rpact: Confirmatory Adaptive Clinical Trial Design and Analysis

Summary

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.

1 Global options

First, load the rpact package

library(rpact)
packageVersion("rpact") 
## [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")

2 Design summaries

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
summary(getDesignGroupSequential(kMax = 1))
## 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
summary(getDesignGroupSequential(kMax = 4, sided = 2))
## 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
summary(getDesignGroupSequential(kMax = 4, sided = 2), digits = 0)
## 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
summary(getDesignGroupSequential(kMax = 1, sided = 2))
## 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
summary(getDesignGroupSequential(futilityBounds = c(-6, 0)))
## 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
summary(getDesignGroupSequential(futilityBounds = c(-6, 0)), digits = 5)
## 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
summary(getDesignInverseNormal(kMax = 1))
## 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
summary(getDesignInverseNormal(futilityBounds = c(0, 1)))
## 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
summary(getDesignInverseNormal(kMax = 1))
## 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
summary(getDesignInverseNormal(kMax = 4, sided = 2))
## 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
summary(getDesignInverseNormal(kMax = 4, sided = 2), digits = 0)
## 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
summary(getDesignInverseNormal(kMax = 1, sided = 2))
## 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
summary(getDesignFisher())
## 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
summary(getDesignFisher(alpha0Vec = c(0.1, 0.2)))
## 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
summary(getDesignFisher(kMax = 1))
## 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
summary(getDesignFisher(kMax = 4, sided = 2), digits = 5)
## 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
summary(getDesignFisher(kMax = 4, sided = 2), digits = 0)
## 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
summary(getDesignFisher(kMax = 1, sided = 2))
## 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

3 Design plan summaries

3.1 Design plan summaries - means

summary(getSampleSizeMeans(sided = 2, alternative = -0.5))
## 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
summary(getSampleSizeMeans(sided = 2), alternative = -0.5) # warning expected
## 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
summary(getSampleSizeMeans(thetaH0 = 0, alternative = 0.5, sided = 1, stDev = 2.5))
## 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
summary(getSampleSizeMeans(thetaH0 = 0, alternative = 0.5, sided = 1, stDev = 1, groups = 1))
## 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
summary(getSampleSizeMeans(thetaH0 = 0, sided = 2, stDev = 1, groups = 1))
## 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
summary(getSampleSizeMeans(thetaH0 = 0, alternative = 1.2, sided = 2, stDev = 5))
## 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
summary(getSampleSizeMeans(thetaH0 = 0, alternative = 1.2, sided = 2, stDev = 5, groups = 1))
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))))
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = 0)
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(kMax = 4, sided = 2)))
## 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
summary(getPowerMeans(getDesignGroupSequential(kMax = 4, sided = 2), 
    maxNumberOfSubjects = 100))
## 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
summary(getSampleSizeMeans(getDesignInverseNormal(futilityBounds = c(1, 2))))
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = 4)
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = 3)
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = 2)
## 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
summary(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = 0)
## 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(getSampleSizeMeans(getDesignGroupSequential(futilityBounds = c(1, 2))), digits = -1)
## 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

3.2 Design plan summaries - rates

summary(getSampleSizeRates(pi2 = 0.3))
## 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
summary(getSampleSizeRates(groups = 1, thetaH0 = 0.3))
## 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
summary(getSampleSizeRates(groups = 1, thetaH0 = 0.45)) 
## 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
summary(getSampleSizeRates(groups = 2, thetaH0 = 0.45, allocationRatioPlanned = 0)) 
## 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
summary(getSampleSizeRates(getDesignGroupSequential(futilityBounds = c(1, 2))))
## 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
summary(getSampleSizeRates(getDesignGroupSequential(kMax = 4, sided = 2)))
## 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
summary(getPowerRates(getDesignGroupSequential(kMax = 4, sided = 2), 
    maxNumberOfSubjects = 100))
## 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

3.3 Design plan summaries - survival

summary(getSampleSizeSurvival())
## 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
summary(getSampleSizeSurvival(lambda2 = 0.3, 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, 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
summary(getSampleSizeSurvival(median2 = 2.3, 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, 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
summary(getSampleSizeSurvival(median1 = 3.2, median2 = 2.3))
## 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
summary(getSampleSizeSurvival(median1 = c(3.1, 3.2), median2 = 2.3))
## 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
summary(getSampleSizeSurvival(lambda2 = 0.3, hazardRatio = c(1.2, 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 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
summary(getSampleSizeSurvival(pi2 = 0.3, 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, 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
summary(getSampleSizeSurvival(pi1 = 0.1, pi2 = 0.3))
## 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
summary(getSampleSizeSurvival(lambda2 = 0.03, lambda1 = c(0.040))) 
## 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
summary(getSampleSizeSurvival(getDesignGroupSequential(futilityBounds = c(1, 2))))
## 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
summary(getSampleSizeSurvival(getDesignGroupSequential(kMax = 4, sided = 2)))
## 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
summary(getSampleSizeSurvival(sided = 2, lambda2 = log(2)/6, lambda1 = log(2)/8))
## 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
summary(getSampleSizeSurvival(getDesignGroupSequential(kMax = 4, sided = 2)))
## 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

4 Simulation results summaries

4.1 Create two typical designs

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))

4.2 Simulation results base

4.2.1 Simulation results base - means

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

4.2.2 Simulation results base - rates

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

4.2.3 Simulation results base - survival

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

4.3 Simulation results multi-arm

4.3.1 Simulation results multi-arm - means

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