided)
Power (calculated)                     0.903

Total sample size (designed)           78

Sample size per group (designed)       39 39
Expected total number of events        7.8
Expected number of events per group    3.9 3.9
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.300  0.300 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.900

Total sample size (designed)           3532

Sample size per group (designed)       1766 1766
Expected total number of events        1059.6
Expected number of events per group    529.8 529.8
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15

Anticipated event probabilities        0.150  0.150 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.902

Total sample size (designed)           240

Sample size per group (designed)       120 120
Expected total number of events        36
Expected number of events per group    18 18
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1

Anticipated event probabilities        0.200  0.200 

Alpha                                  0.200 (two-sided)
                                        (taken as .1 one-sided)
Power (calculated)                     0.802

Total sample size (designed)           290

Sample size per group (designed)       145 145
Expected total number of events        58
Expected number of events per group    29 29
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.900

Total sample size (designed)           1514

Sample size per group (designed)       757 757
Expected total number of events        151.4
Expected number of events per group    75.7 75.7
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2

Anticipated event probabilities        0.250  0.250 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.901

Total sample size (designed)           198

Sample size per group (designed)       99 99
Expected total number of events        49.5
Expected number of events per group    24.75 24.75
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15

Anticipated event probabilities        0.200  0.200 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.901

Total sample size (designed)           300

Sample size per group (designed)       150 150
Expected total number of events        60
Expected number of events per group    30 30
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05

Anticipated event probabilities        0.150  0.150 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (calculated)                     0.900

Total sample size (designed)           2144

Sample size per group (designed)       1072 1072
Expected total number of events        321.6
Expected number of events per group    160.8 160.8
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          substantial-superiority
Number of groups                       2
Favourable/unfavourable outcome        favourable
                                       Inferred by the program
Allocation ratio                       1:3
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the score test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 <= .15
Alternative hypothesis                 H1: pi2 - pi1 > .15

Anticipated event probabilities        0.200  0.500 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.800

Total sample size (calculated)         391

Sample size per group (calculated)     98 293
Expected total number of events        166.1
Expected number of events per group    19.6 146.5
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.7
            p2 = 0.9
         delta = 0.2
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 20
    Group 2: 20
      Total: 40

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 23
    Group 2: 23
      Total: 46


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2
Algorithm used                         2-arm

Anticipated event probabilities        0.300  0.100 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         40

Sample size per group (calculated)     20 20
Expected total number of events        8
Expected number of events per group    6 2
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.75
            p2 = 0.85
         delta = 0.1
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 83
    Group 2: 83
      Total: 166

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 86
    Group 2: 86
      Total: 172


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1
Algorithm used                         2-arm

Anticipated event probabilities        0.250  0.150 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         166

Sample size per group (calculated)     83 83
Expected total number of events        33.2
Expected number of events per group    20.75 12.45
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.8
            p2 = 0.7
         delta = 0.15
         alpha = .05 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 1268
    Group 2: 1268
      Total: 2536

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 1265
    Group 2: 1265
      Total: 2530


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15
Algorithm used                         2-arm

Anticipated event probabilities        0.200  0.300 

Alpha                                  0.050 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         2536

Sample size per group (calculated)     1268 1268
Expected total number of events        634
Expected number of events per group    253.6 380.4
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.85
            p2 = 0.8
         delta = 0.1
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 1209
    Group 2: 1209
      Total: 2418

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 1217
    Group 2: 1217
      Total: 2434


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1
Algorithm used                         2-arm

Anticipated event probabilities        0.150  0.200 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         2418

Sample size per group (calculated)     1209 1209
Expected total number of events        423.15
Expected number of events per group    181.35 241.8
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.9
            p2 = 0.9
         delta = 0.05
         alpha = .05 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 617
    Group 2: 617
      Total: 1234

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 631
    Group 2: 631
      Total: 1262


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05
Algorithm used                         2-arm

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.050 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         1234

Sample size per group (calculated)     617 617
Expected total number of events        123.4
Expected number of events per group    61.7 61.7
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.7
            p2 = 0.75
         delta = 0.15
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:1
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 105
    Group 2: 105
      Total: 210

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 105
    Group 2: 105
      Total: 210


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       equal group sizes
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15
Algorithm used                         2-arm

Anticipated event probabilities        0.300  0.250 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         210

Sample size per group (calculated)     105 105
Expected total number of events        57.75
Expected number of events per group    31.5 26.25
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.7
            p2 = 0.9
         delta = 0.2
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:2
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 17
    Group 2: 34
      Total: 51

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 15
    Group 2: 30
      Total: 45


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:2
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .2
Alternative hypothesis                 H1: pi2 - pi1 < .2
Algorithm used                         2-arm

Anticipated event probabilities        0.300  0.100 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         51

Sample size per group (calculated)     17 34
Expected total number of events        8.5
Expected number of events per group    5.1 3.4
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.75
            p2 = 0.85
         delta = 0.1
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:3
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 61
    Group 2: 182
      Total: 243

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 50
    Group 2: 149
      Total: 199


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:3
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1
Algorithm used                         2-arm

Anticipated event probabilities        0.250  0.150 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         243

Sample size per group (calculated)     61 182
Expected total number of events        42.55
Expected number of events per group    15.25 27.3
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.8
            p2 = 0.7
         delta = 0.15
         alpha = .05 (one-sided)
         power = .9
    allocation = 1:4
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 728
    Group 2: 2912
      Total: 3640

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 687
    Group 2: 2745
      Total: 3432


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:4
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15
Algorithm used                         2-arm

Anticipated event probabilities        0.200  0.300 

Alpha                                  0.050 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         3640

Sample size per group (calculated)     728 2912
Expected total number of events        1019.2
Expected number of events per group    145.6 873.6
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.85
            p2 = 0.8
         delta = 0.1
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:2
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 873
    Group 2: 1745
      Total: 2618

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 838
    Group 2: 1675
      Total: 2513


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:2
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .1
Alternative hypothesis                 H1: pi2 - pi1 < .1
Algorithm used                         2-arm

Anticipated event probabilities        0.150  0.200 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         2618

Sample size per group (calculated)     873 1745
Expected total number of events        479.95
Expected number of events per group    130.95 349
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.9
            p2 = 0.9
         delta = 0.05
         alpha = .05 (one-sided)
         power = .9
    allocation = 1:4
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 386
    Group 2: 1542
      Total: 1928

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 333
    Group 2: 1332
      Total: 1665


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:4
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .05
Alternative hypothesis                 H1: pi2 - pi1 < .05
Algorithm used                         2-arm

Anticipated event probabilities        0.100  0.100 

Alpha                                  0.050 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         1928

Sample size per group (calculated)     386 1542
Expected total number of events        192.8
Expected number of events per group    38.6 154.2
------------------------------------------------------------------------------

+----------------------------------------------------------------------------+
| Sample size calculation for non-inferiority trials using a risk difference |
+----------------------------------------------------------------------------+
            p1 = 0.7
            p2 = 0.75
         delta = 0.15
         alpha = .025 (one-sided)
         power = .9
    allocation = 1:3
not assessable = 0

Sample size using observed values (approximate):
    Group 1: 72
    Group 2: 215
      Total: 287

Sample size using maximum likelihood estimation (more accurate):
    Group 1: 62
    Group 2: 186
      Total: 248


ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        unfavourable
                                       Inferred by the program
Allocation ratio                       1:3
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 >= .15
Alternative hypothesis                 H1: pi2 - pi1 < .15
Algorithm used                         2-arm

Anticipated event probabilities        0.300  0.250 

Alpha                                  0.025 (one-sided)
Power (designed)                       0.900

Total sample size (calculated)         287

Sample size per group (calculated)     72 215
Expected total number of events        75.35
Expected number of events per group    21.6 53.75
------------------------------------------------------------------------------

ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.1.0 04jan2024)
------------------------------------------------------------------------------
A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, 
Ella Marley-Zagar and Ian White
MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK.
------------------------------------------------------------------------------
Type of trial                          non-inferiority
Number of groups                       2
Favourable/unfavourable outcome        favourable
                                       Inferred by the program
Allocation ratio                       1:2
Statistical test assumed               unconditional comparison of 2
                                        binomial proportions
                                        using the wald test
Local or distant                       distant
Continuity correction                  no
Null hypothesis                        H0: pi2 - pi1 <= -.1
Alternative hypothesis                 H1: pi2 - pi1 > -.1

Anticipated event probabilities        0.700  0.750 

Alpha                                  0.050 (two-sided)
                                        (taken as .025 one-sided)
Power (designed)                       0.800

Loss to follow up assumed              20 %

Total sample size (calculated)         398

Sample size per group (calculated)     133 265
Expected total number of events        233.48
Expected number of events per group    74.48 159
------------------------------------------------------------------------------

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*** ARTBIN HAS PASSED ALL SOFTWARE TESTING POINT 1  *********
*************************************************************