This R Markdown document provides many different examples that illustrate the usage of the *R generic function* `summary`

with rpact. This is a technical vignette and is to be considered mainly as a comprehensive overview of the possible summaries in rpact.

**First, load the rpact package**

`## [1] '3.0.3'`

The following options can be set globally:

`rpact.summary.output.size`

: one of c(“small”, “medium”, “large”); defines how many details will be included into the summary; default is “large”, i.e., all available details are displayed.

`rpact.summary.justify`

: one of c(“right”, “left”, “centre”); shall the values be right-justified (the default), left-justified or centered.

`rpact.summary.intervalFormat`

: defines how intervals will be displayed in the summary, default is “[%s; %s]”.

`rpact.summary.digits`

: defines how many digits are to be used for numeric values (default is 3).

`rpact.summary.digits.probs`

: defines how many digits are to be used for numeric values (default is one more than value of rpact.summary.digits, i.e., 4).

`rpact.summary.trim.zeroes`

: if TRUE (default) zeroes will always displayed as “0”, e.g. “0.000” will become “0”.

**Examples**

```
options("rpact.summary.output.size" = "small") # small, medium, large
options("rpact.summary.output.size" = "medium") # small, medium, large
options("rpact.summary.output.size" = "large") # small, medium, large
options("rpact.summary.intervalFormat" = "[%s; %s]")
options("rpact.summary.intervalFormat" = "%s - %s")
options("rpact.summary.enforceIntervalView" = TRUE)
options("rpact.summary.justify" = "left")
options("rpact.summary.justify" = "centre")
options("rpact.summary.justify" = "right")
```

```
summary(getDesignGroupSequential(beta = 0.05, typeOfDesign = "asKD", gammaA = 1,
typeBetaSpending = "bsOF"))
```

```
## Sequential analysis with a maximum of 3 looks (group sequential design)
##
## Kim & DeMets alpha spending design, one-sided local significance level 2.5%,
## power 95%, undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 2.394 2.294 2.200
## Futility boundary (z-value scale) -0.993 0.982
## Cumulative alpha spent 0.0083 0.0167 0.0250
## Overall power 0.4259 0.8092 0.9500
## One-sided local significance level 0.0083 0.0109 0.0139
```

```
## Fixed sample analysis
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## One-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 4 looks (group sequential design)
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Overall power 0.0012 0.1494 0.5227 0.8000
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
```

```
## Sequential analysis with a maximum of 4 looks (group sequential design)
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Cumulative alpha spent 0.000004679 0.001207215 0.008644578 0.024999990
## Overall power 0.001247 0.149399 0.522709 0.800000
## Two-sided local significance level 0.000004679 0.001205239 0.008204894 0.022058711
```

```
## Fixed sample analysis
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Two-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 3 looks (group sequential design)
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) -6.000 0.000
## Cumulative alpha spent 0.0003 0.0072 0.0250
## Overall power 0.0329 0.4426 0.8000
## One-sided local significance level 0.0003 0.0071 0.0225
```

```
## Sequential analysis with a maximum of 3 looks (group sequential design)
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.47109 2.45443 2.00404
## Futility boundary (z-value scale) -6.00000 0.00000
## Cumulative alpha spent 0.000259 0.007160 0.025000
## Overall power 0.032939 0.442575 0.800000
## One-sided local significance level 0.000259 0.007055 0.022533
```

```
## Fixed sample analysis
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## One-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design)
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 0 1.000
## Cumulative alpha spent 0.0003 0.0072 0.0250
## Overall power 0.0377 0.4763 0.8000
## One-sided local significance level 0.0003 0.0071 0.0225
```

```
## Fixed sample analysis
##
## O'Brien & Fleming design, one-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## One-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design)
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Overall power 0.0012 0.1494 0.5227 0.8000
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
```

```
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design)
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Cumulative alpha spent 0.000004679 0.001207215 0.008644578 0.024999990
## Overall power 0.001247 0.149399 0.522709 0.800000
## Two-sided local significance level 0.000004679 0.001205239 0.008204894 0.022058711
```

```
## Fixed sample analysis
##
## O'Brien & Fleming design, two-sided local significance level 2.5%, power 80%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Two-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design)
##
## Fisher's combination test design, one-sided local significance level 2.5%,
## undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (p product scale) 0.0123085 0.0016636 0.0002911
## Cumulative alpha spent 0.0123 0.0196 0.0250
## One-sided local significance level 0.0123 0.0123 0.0123
```

```
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design)
##
## Fisher's combination test design, one-sided local significance level 2.5%,
## undefined endpoint.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (p product scale) 0.0193942 0.0028231 0.0005226
## Futility boundary (separate p-value scale) 0.100 0.200
## Cumulative alpha spent 0.0194 0.0240 0.0250
## One-sided local significance level 0.0194 0.0194 0.0194
```

```
## Fixed sample analysis
##
## Fisher's combination test design, one-sided local significance level 2.5%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (p product scale) 0.025
## One-sided local significance level 0.0250
```

```
## Sequential analysis with a maximum of 4 looks (Fisher's combination test design)
##
## Fisher's combination test design, two-sided local significance level 1.25%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (p product scale) 0.00501771 0.00059549 0.00009426 0.00001716
## Cumulative alpha spent 0.005018 0.008171 0.010556 0.012500
## Two-sided local significance level 0.010035 0.010035 0.010035 0.010035
```

```
## Sequential analysis with a maximum of 4 looks (Fisher's combination test design)
##
## Fisher's combination test design, two-sided local significance level 1.25%,
## undefined endpoint.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (p product scale) 0.00501771 0.00059549 0.00009426 0.00001716
## Cumulative alpha spent 0.005018 0.008171 0.010556 0.012500
## Two-sided local significance level 0.01004 0.01004 0.01004 0.01004
```

```
## Fixed sample analysis
##
## Fisher's combination test design, two-sided local significance level 1.25%,
## undefined endpoint.
##
## Stage Fixed
## Efficacy boundary (p product scale) 0.0125
## Two-sided local significance level 0.0250
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect = -0.5, standard deviation = 1, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 154.6
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.364 - 0.364
##
## Legend:
## (t): treatment effect scale
```

`## Warning: Argument unknown in summary(...): 'alternative' = -0.5 will be ignored`

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects, alt. = 0.2 953.0
## Number of subjects, alt. = 0.4 240.2
## Number of subjects, alt. = 0.6 108.2
## Number of subjects, alt. = 0.8 62.0
## Number of subjects, alt. = 1 40.6
## Two-sided local significance level 0.0250
## Efficacy boundary (t), alt. = 0.2 -0.145 - 0.145
## Efficacy boundary (t), alt. = 0.4 -0.291 - 0.291
## Efficacy boundary (t), alt. = 0.6 -0.437 - 0.437
## Efficacy boundary (t), alt. = 0.8 -0.584 - 0.584
## Efficacy boundary (t), alt. = 1 -0.732 - 0.732
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
summary(getPowerMeans(sided = 1, alternative = c(-0.5,-0.3),
maxNumberOfSubjects = 100, directionUpper = FALSE))
```

```
## Power calculation for a continuous endpoint
##
## Fixed sample analysis.
## The results were calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, power directed towards smaller values,
## H1: effect as specified, standard deviation = 1.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Power, alt. = -0.5 0.6969
## Power, alt. = -0.3 0.3175
## Number of subjects 100.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) -0.397
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect = 0.5, standard deviation = 2.5, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 786.8
## One-sided local significance level 0.0250
## Efficacy boundary (t) 0.350
##
## Legend:
## (t): treatment effect scale
```

```
summary(getPowerMeans(thetaH0 = 0, alternative = 0.5, sided = 1, stDev = 2.5,
maxNumberOfSubjects = 100, directionUpper = FALSE))
```

```
## Power calculation for a continuous endpoint
##
## Fixed sample analysis.
## The results were calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, power directed towards smaller values, H1: effect = 0.5,
## standard deviation = 2.5.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Power 0.0016
## Number of subjects 100.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) -0.992
##
## Legend:
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample t-test (one-sided), H0: mu = 0,
## H1: effect = 0.5, standard deviation = 1, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 33.4
## One-sided local significance level 0.0250
## Efficacy boundary (t) 0.352
##
## Legend:
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample t-test (two-sided), H0: mu = 0,
## H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects, alt. = 0.2 240.1
## Number of subjects, alt. = 0.4 61.9
## Number of subjects, alt. = 0.6 29.0
## Number of subjects, alt. = 0.8 17.5
## Number of subjects, alt. = 1 12.2
## Two-sided local significance level 0.0250
## Efficacy boundary (t), alt. = 0.2 -0.146 - 0.146
## Efficacy boundary (t), alt. = 0.4 -0.292 - 0.292
## Efficacy boundary (t), alt. = 0.6 -0.440 - 0.440
## Efficacy boundary (t), alt. = 0.8 -0.590 - 0.590
## Efficacy boundary (t), alt. = 1 -0.742 - 0.742
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect = 1.2, standard deviation = 5, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 662.6
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.873 - 0.873
##
## Legend:
## (t): treatment effect scale
```

```
summary(getSampleSizeMeans(thetaH0 = 0, alternative = 1.2, sided = 2, stDev = 5,
allocationRatioPlanned = 0))
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect = 1.2, standard deviation = 5, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 662.6
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.873 - 0.873
##
## Legend:
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample t-test (two-sided), H0: mu = 0,
## H1: effect = 1.2, standard deviation = 5, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 167.5
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.874 - 0.874
##
## Legend:
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.0967 0.7030 0.8000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.1209 0.0758
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t), alt. = 0.2 0.322 0.160 0.107
## Efficacy boundary (t), alt. = 0.4 0.655 0.321 0.213
## Efficacy boundary (t), alt. = 0.6 1.013 0.483 0.319
## Efficacy boundary (t), alt. = 0.8 1.413 0.646 0.424
## Efficacy boundary (t), alt. = 1 1.882 0.812 0.528
## Futility boundary (t), alt. = 0.2 0.092 0.130
## Futility boundary (t), alt. = 0.4 0.184 0.261
## Futility boundary (t), alt. = 0.6 0.276 0.391
## Futility boundary (t), alt. = 0.8 0.368 0.522
## Futility boundary (t), alt. = 1 0.459 0.653
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), alt. = 0.2 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.4 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.6 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.8 0.2176 0.6822
## Overall exit probability (under H1), alt. = 1 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.0967 0.6064
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.1209 0.0758
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.09667 0.70304 0.80000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.12094 0.07581
## Cumulative alpha spent 0.0002592 0.0071601 0.0250000
## One-sided local significance level 0.0002592 0.0070554 0.0225331
## Efficacy boundary (t), alt. = 0.2 0.322 0.160 0.107
## Efficacy boundary (t), alt. = 0.4 0.655 0.321 0.213
## Efficacy boundary (t), alt. = 0.6 1.013 0.483 0.319
## Efficacy boundary (t), alt. = 0.8 1.413 0.646 0.424
## Efficacy boundary (t), alt. = 1 1.882 0.812 0.528
## Futility boundary (t), alt. = 0.2 0.0921 0.1303
## Futility boundary (t), alt. = 0.4 0.184 0.261
## Futility boundary (t), alt. = 0.6 0.276 0.391
## Futility boundary (t), alt. = 0.8 0.368 0.522
## Futility boundary (t), alt. = 1 0.459 0.653
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), alt. = 0.2 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.4 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.6 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.8 0.2176 0.6822
## Overall exit probability (under H1), alt. = 1 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0002592 0.0062354
## Exit probability for efficacy (under H1) 0.09667 0.60637
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.12094 0.07581
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
summary(getPowerMeans(getDesignGroupSequential(futilityBounds = c(1, 2)),
maxNumberOfSubjects = 100, alternative = 1))
```

```
## Power calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, power directed towards larger values, H1: effect = 1,
## standard deviation = 1.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.2700 0.9281 0.9563
## Number of subjects 33.3 66.7 100.0
## Exit probability for futility 0.0316 0.0120
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 1.340 0.618 0.406
## Futility boundary (t) 0.352 0.500
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1) 0.3015 0.6702
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.2700 0.6582
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.0316 0.0120
##
## Legend:
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power 0.0012 0.1494 0.5227 0.8000
## Number of subjects, alt. = 0.2 242.3 484.6 726.9 969.2
## Number of subjects, alt. = 0.4 61.1 122.1 183.2 244.2
## Number of subjects, alt. = 0.6 27.5 55.0 82.5 110.0
## Number of subjects, alt. = 0.8 15.8 31.5 47.3 63.0
## Number of subjects, alt. = 1 10.3 20.7 31.0 41.3
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t), alt. = 0.2 -0.602 - 0.602 -0.296 - 0.296 -0.197 - 0.197 -0.147 - 0.147
## Efficacy boundary (t), alt. = 0.4 -1.290 - 1.290 -0.600 - 0.600 -0.395 - 0.395 -0.295 - 0.295
## Efficacy boundary (t), alt. = 0.6 -2.204 - 2.204 -0.923 - 0.923 -0.597 - 0.597 -0.443 - 0.443
## Efficacy boundary (t), alt. = 0.8 -3.652 - 3.652 -1.276 - 1.276 -0.804 - 0.804 -0.592 - 0.592
## Efficacy boundary (t), alt. = 1 -6.468 - 6.468 -1.678 - 1.678 -1.019 - 1.019 -0.742 - 0.742
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1) 0.0012 0.1482 0.3733
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Power calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The results were calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power, alt. = 0 <0.0001 0.0012 0.0086 0.0250
## Overall power, alt. = 0.2 <0.0001 0.0056 0.0382 0.1033
## Overall power, alt. = 0.4 0.0002 0.0328 0.1779 0.3870
## Overall power, alt. = 0.6 0.0010 0.1264 0.4718 0.7564
## Overall power, alt. = 0.8 0.0046 0.3280 0.7831 0.9533
## Overall power, alt. = 1 0.0174 0.5996 0.9491 0.9961
## Number of subjects 25.0 50.0 75.0 100.0
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t) -2.376 - 2.376 -0.974 - 0.974 -0.628 - 0.628 -0.465 - 0.465
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), alt. = 0 <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), alt. = 0.2 <0.0001 0.0056 0.0326
## Exit probability for efficacy (under H1), alt. = 0.4 0.0002 0.0326 0.1451
## Exit probability for efficacy (under H1), alt. = 0.6 0.0010 0.1255 0.3454
## Exit probability for efficacy (under H1), alt. = 0.8 0.0046 0.3234 0.4551
## Exit probability for efficacy (under H1), alt. = 1 0.0174 0.5822 0.3495
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
summary(getPowerMeans(getDesignGroupSequential(kMax = 1, sided = 2),
maxNumberOfSubjects = 100, directionUpper = TRUE))
```

```
## Power calculation for a continuous endpoint
##
## Fixed sample analysis.
## The results were calculated for a two-sample t-test (two-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Power, alt. = 0 0.0250
## Power, alt. = 0.2 0.1055
## Power, alt. = 0.4 0.3947
## Power, alt. = 0.6 0.7642
## Power, alt. = 0.8 0.9561
## Power, alt. = 1 0.9965
## Number of subjects 100.0
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.455 - 0.455
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
summary(getPowerMeans(getDesignGroupSequential(kMax = 1, sided = 1),
maxNumberOfSubjects = 100, directionUpper = FALSE))
```

```
## Power calculation for a continuous endpoint
##
## Fixed sample analysis.
## The results were calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, power directed towards smaller values,
## H1: effect as specified, standard deviation = 1.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Power, alt. = 0 0.0250
## Power, alt. = 0.2 0.0016
## Power, alt. = 0.4 <0.0001
## Power, alt. = 0.6 <0.0001
## Power, alt. = 0.8 <0.0001
## Power, alt. = 1 <0.0001
## Number of subjects 100.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) -0.397
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.0967 0.7030 0.8000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.1209 0.0758
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t), alt. = 0.2 0.322 0.160 0.107
## Efficacy boundary (t), alt. = 0.4 0.655 0.321 0.213
## Efficacy boundary (t), alt. = 0.6 1.013 0.483 0.319
## Efficacy boundary (t), alt. = 0.8 1.413 0.646 0.424
## Efficacy boundary (t), alt. = 1 1.882 0.812 0.528
## Futility boundary (t), alt. = 0.2 0.092 0.130
## Futility boundary (t), alt. = 0.4 0.184 0.261
## Futility boundary (t), alt. = 0.6 0.276 0.391
## Futility boundary (t), alt. = 0.8 0.368 0.522
## Futility boundary (t), alt. = 1 0.459 0.653
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), alt. = 0.2 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.4 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.6 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.8 0.2176 0.6822
## Overall exit probability (under H1), alt. = 1 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.0967 0.6064
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.1209 0.0758
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.4711 2.4544 2.0040
## Futility boundary (z-value scale) 1.0000 2.0000
## Overall power 0.09667 0.70304 0.80000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.12094 0.07581
## Cumulative alpha spent 0.00026 0.00716 0.02500
## One-sided local significance level 0.00026 0.00706 0.02253
## Efficacy boundary (t), alt. = 0.2 0.3217 0.1600 0.1066
## Efficacy boundary (t), alt. = 0.4 0.6548 0.3207 0.2130
## Efficacy boundary (t), alt. = 0.6 1.0127 0.4826 0.3189
## Efficacy boundary (t), alt. = 0.8 1.4130 0.6462 0.4240
## Efficacy boundary (t), alt. = 1 1.8816 0.8123 0.5280
## Futility boundary (t), alt. = 0.2 0.0921 0.1303
## Futility boundary (t), alt. = 0.4 0.1842 0.2608
## Futility boundary (t), alt. = 0.6 0.2761 0.3913
## Futility boundary (t), alt. = 0.8 0.3678 0.5220
## Futility boundary (t), alt. = 1 0.4592 0.6529
## Overall exit probability (under H0) 0.84160 0.14622
## Overall exit probability (under H1), alt. = 0.2 0.21761 0.68219
## Overall exit probability (under H1), alt. = 0.4 0.21761 0.68219
## Overall exit probability (under H1), alt. = 0.6 0.21761 0.68219
## Overall exit probability (under H1), alt. = 0.8 0.21761 0.68219
## Overall exit probability (under H1), alt. = 1 0.21761 0.68219
## Exit probability for efficacy (under H0) 0.00026 0.00624
## Exit probability for efficacy (under H1) 0.09667 0.60637
## Exit probability for futility (under H0) 0.84134 0.13999
## Exit probability for futility (under H1) 0.12094 0.07581
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.0967 0.7030 0.8000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.1209 0.0758
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t), alt. = 0.2 0.322 0.160 0.107
## Efficacy boundary (t), alt. = 0.4 0.655 0.321 0.213
## Efficacy boundary (t), alt. = 0.6 1.013 0.483 0.319
## Efficacy boundary (t), alt. = 0.8 1.413 0.646 0.424
## Efficacy boundary (t), alt. = 1 1.882 0.812 0.528
## Futility boundary (t), alt. = 0.2 0.092 0.130
## Futility boundary (t), alt. = 0.4 0.184 0.261
## Futility boundary (t), alt. = 0.6 0.276 0.391
## Futility boundary (t), alt. = 0.8 0.368 0.522
## Futility boundary (t), alt. = 1 0.459 0.653
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), alt. = 0.2 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.4 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.6 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.8 0.2176 0.6822
## Overall exit probability (under H1), alt. = 1 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.0967 0.6064
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.1209 0.0758
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.47 2.45 2.00
## Futility boundary (z-value scale) 1.00 2.00
## Overall power 0.097 0.703 0.800
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.121 0.076
## Cumulative alpha spent <0.001 0.007 0.025
## One-sided local significance level <0.001 0.007 0.023
## Efficacy boundary (t), alt. = 0.2 0.32 0.16 0.11
## Efficacy boundary (t), alt. = 0.4 0.65 0.32 0.21
## Efficacy boundary (t), alt. = 0.6 1.01 0.48 0.32
## Efficacy boundary (t), alt. = 0.8 1.41 0.65 0.42
## Efficacy boundary (t), alt. = 1 1.88 0.81 0.53
## Futility boundary (t), alt. = 0.2 0.09 0.13
## Futility boundary (t), alt. = 0.4 0.18 0.26
## Futility boundary (t), alt. = 0.6 0.28 0.39
## Futility boundary (t), alt. = 0.8 0.37 0.52
## Futility boundary (t), alt. = 1 0.46 0.65
## Overall exit probability (under H0) 0.842 0.146
## Overall exit probability (under H1), alt. = 0.2 0.218 0.682
## Overall exit probability (under H1), alt. = 0.4 0.218 0.682
## Overall exit probability (under H1), alt. = 0.6 0.218 0.682
## Overall exit probability (under H1), alt. = 0.8 0.218 0.682
## Overall exit probability (under H1), alt. = 1 0.218 0.682
## Exit probability for efficacy (under H0) <0.001 0.006
## Exit probability for efficacy (under H1) 0.097 0.606
## Exit probability for futility (under H0) 0.841 0.140
## Exit probability for futility (under H1) 0.121 0.076
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.09667 0.70304 0.80000
## Number of subjects, alt. = 0.2 472.2 944.4 1416.5
## Number of subjects, alt. = 0.4 118.9 237.8 356.8
## Number of subjects, alt. = 0.6 53.5 107.0 160.5
## Number of subjects, alt. = 0.8 30.6 61.3 91.9
## Number of subjects, alt. = 1 20.1 40.1 60.2
## Exit probability for futility 0.12094 0.07581
## Cumulative alpha spent 0.0002592 0.0071601 0.0250000
## One-sided local significance level 0.0002592 0.0070554 0.0225331
## Efficacy boundary (t), alt. = 0.2 0.322 0.160 0.107
## Efficacy boundary (t), alt. = 0.4 0.655 0.321 0.213
## Efficacy boundary (t), alt. = 0.6 1.013 0.483 0.319
## Efficacy boundary (t), alt. = 0.8 1.413 0.646 0.424
## Efficacy boundary (t), alt. = 1 1.882 0.812 0.528
## Futility boundary (t), alt. = 0.2 0.0921 0.1303
## Futility boundary (t), alt. = 0.4 0.184 0.261
## Futility boundary (t), alt. = 0.6 0.276 0.391
## Futility boundary (t), alt. = 0.8 0.368 0.522
## Futility boundary (t), alt. = 1 0.459 0.653
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), alt. = 0.2 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.4 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.6 0.2176 0.6822
## Overall exit probability (under H1), alt. = 0.8 0.2176 0.6822
## Overall exit probability (under H1), alt. = 1 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0002592 0.0062354
## Exit probability for efficacy (under H1) 0.09667 0.60637
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.12094 0.07581
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample t-test (one-sided),
## H0: mu(1) - mu(2) = 0, H1: effect as specified, standard deviation = 1, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.4710914446541 2.45443229863352 2.00403557995285
## Futility boundary (z-value scale) 1 2
## Overall power 0.0966650610605351 0.70304005701407 0.80000000002314
## Number of subjects, alt. = 0.2 472.175971190466 944.351942380932 1416.5279135714
## Number of subjects, alt. = 0.4 118.918820873684 237.837641747368 356.756462621052
## Number of subjects, alt. = 0.6 53.5130463596028 107.026092719206 160.539139078808
## Number of subjects, alt. = 0.8 30.6352725529709 61.2705451059418 91.9058176589127
## Number of subjects, alt. = 1 20.0614501594328 40.1229003188657 60.1843504782985
## Exit probability for futility 0.120939971783343 0.0758116678791493
## Cumulative alpha spent 0.000259173723496486 0.00716005940148245 0.02499999
## One-sided local significance level 0.000259173723496486 0.00705536161371023 0.0225331246048346
## Efficacy boundary (t), alt. = 0.2 0.321710839190332 0.16003836007769 0.106587932791287
## Efficacy boundary (t), alt. = 0.4 0.654823493383795 0.320689953155161 0.212954736915394
## Efficacy boundary (t), alt. = 0.6 1.01268266453838 0.482561132966479 0.318855026247291
## Efficacy boundary (t), alt. = 0.8 1.41302933799472 0.646240615813088 0.423996481981201
## Efficacy boundary (t), alt. = 1 1.88164819392793 0.812280944461675 0.528020838325742
## Futility boundary (t), alt. = 0.2 0.09213829 0.13033753
## Futility boundary (t), alt. = 0.4 0.18418994 0.26075187
## Futility boundary (t), alt. = 0.6 0.27608063 0.39130341
## Futility boundary (t), alt. = 0.8 0.36776309 0.52201903
## Futility boundary (t), alt. = 1 0.45923643 0.65287366
## Overall exit probability (under H0) 0.841603919792039 0.146222739762505
## Overall exit probability (under H1), alt. = 0.2 0.217605032843878 0.682186663832684
## Overall exit probability (under H1), alt. = 0.4 0.217605032843878 0.682186663832684
## Overall exit probability (under H1), alt. = 0.6 0.217605032843878 0.682186663832684
## Overall exit probability (under H1), alt. = 0.8 0.217605032843878 0.682186663832684
## Overall exit probability (under H1), alt. = 1 0.217605032843878 0.682186663832684
## Exit probability for efficacy (under H0) 0.000259173723496486 0.00623541950983228
## Exit probability for efficacy (under H1) 0.0966650610605351 0.606374995953535
## Exit probability for futility (under H0) 0.841344746068543 0.139987320252672
## Exit probability for futility (under H1) 0.120939971783343 0.0758116678791493
##
## Legend:
## alt.: alternative
## (t): treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample test for rates (one-sided),
## H0: pi(1) - pi(2) = 0, H1: treatment rate pi(1) as specified,
## control rate pi(2) = 0.3, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, pi(1) = 0.4 711.9
## Number of subjects, pi(1) = 0.5 186.0
## Number of subjects, pi(1) = 0.6 83.9
## One-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 0.069
## Efficacy boundary (t), pi(1) = 0.5 0.139
## Efficacy boundary (t), pi(1) = 0.6 0.210
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample test for rates (one-sided),
## H0: pi = 0.3, H1: treatment rate pi as specified, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, pi(1) = 0.4 171.7
## Number of subjects, pi(1) = 0.5 43.5
## Number of subjects, pi(1) = 0.6 19.1
## One-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 0.369
## Efficacy boundary (t), pi(1) = 0.5 0.436
## Efficacy boundary (t), pi(1) = 0.6 0.506
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample test for rates (one-sided),
## H0: pi = 0.45, H1: treatment rate pi as specified, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, pi(1) = 0.4 769.9
## Number of subjects, pi(1) = 0.5 779.4
## Number of subjects, pi(1) = 0.6 85.5
## One-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 0.415
## Efficacy boundary (t), pi(1) = 0.5 0.485
## Efficacy boundary (t), pi(1) = 0.6 0.555
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample test for rates (one-sided),
## H0: pi(1) - pi(2) = 0.45, H1: treatment rate pi(1) as specified,
## control rate pi(2) = 0.2, optimum planned allocation ratio, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, pi(1) = 0.4 86.8
## Number of subjects, pi(1) = 0.5 255.9
## Number of subjects, pi(1) = 0.6 2393.1
## Optimum allocation ratio, pi(1) = 0.4 1.778
## Optimum allocation ratio, pi(1) = 0.5 1.501
## Optimum allocation ratio, pi(1) = 0.6 1.280
## One-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 0.276
## Efficacy boundary (t), pi(1) = 0.5 0.346
## Efficacy boundary (t), pi(1) = 0.6 0.415
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample test for rates (one-sided),
## H0: pi(1) - pi(2) = 0, H1: treatment rate pi(1) as specified,
## control rate pi(2) = 0.2, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.0967 0.7030 0.8000
## Number of subjects, pi(1) = 0.4 97.5 195.0 292.5
## Number of subjects, pi(1) = 0.5 46.2 92.4 138.6
## Number of subjects, pi(1) = 0.6 26.8 53.6 80.4
## Exit probability for futility 0.1209 0.0758
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t), pi(1) = 0.4 0.339 0.158 0.102
## Efficacy boundary (t), pi(1) = 0.5 0.509 0.238 0.152
## Efficacy boundary (t), pi(1) = 0.6 0.669 0.322 0.205
## Futility boundary (t), pi(1) = 0.4 0.087 0.126
## Futility boundary (t), pi(1) = 0.5 0.130 0.190
## Futility boundary (t), pi(1) = 0.6 0.175 0.257
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.4 0.2176 0.6822
## Overall exit probability (under H1), pi(1) = 0.5 0.2176 0.6822
## Overall exit probability (under H1), pi(1) = 0.6 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.0967 0.6064
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.1209 0.0758
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerRates(getDesignGroupSequential(futilityBounds = c(1, 2)),
maxNumberOfSubjects = 100))
```

```
## Power calculation for a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample test for rates (one-sided),
## H0: pi(1) - pi(2) = 0, power directed towards larger values,
## H1: treatment rate pi(1) as specified, control rate pi(2) = 0.2.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power, pi(1) = 0.2 0.0003 0.0065 0.0109
## Overall power, pi(1) = 0.3 0.0025 0.0599 0.0985
## Overall power, pi(1) = 0.4 0.0136 0.2358 0.3411
## Overall power, pi(1) = 0.5 0.0527 0.5384 0.6613
## Number of subjects 33.3 66.7 100.0
## Exit probability for futility, pi(1) = 0.2 0.8413 0.1400
## Exit probability for futility, pi(1) = 0.3 0.6317 0.2464
## Exit probability for futility, pi(1) = 0.4 0.3963 0.2399
## Exit probability for futility, pi(1) = 0.5 0.1970 0.1333
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 0.601 0.285 0.182
## Futility boundary (t) 0.155 0.227
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.2 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.3 0.6342 0.3038
## Overall exit probability (under H1), pi(1) = 0.4 0.4099 0.4621
## Overall exit probability (under H1), pi(1) = 0.5 0.2498 0.6189
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1), pi(1) = 0.2 0.0003 0.0062
## Exit probability for efficacy (under H1), pi(1) = 0.3 0.0025 0.0574
## Exit probability for efficacy (under H1), pi(1) = 0.4 0.0136 0.2222
## Exit probability for efficacy (under H1), pi(1) = 0.5 0.0527 0.4856
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1), pi(1) = 0.2 0.8413 0.1400
## Exit probability for futility (under H1), pi(1) = 0.3 0.6317 0.2464
## Exit probability for futility (under H1), pi(1) = 0.4 0.3963 0.2399
## Exit probability for futility (under H1), pi(1) = 0.5 0.1970 0.1333
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a binary endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The sample size was calculated for a two-sample test for rates (two-sided),
## H0: pi(1) - pi(2) = 0, H1: treatment rate pi(1) as specified,
## control rate pi(2) = 0.2, power 80%.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power 0.0012 0.1494 0.5227 0.8000
## Number of subjects, pi(1) = 0.4 50.1 100.2 150.2 200.3
## Number of subjects, pi(1) = 0.5 23.8 47.5 71.3 95.0
## Number of subjects, pi(1) = 0.6 13.8 27.6 41.5 55.3
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t), pi(1) = 0.4 - 0.646 -0.196 - 0.310 -0.144 - 0.197 -0.113 - 0.144
## Efficacy boundary (t), pi(1) = 0.5 - 0.465 -0.191 - 0.299 -0.154 - 0.217
## Efficacy boundary (t), pi(1) = 0.6 - 0.616 - 0.402 -0.189 - 0.293
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1) 0.0012 0.1482 0.3733
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeRates(getDesignGroupSequential(kMax = 4, sided = 2),
groups = 1, thetaH0 = 0.3))
```

```
## Sample size calculation for a binary endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The sample size was calculated for a one-sample test for rates (two-sided),
## H0: pi = 0.3, H1: treatment rate pi as specified, power 80%.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power 0.0012 0.1494 0.5227 0.8000
## Number of subjects, pi(1) = 0.4 52.7 105.4 158.0 210.7
## Number of subjects, pi(1) = 0.5 13.3 26.7 40.0 53.3
## Number of subjects, pi(1) = 0.6 5.9 11.7 17.6 23.4
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t), pi(1) = 0.4 0.011 - 0.589 0.155 - 0.445 0.204 - 0.396 0.228 - 0.372
## Efficacy boundary (t), pi(1) = 0.5 -0.275 - 0.875 0.013 - 0.587 0.108 - 0.492 0.156 - 0.444
## Efficacy boundary (t), pi(1) = 0.6 -0.567 - 1.167 -0.134 - 0.734 0.011 - 0.589 0.083 - 0.517
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1) 0.0012 0.1482 0.3733
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeRates(getDesignGroupSequential(kMax = 1, sided = 2),
groups = 1, thetaH0 = 0.2, pi1 = c(0.4,0.5)))
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample test for rates (two-sided),
## H0: pi = 0.2, H1: treatment rate pi as specified, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects, pi(1) = 0.4 42.8
## Number of subjects, pi(1) = 0.5 19.3
## Two-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 0.063 - 0.337
## Efficacy boundary (t), pi(1) = 0.5 -0.004 - 0.404
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeRates(getDesignGroupSequential(kMax = 1, sided = 2),
groups = 1, thetaH0 = 0.2, pi1 = 0.4))
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a one-sample test for rates (two-sided),
## H0: pi = 0.2, H1: treatment rate pi = 0.4, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 42.8
## Two-sided local significance level 0.0250
## Efficacy boundary (t) 0.063 - 0.337
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeRates(getDesignGroupSequential(kMax = 1, sided = 2),
groups = 2, thetaH0 = 0, pi1 = 0.25))
```

```
## Sample size calculation for a binary endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample test for rates (two-sided),
## H0: pi(1) - pi(2) = 0, H1; treatment rate pi(1) = 0.25, control rate pi(2) = 0.2,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 2649.3
## Two-sided local significance level 0.0250
## Efficacy boundary (t) -0.034 - 0.036
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Power calculation for a binary endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The results were calculated for a two-sample test for rates (two-sided),
## H0: pi(1) - pi(2) = 0, H1: treatment rate pi(1) as specified,
## control rate pi(2) = 0.2.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power, pi(1) = 0.2 <0.0001 0.0012 0.0086 0.0250
## Overall power, pi(1) = 0.3 <0.0001 0.0077 0.0509 0.1343
## Overall power, pi(1) = 0.4 0.0002 0.0450 0.2280 0.4673
## Overall power, pi(1) = 0.5 0.0014 0.1637 0.5516 0.8226
## Number of subjects 25.0 50.0 75.0 100.0
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t) - 0.453 -0.188 - 0.290 -0.151 - 0.211
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), pi(1) = 0.2 <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), pi(1) = 0.3 <0.0001 0.0076 0.0433
## Exit probability for efficacy (under H1), pi(1) = 0.4 0.0002 0.0448 0.1830
## Exit probability for efficacy (under H1), pi(1) = 0.5 0.0014 0.1622 0.3879
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) as specified, control pi(2) = 0.2,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, pi(1) = 0.4 154.7
## Number of subjects, pi(1) = 0.5 71.0
## Number of subjects, pi(1) = 0.6 40.1
## Number of events, pi(1) = 0.4 46
## Number of events, pi(1) = 0.5 25
## Number of events, pi(1) = 0.6 16
## Analysis time 18.0
## Expected study duration, pi(1) = 0.4 18.0
## Expected study duration, pi(1) = 0.5 18.0
## Expected study duration, pi(1) = 0.6 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t), pi(1) = 0.4 1.785
## Efficacy boundary (t), pi(1) = 0.5 2.210
## Efficacy boundary (t), pi(1) = 0.6 2.686
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 1.2, control lambda(2) = 0.3, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 979.2
## Number of events 945
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 1.136
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 1.2, control median(2) = 2.3, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 978.8
## Number of events 945
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 1.136
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment median(1) = 3.2, control median(2) = 2.3,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 309.7
## Number of events 288
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 0.794
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment median(1) as specified, control median(2) = 2.3,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, median(1) = 3.1 377.9
## Number of subjects, median(1) = 3.2 309.7
## Number of events, median(1) = 3.1 353
## Number of events, median(1) = 3.2 288
## Analysis time 18.0
## Expected study duration, median(1) = 3.1 18.0
## Expected study duration, median(1) = 3.2 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t), median(1) = 3.1 0.812
## Efficacy boundary (t), median(1) = 3.2 0.794
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: hazard ratio as specified, control lambda(2) = 0.3,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects, HR = 1.2 979.2
## Number of subjects, HR = 2 67.0
## Number of events, HR = 1.2 945
## Number of events, HR = 2 66
## Analysis time 18.0
## Expected study duration, HR = 1.2 18.0
## Expected study duration, HR = 2 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t), HR = 1.2 1.136
## Efficacy boundary (t), HR = 2 1.624
##
## Legend:
## HR: hazard ratio
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 1.2, control pi(2) = 0.3, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 2953.8
## Number of events 945
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 1.136
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) = 0.1, control pi(2) = 0.3, power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 106.7
## Number of events 22
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 0.426
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment lambda(1) = 0.04, control lambda(2) = 0.03,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 1126.0
## Number of events 380
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 1.223
##
## Legend:
## (t): approximate treatment effect scale
```

```
piecewiseSurvivalTime <- list(
"0 - <6" = 0.025,
"6 - <9" = 0.04,
"9 - <15" = 0.015,
"15 - <21" = 0.01,
">= 21" = 0.007)
summary(getSampleSizeSurvival(piecewiseSurvivalTime = piecewiseSurvivalTime,
hazardRatio = 1.2))
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 1.2, piecewise survival distribution,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 1.960
## Number of subjects 3350.9
## Number of events 945
## Analysis time 18.0
## Expected study duration 18.0
## One-sided local significance level 0.0250
## Efficacy boundary (t) 1.136
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) as specified, control pi(2) = 0.2,
## power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power 0.0967 0.7030 0.8000
## Number of subjects, pi(1) = 0.4 215.2 278.5 278.5
## Number of subjects, pi(1) = 0.5 97.0 127.9 127.9
## Number of subjects, pi(1) = 0.6 53.6 72.2 72.2
## Exit probability for futility 0.1209 0.0758
## Cumulative number of events, pi(1) = 0.4 28 55 83
## Cumulative number of events, pi(1) = 0.5 15 30 44
## Cumulative number of events, pi(1) = 0.6 10 19 29
## Analysis time, pi(1) = 0.4 9.3 13.5 18.0
## Analysis time, pi(1) = 0.5 9.1 13.4 18.0
## Analysis time, pi(1) = 0.6 8.9 13.1 18.0
## Expected study duration, pi(1) = 0.4 13.0
## Expected study duration, pi(1) = 0.5 12.9
## Expected study duration, pi(1) = 0.6 12.7
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t), pi(1) = 0.4 3.761 1.939 1.555
## Efficacy boundary (t), pi(1) = 0.5 6.127 2.475 1.830
## Efficacy boundary (t), pi(1) = 0.6 9.575 3.094 2.123
## Futility boundary (t), pi(1) = 0.4 1.465 1.715
## Futility boundary (t), pi(1) = 0.5 1.686 2.093
## Futility boundary (t), pi(1) = 0.6 1.917 2.510
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.4 0.2176 0.6822
## Overall exit probability (under H1), pi(1) = 0.5 0.2176 0.6822
## Overall exit probability (under H1), pi(1) = 0.6 0.2176 0.6822
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) 0.0967 0.6064
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.1209 0.0758
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(futilityBounds = c(1, 2)),
median1 = 37, median2 = 32, maxNumberOfSubjects = 100, maxNumberOfEvents = 60))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, power directed towards larger values,
## H1: treatment median(1) = 37, control median(2) = 32.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power <0.0001 0.0016 0.0026
## Number of subjects 100.0 100.0 100.0
## Exit probability for futility 0.9074 0.0870
## Expected number of events 21.9
## Cumulative number of events 20 40 60
## Analysis time 17.2 31.4 51.6
## Expected study duration 18.6
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 4.722 2.173 1.678
## Futility boundary (t) 1.564 1.882
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1) 0.9074 0.0886
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1) <0.0001 0.0016
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1) 0.9074 0.0870
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(futilityBounds = c(1, 2)),
maxNumberOfSubjects = 100, maxNumberOfEvents = 60))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, power directed towards larger values,
## H1: treatment pi(1) as specified, control pi(2) = 0.2.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Futility boundary (z-value scale) 1.000 2.000
## Overall power, pi(1) = 0.2 0.0003 0.0065 0.0109
## Overall power, pi(1) = 0.3 0.0077 0.1543 0.2357
## Overall power, pi(1) = 0.4 0.0527 0.5382 0.6611
## Overall power, pi(1) = 0.5 0.1745 0.8481 0.9049
## Number of subjects, pi(1) = 0.2 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.3 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.4 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.5 100.0 100.0 100.0
## Exit probability for futility, pi(1) = 0.2 0.8413 0.1400
## Exit probability for futility, pi(1) = 0.3 0.4806 0.2580
## Exit probability for futility, pi(1) = 0.4 0.1971 0.1334
## Exit probability for futility, pi(1) = 0.5 0.0625 0.0318
## Expected number of events, pi(1) = 0.2 23.4
## Expected number of events, pi(1) = 0.3 32.4
## Expected number of events, pi(1) = 0.4 37.6
## Expected number of events, pi(1) = 0.5 36.4
## Cumulative number of events 20 40 60
## Analysis time, pi(1) = 0.2 18.1 33.6 55.4
## Analysis time, pi(1) = 0.3 15.4 27.6 45.0
## Analysis time, pi(1) = 0.4 13.6 23.6 38.5
## Analysis time, pi(1) = 0.5 12.3 20.7 33.9
## Expected study duration, pi(1) = 0.2 20.8
## Expected study duration, pi(1) = 0.3 23.5
## Expected study duration, pi(1) = 0.4 23.1
## Expected study duration, pi(1) = 0.5 19.5
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 4.722 2.173 1.678
## Futility boundary (t) 1.564 1.882
## Overall exit probability (under H0) 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.2 0.8416 0.1462
## Overall exit probability (under H1), pi(1) = 0.3 0.4883 0.4046
## Overall exit probability (under H1), pi(1) = 0.4 0.2498 0.6189
## Overall exit probability (under H1), pi(1) = 0.5 0.2369 0.7055
## Exit probability for efficacy (under H0) 0.0003 0.0062
## Exit probability for efficacy (under H1), pi(1) = 0.2 0.0003 0.0062
## Exit probability for efficacy (under H1), pi(1) = 0.3 0.0077 0.1466
## Exit probability for efficacy (under H1), pi(1) = 0.4 0.0527 0.4855
## Exit probability for efficacy (under H1), pi(1) = 0.5 0.1745 0.6736
## Exit probability for futility (under H0) 0.8413 0.1400
## Exit probability for futility (under H1), pi(1) = 0.2 0.8413 0.1400
## Exit probability for futility (under H1), pi(1) = 0.3 0.4806 0.2580
## Exit probability for futility (under H1), pi(1) = 0.4 0.1971 0.1334
## Exit probability for futility (under H1), pi(1) = 0.5 0.0625 0.0318
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) as specified, control pi(2) = 0.2,
## power 80%.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power 0.0012 0.1494 0.5227 0.8000
## Number of subjects, pi(1) = 0.4 126.6 182.5 190.5 190.5
## Number of subjects, pi(1) = 0.5 56.9 82.6 87.5 87.5
## Number of subjects, pi(1) = 0.6 31.3 45.8 49.4 49.4
## Cumulative number of events, pi(1) = 0.4 15 29 43 57
## Cumulative number of events, pi(1) = 0.5 8 16 23 31
## Cumulative number of events, pi(1) = 0.6 5 10 15 20
## Analysis time, pi(1) = 0.4 8.0 11.5 14.6 18.0
## Analysis time, pi(1) = 0.5 7.8 11.3 14.4 18.0
## Analysis time, pi(1) = 0.6 7.6 11.1 14.2 18.0
## Expected study duration, pi(1) = 0.4 15.7
## Expected study duration, pi(1) = 0.5 15.7
## Expected study duration, pi(1) = 0.6 15.6
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t), pi(1) = 0.4 0.087 - 11.467 0.295 - 3.386 0.443 - 2.255 0.543 - 1.840
## Efficacy boundary (t), pi(1) = 0.5 0.035 - 28.174 0.188 - 5.308 0.329 - 3.043 0.434 - 2.304
## Efficacy boundary (t), pi(1) = 0.6 0.016 - 64.101 0.125 - 8.006 0.250 - 4.002 0.353 - 2.830
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1) 0.0012 0.1482 0.3733
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(kMax = 4, sided = 2),
maxNumberOfSubjects = 100, maxNumberOfEvents = 60))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The results were calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) as specified, control pi(2) = 0.2.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power, pi(1) = 0.2 <0.0001 0.0012 0.0086 0.0250
## Overall power, pi(1) = 0.3 0.0001 0.0254 0.1446 0.3285
## Overall power, pi(1) = 0.4 0.0015 0.1662 0.5565 0.8263
## Overall power, pi(1) = 0.5 0.0086 0.4469 0.8779 0.9829
## Number of subjects, pi(1) = 0.2 100.0 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.3 100.0 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.4 96.5 100.0 100.0 100.0
## Number of subjects, pi(1) = 0.5 87.6 100.0 100.0 100.0
## Expected number of events, pi(1) = 0.2 59.9
## Expected number of events, pi(1) = 0.3 57.4
## Expected number of events, pi(1) = 0.4 49.1
## Expected number of events, pi(1) = 0.5 40.0
## Cumulative number of events 15 30 45 60
## Analysis time, pi(1) = 0.2 14.9 25.3 38.3 55.4
## Analysis time, pi(1) = 0.3 12.9 21.1 31.3 45.0
## Analysis time, pi(1) = 0.4 11.6 18.2 26.7 38.5
## Analysis time, pi(1) = 0.5 10.5 16.1 23.4 33.9
## Expected study duration, pi(1) = 0.2 55.2
## Expected study duration, pi(1) = 0.3 42.8
## Expected study duration, pi(1) = 0.4 30.5
## Expected study duration, pi(1) = 0.5 21.4
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t) 0.094 - 10.638 0.307 - 3.262 0.455 - 2.199 0.554 - 1.806
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), pi(1) = 0.2 <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1), pi(1) = 0.3 0.0001 0.0253 0.1192
## Exit probability for efficacy (under H1), pi(1) = 0.4 0.0015 0.1647 0.3903
## Exit probability for efficacy (under H1), pi(1) = 0.5 0.0086 0.4383 0.4310
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Fixed sample analysis.
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment lambda(1) = 0.087, control lambda(2) = 0.116,
## power 80%.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Number of subjects 675.7
## Number of events 460
## Analysis time 18.0
## Expected study duration 18.0
## Two-sided local significance level 0.0250
## Efficacy boundary (t) 0.811 - 1.233
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(sided = 2, maxNumberOfSubjects = 200, maxNumberOfEvents = 40,
lambda2 = log(2)/6, lambda1 = log(2)/8))
```

```
## Power calculation for a survival endpoint
##
## Fixed sample analysis.
## The results were calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment lambda(1) = 0.087, control lambda(2) = 0.116.
##
## Stage Fixed
## Efficacy boundary (z-value scale) 2.241
## Power 0.0923
## Number of subjects 130.2
## Number of events 40
## Analysis time 7.8
## Expected study duration 7.8
## Two-sided local significance level 0.0250
## Efficacy boundary (t) 0.492 - 2.032
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeSurvival(getDesignGroupSequential(sided = 2),
lambda2 = log(2)/6, hazardRatio = c(0.55),
accrualTime = c(0,10), accrualIntensity = 60))
```

`## Warning: Accrual duration longer than maximal study duration (time to maximal number of events); followUpTime = -2.959`

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 0.55, control lambda(2) = 0.116, power 80%.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.935 2.783 2.272
## Overall power 0.0160 0.4013 0.8000
## Number of subjects 232.9 338.1 422.5
## Cumulative number of events 36 72 108
## Analysis time 3.9 5.6 7.0
## Expected study duration 6.4
## Cumulative alpha spent <0.0001 0.0054 0.0250
## Two-sided local significance level <0.0001 0.0054 0.0231
## Efficacy boundary (t) 0.269 - 3.721 0.518 - 1.929 0.645 - 1.550
## Exit probability for efficacy (under H0) <0.0001 0.0053
## Exit probability for efficacy (under H1) 0.0160 0.3853
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(kMax = 2), maxNumberOfEvents = 200,
maxNumberOfSubjects = 400, lambda2 = log(2) / 60, lambda1 = log(2) / 50,
dropoutRate1 = 0.025, dropoutRate2 = 0.025, dropoutTime = 12,
accrualTime = 0, accrualIntensity = 30))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 2 looks (group sequential design).
## The results were calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, power directed towards larger values,
## H1: treatment lambda(1) = 0.014, control lambda(2) = 0.012.
##
## Stage 1 2
## Information rate 50% 100%
## Efficacy boundary (z-value scale) 2.797 1.977
## Overall power 0.0297 0.2489
## Number of subjects 400.0 400.0
## Expected number of events 197.0
## Cumulative number of events 100 200
## Analysis time 30.1 66.0
## Expected study duration 64.9
## Cumulative alpha spent 0.0026 0.0250
## One-sided local significance level 0.0026 0.0240
## Efficacy boundary (t) 1.749 1.323
## Exit probability for efficacy (under H0) 0.0026
## Exit probability for efficacy (under H1) 0.0297
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(kMax = 3), maxNumberOfEvents = 200,
maxNumberOfSubjects = 400, lambda2 = log(2) / 60,
lambda1 = c(log(2) / 50, log(2) / 60),
dropoutRate1 = 0.025, dropoutRate2 = 0.025, dropoutTime = 12,
accrualTime = 0, accrualIntensity = 30))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, power directed towards larger values,
## H1: treatment lambda(1) as specified, control lambda(2) = 0.012.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Overall power, lambda(1) = 0.014 0.0032 0.0810 0.2464
## Overall power, lambda(1) = 0.012 0.0003 0.0072 0.0250
## Number of subjects, lambda(1) = 0.014 400.0 400.0 400.0
## Number of subjects, lambda(1) = 0.012 400.0 400.0 400.0
## Expected number of events, lambda(1) = 0.014 194.4
## Expected number of events, lambda(1) = 0.012 199.5
## Cumulative number of events 67 134 200
## Analysis time, lambda(1) = 0.014 21.4 40.0 66.0
## Analysis time, lambda(1) = 0.012 22.8 43.5 72.3
## Expected study duration, lambda(1) = 0.014 63.8
## Expected study duration, lambda(1) = 0.012 72.1
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 2.340 1.530 1.328
## Exit probability for efficacy (under H0) 0.0003 0.0069
## Exit probability for efficacy (under H1), lambda(1) = 0.014 0.0032 0.0778
## Exit probability for efficacy (under H1), lambda(1) = 0.012 0.0003 0.0069
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getPowerSurvival(getDesignGroupSequential(kMax = 3), maxNumberOfEvents = 200,
maxNumberOfSubjects = 400, lambda2 = log(2) / 60, hazardRatio = c(0.7, 0.8),
directionUpper = FALSE, dropoutRate1 = 0.025, dropoutRate2 = 0.025,
dropoutTime = 12, accrualTime = 0, accrualIntensity = 30))
```

```
## Power calculation for a survival endpoint
##
## Sequential analysis with a maximum of 3 looks (group sequential design).
## The results were calculated for a two-sample logrank test (one-sided),
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: hazard ratio as specified, control lambda(2) = 0.012.
##
## Stage 1 2 3
## Information rate 33.3% 66.7% 100%
## Efficacy boundary (z-value scale) 3.471 2.454 2.004
## Overall power, HR = 0.7 0.0220 0.3472 0.7051
## Overall power, HR = 0.8 0.0052 0.1224 0.3448
## Number of subjects, HR = 0.7 400.0 400.0 400.0
## Number of subjects, HR = 0.8 400.0 400.0 400.0
## Expected number of events, HR = 0.7 175.4
## Expected number of events, HR = 0.8 191.5
## Cumulative number of events 67 134 200
## Analysis time, HR = 0.7 25.8 50.6 86.2
## Analysis time, HR = 0.8 24.7 47.8 80.7
## Expected study duration, HR = 0.7 73.3
## Expected study duration, HR = 0.8 76.5
## Cumulative alpha spent 0.0003 0.0072 0.0250
## One-sided local significance level 0.0003 0.0071 0.0225
## Efficacy boundary (t) 0.427 0.654 0.753
## Exit probability for efficacy (under H0) 0.0003 0.0069
## Exit probability for efficacy (under H1), HR = 0.7 0.0220 0.3253
## Exit probability for efficacy (under H1), HR = 0.8 0.0052 0.1172
##
## Legend:
## HR: hazard ratio
## (t): approximate treatment effect scale
```

```
design <- getDesignGroupSequential(sided = 2, alpha = 0.05, beta = 0.2,
informationRates = c(0.6, 1), typeOfDesign = "asOF", twoSidedPower = FALSE)
summary(getSampleSizeSurvival(design,
lambda2 = log(2) / 60, hazardRatio = 0.74,
dropoutRate1 = 0.025, dropoutRate2 = 0.025, dropoutTime = 12,
accrualTime = 0, accrualIntensity = 30,
followUpTime = 12))
```

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 2 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: hazard ratio = 0.74, control lambda(2) = 0.012, power 80%.
##
## Stage 1 2
## Information rate 60% 100%
## Efficacy boundary (z-value scale) 2.669 1.981
## Overall power 0.3123 0.8000
## Number of subjects 1211.4 1294.4
## Cumulative number of events 210 350
## Analysis time 40.4 55.1
## Expected study duration 50.5
## Cumulative alpha spent 0.0076 0.0500
## Two-sided local significance level 0.0076 0.0476
## Efficacy boundary (t) 0.692 - 1.446 0.809 - 1.236
## Exit probability for efficacy (under H0) 0.0076
## Exit probability for efficacy (under H1) 0.3123
##
## Legend:
## (t): approximate treatment effect scale
```

```
summary(getSampleSizeSurvival(design,
lambda2 = log(2) / 60, lambda1 = log(2) / 50,
dropoutRate1 = 0.025, dropoutRate2 = 0.025, dropoutTime = 12,
accrualTime = 0, accrualIntensity = 30,
followUpTime = 12))
```

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 2 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment lambda(1) = 0.014, control lambda(2) = 0.012,
## power 80%.
##
## Stage 1 2
## Information rate 60% 100%
## Efficacy boundary (z-value scale) 2.669 1.981
## Overall power 0.3123 0.8000
## Number of subjects 1899.9 2249.7
## Cumulative number of events 572 953
## Analysis time 63.3 87.0
## Expected study duration 79.6
## Cumulative alpha spent 0.0076 0.0500
## Two-sided local significance level 0.0076 0.0476
## Efficacy boundary (t) 0.800 - 1.250 0.880 - 1.137
## Exit probability for efficacy (under H0) 0.0076
## Exit probability for efficacy (under H1) 0.3123
##
## Legend:
## (t): approximate treatment effect scale
```

```
## Sample size calculation for a survival endpoint
##
## Sequential analysis with a maximum of 4 looks (group sequential design).
## The sample size was calculated for a two-sample logrank test (two-sided),
## H0: hazard ratio = 1, H1: treatment pi(1) as specified, control pi(2) = 0.2,
## power 80%.
##
## Stage 1 2 3 4
## Information rate 25% 50% 75% 100%
## Efficacy boundary (z-value scale) 4.579 3.238 2.644 2.289
## Overall power 0.0012 0.1494 0.5227 0.8000
## Number of subjects, pi(1) = 0.4 126.6 182.5 190.5 190.5
## Number of subjects, pi(1) = 0.5 56.9 82.6 87.5 87.5
## Number of subjects, pi(1) = 0.6 31.3 45.8 49.4 49.4
## Cumulative number of events, pi(1) = 0.4 15 29 43 57
## Cumulative number of events, pi(1) = 0.5 8 16 23 31
## Cumulative number of events, pi(1) = 0.6 5 10 15 20
## Analysis time, pi(1) = 0.4 8.0 11.5 14.6 18.0
## Analysis time, pi(1) = 0.5 7.8 11.3 14.4 18.0
## Analysis time, pi(1) = 0.6 7.6 11.1 14.2 18.0
## Expected study duration, pi(1) = 0.4 15.7
## Expected study duration, pi(1) = 0.5 15.7
## Expected study duration, pi(1) = 0.6 15.6
## Cumulative alpha spent <0.0001 0.0012 0.0086 0.0250
## Two-sided local significance level <0.0001 0.0012 0.0082 0.0221
## Efficacy boundary (t), pi(1) = 0.4 0.087 - 11.467 0.295 - 3.386 0.443 - 2.255 0.543 - 1.840
## Efficacy boundary (t), pi(1) = 0.5 0.035 - 28.174 0.188 - 5.308 0.329 - 3.043 0.434 - 2.304
## Efficacy boundary (t), pi(1) = 0.6 0.016 - 64.101 0.125 - 8.006 0.250 - 4.002 0.353 - 2.830
## Exit probability for efficacy (under H0) <0.0001 0.0012 0.0074
## Exit probability for efficacy (under H1) 0.0012 0.1482 0.3733
##
## Legend:
## (t): approximate treatment effect scale
```

```
design <- getDesignInverseNormal(kMax = 3, alpha = 0.025,
futilityBounds = c(-0.5, 0), bindingFutility = FALSE,
typeOfDesign = "WT", deltaWT = 0.25,
informationRates = c(0.4, 0.7, 1))
designF <- getDesignFisher(kMax = 3, alpha = 0.025,
alpha0Vec = c(0.5, 0.4), bindingFutility = FALSE,
informationRates = c(0.4, 0.7, 1))
```

```
summary(getSimulationMeans(design = design, plannedSubjects = c(40, 70, 100),
groups = 1,
alternative = seq(0,0.4,0.1),
stDev = 1.2,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design).
## The results were simulated for a one-sample t-test (normal approximation),
## H0: mu = 0, power directed towards larger values, H1: effect as specified,
## standard deviation = 1.2, planned cumulative sample size = c(40, 70, 100),
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 0.632 0.548 0.548
## Efficacy boundary (z-value scale) 2.631 2.287 2.092
## Futility boundary (z-value scale) -0.500 0.000
## Overall power, alt. = 0 0.0040 0.0110 0.0270
## Overall power, alt. = 0.1 0.0160 0.0690 0.1240
## Overall power, alt. = 0.2 0.0530 0.2030 0.3570
## Overall power, alt. = 0.3 0.1510 0.4700 0.7160
## Overall power, alt. = 0.4 0.2630 0.6960 0.9090
## Expected number of subjects, alt. = 0 73.8
## Expected number of subjects, alt. = 0.1 84.8
## Expected number of subjects, alt. = 0.2 86.9
## Expected number of subjects, alt. = 0.3 80.0
## Expected number of subjects, alt. = 0.4 71.0
## Stagewise number of subjects, alt. = 0 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.1 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.2 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.3 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.4 40.0 30.0 30.0
## Exit probability for futility, alt. = 0 0.3200 0.2170
## Exit probability for futility, alt. = 0.1 0.1490 0.1220
## Exit probability for futility, alt. = 0.2 0.0700 0.0420
## Exit probability for futility, alt. = 0.3 0.0160 0.0120
## Exit probability for futility, alt. = 0.4 0.0030 0.0010
## Conditional power (achieved), alt. = 0 0.0839 0.0958
## Conditional power (achieved), alt. = 0.1 0.1438 0.1542
## Conditional power (achieved), alt. = 0.2 0.2534 0.2595
## Conditional power (achieved), alt. = 0.3 0.3835 0.3894
## Conditional power (achieved), alt. = 0.4 0.4744 0.4814
##
## Legend:
## alt.: alternative
```

```
summary(getSimulationMeans(design = design, plannedSubjects = c(40,70,100),
alternative = seq(0,0.8,0.2),
stDev = 1.2,
allocationRatioPlanned = 2,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample t-test (normal approximation),
## H0: mu(1) - mu(2) = 0, power directed towards larger values,
## H1: effect as specified, standard deviation = 1.2,
## planned cumulative sample size = c(40, 70, 100), planned allocation ratio = 2,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 0.632 0.548 0.548
## Efficacy boundary (z-value scale) 2.631 2.287 2.092
## Futility boundary (z-value scale) -0.500 0.000
## Overall power, alt. = 0 0.0040 0.0110 0.0270
## Overall power, alt. = 0.2 0.0140 0.0630 0.1190
## Overall power, alt. = 0.4 0.0420 0.1840 0.3290
## Overall power, alt. = 0.6 0.1310 0.4030 0.6500
## Overall power, alt. = 0.8 0.2310 0.6520 0.8660
## Expected number of subjects, alt. = 0 73.8
## Expected number of subjects, alt. = 0.2 84.8
## Expected number of subjects, alt. = 0.4 87.4
## Expected number of subjects, alt. = 0.6 82.2
## Expected number of subjects, alt. = 0.8 73.1
## Stagewise number of subjects, alt. = 0 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.2 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.4 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.6 40.0 30.0 30.0
## Stagewise number of subjects, alt. = 0.8 40.0 30.0 30.0
## Exit probability for futility, alt. = 0 0.3200 0.2170
## Exit probability for futility, alt. = 0.2 0.1470 0.1370
## Exit probability for futility, alt. = 0.4 0.0720 0.0500
## Exit probability for futility, alt. = 0.6 0.0220 0.0140
## Exit probability for futility, alt. = 0.8 0.0060 0.0020
## Conditional power (achieved), alt. = 0 0.0839 0.0958
## Conditional power (achieved), alt. = 0.2 0.1366 0.1441
## Conditional power (achieved), alt. = 0.4 0.2398 0.2430
## Conditional power (achieved), alt. = 0.6 0.3535 0.3723
## Conditional power (achieved), alt. = 0.8 0.4506 0.4427
##
## Legend:
## alt.: alternative
```

```
summary(getSimulationMeans(design = design, plannedSubjects = c(40,70,100),
alternative = seq(0,0.8,0.2),
stDev = 1.2,
conditionalPower = 0.8,
minNumberOfSubjectsPerStage = c(40,20,20),
maxNumberOfSubjectsPerStage = c(40,100,100),
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample t-test (normal approximation),
## H0: mu(1) - mu(2) = 0, power directed towards larger values,
## H1: effect as specified, standard deviation = 1.2,
## planned cumulative sample size = c(40, 70, 100),
## sample size reassessment: conditional power = 0.8,
## minimum subjects per stage = c(40, 20, 20),
## maximum subjects per stage = c(40, 100, 100), simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 0.632 0.548 0.548
## Efficacy boundary (z-value scale) 2.631 2.287 2.092
## Futility boundary (z-value scale) -0.500 0.000
## Overall power, alt. = 0 0.0040 0.0110 0.0270
## Overall power, alt. = 0.2 0.0200 0.0890 0.2120
## Overall power, alt. = 0.4 0.0420 0.2760 0.6120
## Overall power, alt. = 0.6 0.1340 0.6420 0.9150
## Overall power, alt. = 0.8 0.2780 0.8780 0.9870
## Expected number of subjects, alt. = 0 149.5
## Expected number of subjects, alt. = 0.2 183.7
## Expected number of subjects, alt. = 0.4 172.7
## Expected number of subjects, alt. = 0.6 128.1
## Expected number of subjects, alt. = 0.8 94.7
## Stagewise number of subjects, alt. = 0 40.0 96.3 98.3
## Stagewise number of subjects, alt. = 0.2 40.0 93.5 96.4
## Stagewise number of subjects, alt. = 0.4 40.0 85.2 87.4
## Stagewise number of subjects, alt. = 0.6 40.0 74.8 74.0
## Stagewise number of subjects, alt. = 0.8 40.0 65.6 64.0
## Exit probability for futility, alt. = 0 0.3200 0.2170
## Exit probability for futility, alt. = 0.2 0.1470 0.0810
## Exit probability for futility, alt. = 0.4 0.0650 0.0110
## Exit probability for futility, alt. = 0.6 0.0210 0
## Exit probability for futility, alt. = 0.8 0.0040 0
## Conditional power (achieved), alt. = 0 0.1486 0.1281
## Conditional power (achieved), alt. = 0.2 0.2464 0.2557
## Conditional power (achieved), alt. = 0.4 0.3542 0.4626
## Conditional power (achieved), alt. = 0.6 0.5218 0.6472
## Conditional power (achieved), alt. = 0.8 0.6118 0.7064
##
## Legend:
## alt.: alternative
```

```
summary(getSimulationMeans(design = design, plannedSubjects = c(40,70,100),
alternative = seq(0,0.8,0.2),
stDev = 1.2,
conditionalPower = 0.8,
minNumberOfSubjectsPerStage = c(40,20,20),
maxNumberOfSubjectsPerStage = c(40,100,100),
thetaH1 = 0.6, stDevH1 = 1.5,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a continuous endpoint
##
## Sequential analysis with a maximum of 3 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample t-test (normal approximation),
## H0: mu(1) - mu(2) = 0, power directed towards larger values,
## H1: effect as specified, standard deviation = 1.2,
## planned cumulative sample size = c(40, 70, 100),
## sample size reassessment: conditional power = 0.8,
## minimum subjects per stage = c(40, 20, 20),
## maximum subjects per stage = c(40, 100, 100), theta H1 = 0.6,
## standard deviation H1 = 1.5, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 0.632 0.548 0.548
## Efficacy boundary (z-value scale) 2.631 2.287 2.092
## Futility boundary (z-value scale) -0.500 0.000
## Overall power, alt. = 0 0.0040 0.0110 0.0270
## Overall power, alt. = 0.2 0.0190 0.0960 0.2090
## Overall power, alt. = 0.4 0.0390 0.3250 0.6260
## Overall power, alt. = 0.6 0.1330 0.7100 0.9300
## Overall power, alt. = 0.8 0.2830 0.9320 0.9930
## Expected number of subjects, alt. = 0 151.5
## Expected number of subjects, alt. = 0.2 186.1
## Expected number of subjects, alt. = 0.4 179.3
## Expected number of subjects, alt. = 0.6 139.1
## Expected number of subjects, alt. = 0.8 108.2
## Stagewise number of subjects, alt. = 0 40.0 99.3 98.1
## Stagewise number of subjects, alt. = 0.2 40.0 98.6 95.0
## Stagewise number of subjects, alt. = 0.4 40.0 96.8 86.6
## Stagewise number of subjects, alt. = 0.6 40.0 93.5 75.7
## Stagewise number of subjects, alt. = 0.8 40.0 88.9 73.3
## Exit probability for futility, alt. = 0 0.3200 0.2170
## Exit probability for futility, alt. = 0.2 0.1500 0.0790
## Exit probability for futility, alt. = 0.4 0.0610 0.0110
## Exit probability for futility, alt. = 0.6 0.0230 0
## Exit probability for futility, alt. = 0.8 0.0030 0
## Conditional power (achieved), alt. = 0 0.2206 0.3011
## Conditional power (achieved), alt. = 0.2 0.3112 0.4507
## Conditional power (achieved), alt. = 0.4 0.4009 0.5970
## Conditional power (achieved), alt. = 0.6 0.5292 0.7151
## Conditional power (achieved), alt. = 0.8 0.6066 0.7396
##
## Legend:
## alt.: alternative
```

```
summary(getSimulationRates(design = designF, plannedSubjects = c(40,70,100),
groups = 1,
thetaH0 = 0.2,
pi1 = seq(0.05,0.2,0.05),
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a one-sample test for rates (normal approximation),
## H0: pi = 0.2, power directed towards smaller values,
## H1: treatment rate pi as specified, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 0.866 0.866
## Efficacy boundary (p product scale) 0.013187 0.002705 0.000641
## Futility boundary (separate p-value scale) 0.500 0.400
## Overall power, pi(1) = 0.05 0.6790 0.9040 0.9780
## Overall power, pi(1) = 0.1 0.2150 0.3760 0.5540
## Overall power, pi(1) = 0.15 0.0390 0.0670 0.1070
## Overall power, pi(1) = 0.2 0.0090 0.0100 0.0110
## Expected number of subjects, pi(1) = 0.05 52.4
## Expected number of subjects, pi(1) = 0.1 78.0
## Expected number of subjects, pi(1) = 0.15 76.9
## Expected number of subjects, pi(1) = 0.2 58.0
## Stagewise number of subjects, pi(1) = 0.05 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.1 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.15 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.2 40.0 30.0 30.0
## Exit probability for futility, pi(1) = 0.05 0.0010 0.0020
## Exit probability for futility, pi(1) = 0.1 0.0410 0.0600
## Exit probability for futility, pi(1) = 0.15 0.2250 0.2150
## Exit probability for futility, pi(1) = 0.2 0.5680 0.2440
## Conditional power (achieved), pi(1) = 0.05 0.4489 0.5698
## Conditional power (achieved), pi(1) = 0.1 0.2752 0.3434
## Conditional power (achieved), pi(1) = 0.15 0.1405 0.1871
## Conditional power (achieved), pi(1) = 0.2 0.0820 0.0932
```

```
summary(getSimulationRates(design = designF, plannedSubjects = c(40,70,100),
thetaH0 = -0.2,
pi1 = seq(0.05,0.2,0.05),
pi2 = 0.4,
allocationRatioPlanned = 2,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a two-sample test for rates (normal approximation),
## H0: pi(1) - pi(2) = -0.2, power directed towards smaller values,
## H1: treatment rate pi(1) as specified, control rate pi(2) = 0.4,
## planned cumulative sample size = c(40, 70, 100), planned allocation ratio = 2,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 0.866 0.866
## Efficacy boundary (p product scale) 0.013187 0.002705 0.000641
## Futility boundary (separate p-value scale) 0.500 0.400
## Overall power, pi(1) = 0.05 0.1780 0.2890 0.3760
## Overall power, pi(1) = 0.1 0.0810 0.1270 0.1740
## Overall power, pi(1) = 0.15 0.0320 0.0570 0.0710
## Overall power, pi(1) = 0.2 0.0110 0.0150 0.0180
## Expected number of subjects, pi(1) = 0.05 71.2
## Expected number of subjects, pi(1) = 0.1 70.6
## Expected number of subjects, pi(1) = 0.15 66.2
## Expected number of subjects, pi(1) = 0.2 61.2
## Stagewise number of subjects, pi(1) = 0.05 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.1 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.15 40.0 30.0 30.0
## Stagewise number of subjects, pi(1) = 0.2 40.0 30.0 30.0
## Exit probability for futility, pi(1) = 0.05 0.1720 0.1490
## Exit probability for futility, pi(1) = 0.1 0.2670 0.2370
## Exit probability for futility, pi(1) = 0.15 0.4000 0.2370
## Exit probability for futility, pi(1) = 0.2 0.4910 0.2860
## Conditional power (achieved), pi(1) = 0.05 0.2199 0.2413
## Conditional power (achieved), pi(1) = 0.1 0.1698 0.1753
## Conditional power (achieved), pi(1) = 0.15 0.1274 0.1280
## Conditional power (achieved), pi(1) = 0.2 0.0988 0.1051
```

```
summary(getSimulationRates(design = designF, plannedSubjects = c(40,70,100),
thetaH0 = -0.2,
pi1 = seq(0.05,0.2,0.05),
pi2 = 0.4,
allocationRatioPlanned = 2,
directionUpper = FALSE,
conditionalPower = 0.8,
minNumberOfSubjectsPerStage = c(40,20,20),
maxNumberOfSubjectsPerStage = c(40,100,100),
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a two-sample test for rates (normal approximation),
## H0: pi(1) - pi(2) = -0.2, power directed towards smaller values,
## H1: treatment rate pi(1) as specified, control rate pi(2) = 0.4,
## planned cumulative sample size = c(40, 70, 100), planned allocation ratio = 2,
## sample size reassessment: conditional power = 0.8,
## minimum subjects per stage = c(40, 20, 20),
## maximum subjects per stage = c(40, 100, 100), simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 0.866 0.866
## Efficacy boundary (p product scale) 0.013187 0.002705 0.000641
## Futility boundary (separate p-value scale) 0.500 0.400
## Overall power, pi(1) = 0.05 0.1750 0.4100 0.5860
## Overall power, pi(1) = 0.1 0.0760 0.1590 0.2500
## Overall power, pi(1) = 0.15 0.0340 0.0640 0.0820
## Overall power, pi(1) = 0.2 0.0110 0.0140 0.0160
## Expected number of subjects, pi(1) = 0.05 136.0
## Expected number of subjects, pi(1) = 0.1 138.2
## Expected number of subjects, pi(1) = 0.15 127.2
## Expected number of subjects, pi(1) = 0.2 106.7
## Stagewise number of subjects, pi(1) = 0.05 40.0 92.5 98.4
## Stagewise number of subjects, pi(1) = 0.1 40.0 93.4 97.8
## Stagewise number of subjects, pi(1) = 0.15 40.0 96.1 99.5
## Stagewise number of subjects, pi(1) = 0.2 40.0 96.8 99.7
## Exit probability for futility, pi(1) = 0.05 0.1760 0.0490
## Exit probability for futility, pi(1) = 0.1 0.2850 0.1620
## Exit probability for futility, pi(1) = 0.15 0.4010 0.2050
## Exit probability for futility, pi(1) = 0.2 0.4960 0.3000
## Conditional power (achieved), pi(1) = 0.05 0.4075 0.3830
## Conditional power (achieved), pi(1) = 0.1 0.3286 0.2884
## Conditional power (achieved), pi(1) = 0.15 0.2713 0.2133
## Conditional power (achieved), pi(1) = 0.2 0.2090 0.1542
```

```
summary(getSimulationRates(design = designF, plannedSubjects = c(40,70,100),
thetaH0 = -0.2,
pi1 = seq(0.05,0.2,0.05),
pi2 = 0.4,
allocationRatioPlanned = 2,
directionUpper = FALSE,
conditionalPower = 0.8,
minNumberOfSubjectsPerStage = c(40,20,20),
maxNumberOfSubjectsPerStage = c(40,100,100),
pi1H1 = 0.1, pi2H1 = 0.4,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a binary endpoint
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a two-sample test for rates (normal approximation),
## H0: pi(1) - pi(2) = -0.2, power directed towards smaller values,
## H1: treatment rate pi(1) as specified, control rate pi(2) = 0.4,
## planned cumulative sample size = c(40, 70, 100), planned allocation ratio = 2,
## sample size reassessment: conditional power = 0.8,
## minimum subjects per stage = c(40, 20, 20),
## maximum subjects per stage = c(40, 100, 100), pi(treatment)H1 = 0.1,
## pi(control)H1 = 0.4, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 0.866 0.866
## Efficacy boundary (p product scale) 0.013187 0.002705 0.000641
## Futility boundary (separate p-value scale) 0.500 0.400
## Overall power, pi(1) = 0.05 0.1730 0.4190 0.5920
## Overall power, pi(1) = 0.1 0.0770 0.1750 0.2690
## Overall power, pi(1) = 0.15 0.0320 0.0620 0.0820
## Overall power, pi(1) = 0.2 0.0110 0.0150 0.0170
## Expected number of subjects, pi(1) = 0.05 141.1
## Expected number of subjects, pi(1) = 0.1 141.7
## Expected number of subjects, pi(1) = 0.15 130.9
## Expected number of subjects, pi(1) = 0.2 108.6
## Stagewise number of subjects, pi(1) = 0.05 40.0 100.0 100.0
## Stagewise number of subjects, pi(1) = 0.1 40.0 100.0 100.0
## Stagewise number of subjects, pi(1) = 0.15 40.0 100.0 100.0
## Stagewise number of subjects, pi(1) = 0.2 40.0 100.0 100.0
## Exit probability for futility, pi(1) = 0.05 0.1760 0.0450
## Exit probability for futility, pi(1) = 0.1 0.2950 0.1410
## Exit probability for futility, pi(1) = 0.15 0.3970 0.2030
## Exit probability for futility, pi(1) = 0.2 0.4940 0.3000
## Conditional power (achieved), pi(1) = 0.05 0.1821 0.2480
## Conditional power (achieved), pi(1) = 0.1 0.1563 0.2001
## Conditional power (achieved), pi(1) = 0.15 0.1330 0.1666
## Conditional power (achieved), pi(1) = 0.2 0.1162 0.1309
```

```
design <- getDesignInverseNormal(alpha = 0.05, kMax = 4, futilityBounds = c(0,0,0),
sided = 1, typeOfDesign = "WT", deltaWT = 0.1)
summary(getSimulationSurvival(design,
lambda2 = log(2) / 60, lambda1 = c(log(2) / 80),
plannedEvents = c(50, 100, 150, 200),
maxNumberOfSubjects = 400,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234), digits = 0)
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: treatment lambda(1) = 0.009, control lambda(2) = 0.012,
## planned cumulative events = c(50, 100, 150, 200), maximum number of subjects = 400,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0.000 0.000 0.000
## Overall power 0.0240 0.2260 0.4550 0.6190
## Expected number of subjects 400.0
## Number of subjects 400.0 400.0 400.0 400.0
## Exit probability for futility 0.1230 0.0210 0.0070
## Expected number of events 143.9
## Cumulative number of events 50 100 150 200
## Analysis time 19.30 34.51 52.73 74.94
## Expected study duration 52.52
## Conditional power (achieved) 0.3355 0.3758 0.3823
```

```
summary(getSimulationSurvival(design,
median2 = 60, median1 = 80,
plannedEvents = c(50, 100, 150, 200),
maxNumberOfSubjects = 400,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: treatment median(1) = 80, control median(2) = 60,
## planned cumulative events = c(50, 100, 150, 200), maximum number of subjects = 400,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power 0.0240 0.2260 0.4550 0.6190
## Expected number of subjects 400.0
## Number of subjects 400.0 400.0 400.0 400.0
## Exit probability for futility 0.1230 0.0210 0.0070
## Expected number of events 143.9
## Cumulative number of events 50 100 150 200
## Analysis time 19.3 34.5 52.7 74.9
## Expected study duration 52.5
## Conditional power (achieved) 0.3355 0.3758 0.3823
```

```
summary(getSimulationSurvival(design,
median2 = 60, median1 = c(50, 80),
plannedEvents = c(50, 100, 150, 200),
maxNumberOfSubjects = 400,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: treatment median(1) as specified, control median(2) = 60,
## planned cumulative events = c(50, 100, 150, 200), maximum number of subjects = 400,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, median(1) = 50 0 0.0020 0.0030 0.0040
## Overall power, median(1) = 80 0.0180 0.1770 0.4000 0.5810
## Expected number of subjects, median(1) = 50 400.0
## Expected number of subjects, median(1) = 80 400.0
## Number of subjects, median(1) = 50 400.0 400.0 400.0 400.0
## Number of subjects, median(1) = 80 400.0 400.0 400.0 400.0
## Exit probability for futility, median(1) = 50 0.7130 0.1380 0.0640
## Exit probability for futility, median(1) = 80 0.1480 0.0280 0.0060
## Expected number of events, median(1) = 50 75.8
## Expected number of events, median(1) = 80 145.0
## Cumulative number of events, median(1) = 50 50 100 150 200
## Cumulative number of events, median(1) = 80 50 100 150 200
## Analysis time, median(1) = 50 16.6 28.7 43.3 60.1
## Analysis time, median(1) = 80 19.3 34.6 52.8 74.6
## Expected study duration, median(1) = 50 23.6
## Expected study duration, median(1) = 80 53.0
## Conditional power (achieved), median(1) = 50 0.0734 0.0778 0.0476
## Conditional power (achieved), median(1) = 80 0.3216 0.3587 0.3803
```

```
summary(getSimulationSurvival(design,
lambda2 = log(2) / 60, hazardRatio = c(1.2, 1.4),
plannedEvents = c(50, 100, 150, 200),
maxNumberOfSubjects = 400,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: hazard ratio as specified, control lambda(2) = 0.012,
## planned cumulative events = c(50, 100, 150, 200), maximum number of subjects = 400,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, HR = 1.2 0 0.0020 0.0030 0.0040
## Overall power, HR = 1.4 0 0 0 0
## Expected number of subjects, HR = 1.2 400.0
## Expected number of subjects, HR = 1.4 400.0
## Number of subjects, HR = 1.2 400.0 400.0 400.0 400.0
## Number of subjects, HR = 1.4 400.0 400.0 400.0 400.0
## Exit probability for futility, HR = 1.2 0.7130 0.1380 0.0640
## Exit probability for futility, HR = 1.4 0.8820 0.0850 0.0250
## Expected number of events, HR = 1.2 75.8
## Expected number of events, HR = 1.4 58.0
## Cumulative number of events, HR = 1.2 50 100 150 200
## Cumulative number of events, HR = 1.4 50 100 150 200
## Analysis time, HR = 1.2 16.6 28.7 43.3 60.1
## Analysis time, HR = 1.4 15.8 26.7 40.0 56.5
## Expected study duration, HR = 1.2 23.6
## Expected study duration, HR = 1.4 17.6
## Conditional power (achieved), HR = 1.2 0.0734 0.0778 0.0476
## Conditional power (achieved), HR = 1.4 0.0326 0.0315 0.0102
##
## Legend:
## HR: hazard ratio
```

```
summary(getSimulationSurvival(design,
lambda2 = log(2) / 60, hazardRatio = c(1.2, 1.4),
plannedEvents = c(50, 100, 150, 200),
maxNumberOfSubjects = 400,
directionUpper = FALSE,
allocation1 = 1, allocation2 = 2,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1, power directed towards smaller values,
## H1: hazard ratio as specified, control lambda(2) = 0.012,
## planned cumulative events = c(50, 100, 150, 200), planned allocation ratio = 0.5,
## maximum number of subjects = 400, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, HR = 1.2 0 0 0 0.0010
## Overall power, HR = 1.4 0 0 0 0
## Expected number of subjects, HR = 1.2 400.0
## Expected number of subjects, HR = 1.4 400.0
## Number of subjects, HR = 1.2 400.0 400.0 400.0 400.0
## Number of subjects, HR = 1.4 400.0 400.0 400.0 400.0
## Exit probability for futility, HR = 1.2 0.7500 0.1330 0.0440
## Exit probability for futility, HR = 1.4 0.8910 0.0740 0.0240
## Expected number of events, HR = 1.2 72.0
## Expected number of events, HR = 1.4 57.8
## Cumulative number of events, HR = 1.2 50 100 150 200
## Cumulative number of events, HR = 1.4 50 100 150 200
## Analysis time, HR = 1.2 16.9 29.3 44.2 62.1
## Analysis time, HR = 1.4 16.3 27.8 41.8 58.6
## Expected study duration, HR = 1.2 23.0
## Expected study duration, HR = 1.4 18.3
## Conditional power (achieved), HR = 1.2 0.0840 0.1031 0.0860
## Conditional power (achieved), HR = 1.4 0.0682 0.0395 0.0297
##
## Legend:
## HR: hazard ratio
```

```
summary(getSimulationSurvival(design = design,
plannedEvents = c(40,70,100,150),
maxNumberOfSubjects = 400,
thetaH0 = 1.2,
pi1 = seq(0.1,0.25,0.05),
pi2 = 0.2,
allocation1 = 2,
directionUpper = FALSE,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1.2, power directed towards smaller values,
## H1: treatment pi(1) as specified, control pi(2) = 0.2,
## planned cumulative events = c(40, 70, 100, 150), planned allocation ratio = 2,
## maximum number of subjects = 400, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, pi(1) = 0.1 0.4690 0.9460 0.9940 0.9990
## Overall power, pi(1) = 0.15 0.0740 0.4420 0.7090 0.8610
## Overall power, pi(1) = 0.2 0.0060 0.0620 0.1560 0.2520
## Overall power, pi(1) = 0.25 0 0.0080 0.0200 0.0250
## Expected number of subjects, pi(1) = 0.1 399.9
## Expected number of subjects, pi(1) = 0.15 399.7
## Expected number of subjects, pi(1) = 0.2 395.2
## Expected number of subjects, pi(1) = 0.25 377.4
## Number of subjects, pi(1) = 0.1 399.8 400.0 400.0 400.0
## Number of subjects, pi(1) = 0.15 397.2 400.0 400.0 400.0
## Number of subjects, pi(1) = 0.2 383.0 400.0 400.0 400.0
## Number of subjects, pi(1) = 0.25 359.2 400.0 400.0 400.0
## Exit probability for futility, pi(1) = 0.1 0.0010 0 0
## Exit probability for futility, pi(1) = 0.15 0.0420 0.0070 0.0020
## Exit probability for futility, pi(1) = 0.2 0.2750 0.0790 0.0330
## Exit probability for futility, pi(1) = 0.25 0.5540 0.1320 0.0750
## Expected number of events, pi(1) = 0.1 57.7
## Expected number of events, pi(1) = 0.15 93.8
## Expected number of events, pi(1) = 0.2 101.9
## Expected number of events, pi(1) = 0.25 73.5
## Cumulative number of events, pi(1) = 0.1 40 70 100 150
## Cumulative number of events, pi(1) = 0.15 40 70 100 150
## Cumulative number of events, pi(1) = 0.2 40 70 100 150
## Cumulative number of events, pi(1) = 0.25 40 70 100 150
## Analysis time, pi(1) = 0.1 14.9 22.1 30.0 46.5
## Analysis time, pi(1) = 0.15 13.1 18.8 25.0 37.1
## Analysis time, pi(1) = 0.2 11.7 16.4 21.5 31.4
## Analysis time, pi(1) = 0.25 10.8 14.9 19.2 27.6
## Expected study duration, pi(1) = 0.1 19.2
## Expected study duration, pi(1) = 0.15 24.2
## Expected study duration, pi(1) = 0.2 22.6
## Expected study duration, pi(1) = 0.25 15.7
## Conditional power (achieved), pi(1) = 0.1 0.7311 0.6144 0.6388
## Conditional power (achieved), pi(1) = 0.15 0.4014 0.4159 0.4513
## Conditional power (achieved), pi(1) = 0.2 0.1930 0.2203 0.3010
## Conditional power (achieved), pi(1) = 0.25 0.0997 0.1140 0.1443
```

```
summary(getSimulationSurvival(design = design,
plannedEvents = c(40,70,100,150),
maxNumberOfSubjects = 600,
thetaH0 = 1.2,
pi1 = seq(0.1,0.25,0.05),
pi2 = 0.2,
allocation1 = 2,
directionUpper = FALSE,
conditionalPower = 0.8,
minNumberOfEventsPerStage = c(40,20,20,20),
maxNumberOfEventsPerStage = c(40,100,100,100),
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1.2, power directed towards smaller values,
## H1: treatment pi(1) as specified, control pi(2) = 0.2,
## planned cumulative events = c(40, 70, 100, 150), planned allocation ratio = 2,
## sample size reassessment: conditional power = 0.8,
## minimum events per stage = c(40, 20, 20, 20),
## maximum events per stage = c(40, 100, 100, 100), maximum number of subjects = 600,
## simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, pi(1) = 0.1 0.4490 0.9760 0.9980 0.9980
## Overall power, pi(1) = 0.15 0.0720 0.5670 0.8670 0.9290
## Overall power, pi(1) = 0.2 0.0110 0.0830 0.2190 0.3670
## Overall power, pi(1) = 0.25 0.0010 0.0010 0.0090 0.0210
## Expected number of subjects, pi(1) = 0.1 589.6
## Expected number of subjects, pi(1) = 0.15 589.5
## Expected number of subjects, pi(1) = 0.2 564.3
## Expected number of subjects, pi(1) = 0.25 508.1
## Number of subjects, pi(1) = 0.1 576.9 600.0 600.0
## Number of subjects, pi(1) = 0.15 522.5 599.6 600.0 600.0
## Number of subjects, pi(1) = 0.2 474.5 598.5 600.0 600.0
## Number of subjects, pi(1) = 0.25 434.7 598.3 600.0 600.0
## Exit probability for futility, pi(1) = 0.1 0.0020 0 0
## Exit probability for futility, pi(1) = 0.15 0.0610 0.0010 0
## Exit probability for futility, pi(1) = 0.2 0.2720 0.0520 0.0080
## Exit probability for futility, pi(1) = 0.25 0.5530 0.1760 0.0780
## Expected number of events, pi(1) = 0.1 65.6
## Expected number of events, pi(1) = 0.15 132.8
## Expected number of events, pi(1) = 0.2 200.6
## Expected number of events, pi(1) = 0.25 126.9
## Cumulative number of events, pi(1) = 0.1 40 85 125 125
## Cumulative number of events, pi(1) = 0.15 40 111 181 261
## Cumulative number of events, pi(1) = 0.2 40 129 219 316
## Cumulative number of events, pi(1) = 0.25 40 136 233 331
## Analysis time, pi(1) = 0.1 11.8 19.1 22.4
## Analysis time, pi(1) = 0.15 10.5 19.7 30.7 45.2
## Analysis time, pi(1) = 0.2 9.5 19.1 30.8 47.8
## Analysis time, pi(1) = 0.25 8.7 17.6 28.0 41.9
## Expected study duration, pi(1) = 0.1 16.0
## Expected study duration, pi(1) = 0.15 23.4
## Expected study duration, pi(1) = 0.2 30.6
## Expected study duration, pi(1) = 0.25 18.2
## Conditional power (achieved), pi(1) = 0.1 0.7901 0.8140
## Conditional power (achieved), pi(1) = 0.15 0.5511 0.6627 0.6403
## Conditional power (achieved), pi(1) = 0.2 0.3192 0.3477 0.3627
## Conditional power (achieved), pi(1) = 0.25 0.2115 0.1616 0.1329
```

```
summary(getSimulationSurvival(design = design,
plannedEvents = c(40,70,100,150),
maxNumberOfSubjects = 600,
thetaH0 = 1.2,
pi1 = seq(0.1,0.25,0.05),
pi2 = 0.2,
allocation1 = 2,
directionUpper = FALSE,
conditionalPower = 0.8,
minNumberOfEventsPerStage = c(40,20,20,20),
maxNumberOfEventsPerStage = c(40,100,100,100),
thetaH1 = 1,
maxNumberOfIterations = 1000,
seed = 1234))
```

```
## Simulation of a survival endpoint
##
## Sequential analysis with a maximum of 4 looks
## (inverse normal combination test design).
## The results were simulated for a two-sample logrank test,
## H0: hazard ratio = 1.2, power directed towards smaller values,
## H1: treatment pi(1) as specified, control pi(2) = 0.2,
## planned cumulative events = c(40, 70, 100, 150), planned allocation ratio = 2,
## sample size reassessment: conditional power = 0.8,
## minimum events per stage = c(40, 20, 20, 20),
## maximum events per stage = c(40, 100, 100, 100), thetaH1 = 0.833,
## maximum number of subjects = 600, simulation runs = 1000, seed = 1234.
##
## Stage 1 2 3 4
## Fixed weight 0.5 0.5 0.5 0.5
## Efficacy boundary (z-value scale) 3.069 2.326 1.978 1.763
## Futility boundary (z-value scale) 0 0 0
## Overall power, pi(1) = 0.1 0.4490 0.9970 0.9980 0.9980
## Overall power, pi(1) = 0.15 0.0720 0.6740 0.9060 0.9350
## Overall power, pi(1) = 0.2 0.0110 0.1030 0.2520 0.3910
## Overall power, pi(1) = 0.25 0.0010 0.0030 0.0110 0.0220
## Expected number of subjects, pi(1) = 0.1 589.6
## Expected number of subjects, pi(1) = 0.15 589.7
## Expected number of subjects, pi(1) = 0.2 564.5
## Expected number of subjects, pi(1) = 0.25 508.4
## Number of subjects, pi(1) = 0.1 576.9 600.0 600.0
## Number of subjects, pi(1) = 0.15 522.5 600.0 600.0 600.0
## Number of subjects, pi(1) = 0.2 474.5 600.0 600.0 600.0
## Number of subjects, pi(1) = 0.25 434.7 600.0 600.0 600.0
## Exit probability for futility, pi(1) = 0.1 0.0020 0 0
## Exit probability for futility, pi(1) = 0.15 0.0610 0.0010 0
## Exit probability for futility, pi(1) = 0.2 0.2720 0.0520 0.0080
## Exit probability for futility, pi(1) = 0.25 0.5530 0.1760 0.0810
## Expected number of events, pi(1) = 0.1 95.0
## Expected number of events, pi(1) = 0.15 156.3
## Expected number of events, pi(1) = 0.2 210.6
## Expected number of events, pi(1) = 0.25 129.3
## Cumulative number of events, pi(1) = 0.1 40 140 240 240
## Cumulative number of events, pi(1) = 0.15 40 140 240 340
## Cumulative number of events, pi(1) = 0.2 40 140 240 340
## Cumulative number of events, pi(1) = 0.25 40 140 240 340
## Analysis time, pi(1) = 0.1 11.8 28.5 52.1
## Analysis time, pi(1) = 0.15 10.5 23.6 39.7 61.5
## Analysis time, pi(1) = 0.2 9.5 20.4 33.5 51.1
## Analysis time, pi(1) = 0.25 8.7 18.0 29.1 43.8
## Expected study duration, pi(1) = 0.1 21.0
## Expected study duration, pi(1) = 0.15 26.8
## Expected study duration, pi(1) = 0.2 32.1
## Expected study duration, pi(1) = 0.25 18.5
## Conditional power (achieved), pi(1) = 0.1 0.4405 0.6022
## Conditional power (achieved), pi(1) = 0.15 0.2556 0.4813 0.5406
## Conditional power (achieved), pi(1) = 0.2 0.1305 0.2567 0.3413
## Conditional power (achieved), pi(1) = 0.25 0.0794 0.1206 0.1487
```

```
options("rpact.summary.output.size" = "medium") # small, medium, large
design <- getDesignFisher(alpha = 0.05, kMax = 3)
summary(getSimulationMultiArmMeans(design = design,
plannedSubjects = c(40,70,100),
activeArms = 3,
typeOfShape = "linear",
typeOfSelection = "rBest",
rValue = 2,
stDev = 1.2,
maxNumberOfIterations = 100,
seed = 1234))
```

```
## Simulation of a continuous endpoint (multi-arm design)
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a multi-arm comparisons for means
## (3 treatments vs. control), H0: mu(i) - mu(control) = 0, H1: effect as specified,
## standard deviation = 1.2, planned cumulative sample size = c(40, 70, 100),
## intersection test = Dunnett, effect shape = linear, selection = r best, r = 2,
## effect measure based on effect estimate, success criterion: all,
## simulation runs = 100, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 1 1
## Efficacy boundary (p product scale) 0.0255136 0.0038966 0.0007481
## Reject at least one, mu_max = 0 0.0500
## Reject at least one, mu_max = 0.2 0.2100
## Reject at least one, mu_max = 0.4 0.5400
## Reject at least one, mu_max = 0.6 0.8500
## Reject at least one, mu_max = 0.8 1.0000
## Reject at least one, mu_max = 1 1.0000
## Success per stage, mu_max = 0 0 0.0200 0
## Success per stage, mu_max = 0.2 0 0.0200 0.0300
## Success per stage, mu_max = 0.4 0.0200 0.1400 0.0400
## Success per stage, mu_max = 0.6 0.0900 0.2900 0.1200
## Success per stage, mu_max = 0.8 0.1700 0.4800 0.1900
## Success per stage, mu_max = 1 0.2800 0.5800 0.1200
## Expected number of subjects, mu_max = 0 338.2
## Expected number of subjects, mu_max = 0.2 338.2
## Expected number of subjects, mu_max = 0.4 323.8
## Expected number of subjects, mu_max = 0.6 297.7
## Expected number of subjects, mu_max = 0.8 266.2
## Expected number of subjects, mu_max = 1 237.4
## Overall exit probability, mu_max = 0 0 0.0200
## Overall exit probability, mu_max = 0.2 0 0.0200
## Overall exit probability, mu_max = 0.4 0.0200 0.1400
## Overall exit probability, mu_max = 0.6 0.0900 0.2900
## Overall exit probability, mu_max = 0.8 0.1700 0.4800
## Overall exit probability, mu_max = 1 0.2800 0.5800
## Stagewise number of subjects, mu_max = 0
## treatment arm 1 40.0 19.2 19.3
## treatment arm 2 40.0 18.9 19.0
## treatment arm 3 40.0 21.9 21.7
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.2
## treatment arm 1 40.0 15.9 16.2
## treatment arm 2 40.0 19.2 19.0
## treatment arm 3 40.0 24.9 24.8
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.4
## treatment arm 1 40.0 12.6 13.9
## treatment arm 2 40.0 20.8 20.0
## treatment arm 3 40.0 26.6 26.1
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.6
## treatment arm 1 40.0 9.6 11.1
## treatment arm 2 40.0 22.4 21.3
## treatment arm 3 40.0 28.0 27.6
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.8
## treatment arm 1 40.0 4.3 6.0
## treatment arm 2 40.0 26.0 24.0
## treatment arm 3 40.0 29.6 30.0
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 1
## treatment arm 1 40.0 2.1 6.4
## treatment arm 2 40.0 27.9 23.6
## treatment arm 3 40.0 30.0 30.0
## control arm 40.0 30.0 30.0
## Selected arms, mu_max = 0
## treatment arm 1 1.0000 0.6400 0.6300
## treatment arm 2 1.0000 0.6300 0.6200
## treatment arm 3 1.0000 0.7300 0.7100
## Selected arms, mu_max = 0.2
## treatment arm 1 1.0000 0.5300 0.5300
## treatment arm 2 1.0000 0.6400 0.6200
## treatment arm 3 1.0000 0.8300 0.8100
## Selected arms, mu_max = 0.4
## treatment arm 1 1.0000 0.4100 0.3900
## treatment arm 2 1.0000 0.6800 0.5600
## treatment arm 3 1.0000 0.8700 0.7300
## Selected arms, mu_max = 0.6
## treatment arm 1 1.0000 0.2900 0.2300
## treatment arm 2 1.0000 0.6800 0.4400
## treatment arm 3 1.0000 0.8500 0.5700
## Selected arms, mu_max = 0.8
## treatment arm 1 1.0000 0.1200 0.0700
## treatment arm 2 1.0000 0.7200 0.2800
## treatment arm 3 1.0000 0.8200 0.3500
## Selected arms, mu_max = 1
## treatment arm 1 1.0000 0.0500 0.0300
## treatment arm 2 1.0000 0.6700 0.1100
## treatment arm 3 1.0000 0.7200 0.1400
## Number of active arms, mu_max = 0 3.000 2.000 2.000
## Number of active arms, mu_max = 0.2 3.000 2.000 2.000
## Number of active arms, mu_max = 0.4 3.000 2.000 2.000
## Number of active arms, mu_max = 0.6 3.000 2.000 2.000
## Number of active arms, mu_max = 0.8 3.000 2.000 2.000
## Number of active arms, mu_max = 1 3.000 2.000 2.000
##
## Legend:
## (i): treatment arm i
```

```
summary(getSimulationMultiArmMeans(design = design,
plannedSubjects = c(40,70,100),
activeArms = 3,
typeOfShape = "sigmoidEmax",
gED50 = 2,
typeOfSelection = "rBest",
rValue = 2,
stDev = 1.2,
maxNumberOfIterations = 100,
seed = 1234))
```

```
## Simulation of a continuous endpoint (multi-arm design)
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a multi-arm comparisons for means
## (3 treatments vs. control), H0: mu(i) - mu(control) = 0, H1: effect as specified,
## standard deviation = 1.2, planned cumulative sample size = c(40, 70, 100),
## intersection test = Dunnett, effect shape = sigmoid emax, slope = 1, ED50 = 2,
## selection = r best, r = 2, effect measure based on effect estimate,
## success criterion: all, simulation runs = 100, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 1 1
## Efficacy boundary (p product scale) 0.0255136 0.0038966 0.0007481
## Reject at least one, mu_max = 0 0.0500
## Reject at least one, mu_max = 0.2 0.1400
## Reject at least one, mu_max = 0.4 0.2900
## Reject at least one, mu_max = 0.6 0.4800
## Reject at least one, mu_max = 0.8 0.7100
## Reject at least one, mu_max = 1 0.9100
## Success per stage, mu_max = 0 0 0.0200 0
## Success per stage, mu_max = 0.2 0 0.0200 0.0100
## Success per stage, mu_max = 0.4 0.0200 0.0400 0.0400
## Success per stage, mu_max = 0.6 0.0400 0.1600 0.0500
## Success per stage, mu_max = 0.8 0.0700 0.2400 0.1100
## Success per stage, mu_max = 1 0.2000 0.4000 0.0900
## Expected number of subjects, mu_max = 0 338.2
## Expected number of subjects, mu_max = 0.2 338.2
## Expected number of subjects, mu_max = 0.4 332.8
## Expected number of subjects, mu_max = 0.6 318.4
## Expected number of subjects, mu_max = 0.8 305.8
## Expected number of subjects, mu_max = 1 268.0
## Overall exit probability, mu_max = 0 0 0.0200
## Overall exit probability, mu_max = 0.2 0 0.0200
## Overall exit probability, mu_max = 0.4 0.0200 0.0400
## Overall exit probability, mu_max = 0.6 0.0400 0.1600
## Overall exit probability, mu_max = 0.8 0.0700 0.2400
## Overall exit probability, mu_max = 1 0.2000 0.4000
## Stagewise number of subjects, mu_max = 0
## treatment arm 1 40.0 19.2 19.3
## treatment arm 2 40.0 18.9 19.0
## treatment arm 3 40.0 21.9 21.7
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.2
## treatment arm 1 40.0 17.4 17.8
## treatment arm 2 40.0 20.1 19.9
## treatment arm 3 40.0 22.5 22.3
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.4
## treatment arm 1 40.0 17.1 17.6
## treatment arm 2 40.0 20.8 20.7
## treatment arm 3 40.0 22.0 21.7
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.6
## treatment arm 1 40.0 15.9 16.5
## treatment arm 2 40.0 18.8 19.1
## treatment arm 3 40.0 25.3 24.4
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 0.8
## treatment arm 1 40.0 12.6 12.2
## treatment arm 2 40.0 22.9 23.5
## treatment arm 3 40.0 24.5 24.3
## control arm 40.0 30.0 30.0
## Stagewise number of subjects, mu_max = 1
## treatment arm 1 40.0 12.4 16.5
## treatment arm 2 40.0 20.2 18.0
## treatment arm 3 40.0 27.4 25.5
## control arm 40.0 30.0 30.0
## Selected arms, mu_max = 0
## treatment arm 1 1.0000 0.6400 0.6300
## treatment arm 2 1.0000 0.6300 0.6200
## treatment arm 3 1.0000 0.7300 0.7100
## Selected arms, mu_max = 0.2
## treatment arm 1 1.0000 0.5800 0.5800
## treatment arm 2 1.0000 0.6700 0.6500
## treatment arm 3 1.0000 0.7500 0.7300
## Selected arms, mu_max = 0.4
## treatment arm 1 1.0000 0.5600 0.5500
## treatment arm 2 1.0000 0.6800 0.6500
## treatment arm 3 1.0000 0.7200 0.6800
## Selected arms, mu_max = 0.6
## treatment arm 1 1.0000 0.5100 0.4400
## treatment arm 2 1.0000 0.6000 0.5100
## treatment arm 3 1.0000 0.8100 0.6500
## Selected arms, mu_max = 0.8
## treatment arm 1 1.0000 0.3900 0.2800
## treatment arm 2 1.0000 0.7100 0.5400
## treatment arm 3 1.0000 0.7600 0.5600
## Selected arms, mu_max = 1
## treatment arm 1 1.0000 0.3300 0.2200
## treatment arm 2 1.0000 0.5400 0.2400
## treatment arm 3 1.0000 0.7300 0.3400
## Number of active arms, mu_max = 0 3.000 2.000 2.000
## Number of active arms, mu_max = 0.2 3.000 2.000 2.000
## Number of active arms, mu_max = 0.4 3.000 2.000 2.000
## Number of active arms, mu_max = 0.6 3.000 2.000 2.000
## Number of active arms, mu_max = 0.8 3.000 2.000 2.000
## Number of active arms, mu_max = 1 3.000 2.000 2.000
##
## Legend:
## (i): treatment arm i
```

```
summary(getSimulationMultiArmMeans(design = design,
plannedSubjects = c(40,70,100),
activeArms = 3,
typeOfShape = "linear",
typeOfSelection = "rBest",
rValue = 2,
stDev = 1.2,
conditionalPower = 0.8,
minNumberOfSubjectsPerStage = c(40,20,20),
maxNumberOfSubjectsPerStage = c(40,100,100),
maxNumberOfIterations = 100,
seed = 1234))
```

```
## Simulation of a continuous endpoint (multi-arm design)
##
## Sequential analysis with a maximum of 3 looks (Fisher's combination test design).
## The results were simulated for a multi-arm comparisons for means
## (3 treatments vs. control), H0: mu(i) - mu(control) = 0, H1: effect as specified,
## standard deviation = 1.2, planned cumulative sample size = c(40, 70, 100),
## intersection test = Dunnett, effect shape = linear, selection = r best, r = 2,
## effect measure based on effect estimate, success criterion: all,
## sample size reassessment: conditional power = 0.8,
## minimum subjects per stage = c(40, 20, 20),
## maximum subjects per stage = c(40, 100, 100), simulation runs = 100, seed = 1234.
##
## Stage 1 2 3
## Fixed weight 1 1 1
## Efficacy boundary (p product scale) 0.0255136 0.0038966 0.0007481
## Reject at least one, mu_max = 0 0.0500
## Reject at least one, mu_max = 0.2 0.3800
## Reject at least one, mu_max = 0.4 0.8800
## Reject at least one, mu_max = 0.6 0.9900
## Reject at least one, mu_max = 0.8 1.0000
## Reject at least one, mu_max = 1 1.0000
## Success per stage, mu_max = 0 0 0.0200 0
## Success per stage, mu_max = 0.2 0 0.0200 0.0800
## Success per stage, mu_max = 0.4 0.0200 0.2000 0.1000
## Success per stage, mu_max = 0.6 0.0900 0.4800 0.1200
## Success per stage, mu_max = 0.8 0.1700 0.5500 0.1500
## Success per stage, mu_max = 1 0.2800 0.5900 0.0600
## Expected number of subjects, mu_max = 0 749.3
## Expected number of subjects, mu_max = 0.2 705.9
## Expected number of subjects, mu_max = 0.4 563.2
## Expected number of subjects, mu_max = 0.6 392.4
## Expected number of subjects, mu_max = 0.8 288.9
## Expected number of subjects, mu_max = 1 232.8
## Overall exit probability, mu_max = 0 0 0.0200
## Overall exit probability, mu_max = 0.2 0 0.0200
## Overall exit probability, mu_max = 0.4 0.0200 0.2000
## Overall exit probability, mu_max = 0.6 0.0900 0.4800
## Overall exit probability, mu_max = 0.8 0.1700 0.5500
## Overall exit probability, mu_max = 1 0.2800 0.5900
## Stagewise number of subjects, mu_max = 0
## treatment arm 1 40.0 63.4 64.3
## treatment arm 2 40.0 62.0 63.3
## treatment arm 3 40.0 71.4 72.4
## control arm 40.0 98.4 100.0
## Stagewise number of subjects, mu_max = 0.2
## treatment arm 1
```