getSimulationSurvival {rpact}  R Documentation 
Returns the analysis times, power, stopping probabilities, conditional power, and expected sample size for testing the hazard ratio in a two treatment groups survival design.
getSimulationSurvival(
design = NULL,
...,
thetaH0 = 1,
directionUpper = TRUE,
pi1 = NA_real_,
pi2 = NA_real_,
lambda1 = NA_real_,
lambda2 = NA_real_,
median1 = NA_real_,
median2 = NA_real_,
hazardRatio = NA_real_,
kappa = 1,
piecewiseSurvivalTime = NA_real_,
allocation1 = 1,
allocation2 = 1,
eventTime = 12,
accrualTime = c(0, 12),
accrualIntensity = 0.1,
accrualIntensityType = c("auto", "absolute", "relative"),
dropoutRate1 = 0,
dropoutRate2 = 0,
dropoutTime = 12,
maxNumberOfSubjects = NA_real_,
plannedEvents = NA_real_,
minNumberOfEventsPerStage = NA_real_,
maxNumberOfEventsPerStage = NA_real_,
conditionalPower = NA_real_,
thetaH1 = NA_real_,
maxNumberOfIterations = 1000L,
maxNumberOfRawDatasetsPerStage = 0,
longTimeSimulationAllowed = FALSE,
seed = NA_real_,
calcEventsFunction = NULL,
showStatistics = FALSE
)
design 
The trial design. If no trial design is specified, a fixed sample size design is used.
In this case, Type I error rate 
... 
Ensures that all arguments (starting from the "...") are to be named and that a warning will be displayed if unknown arguments are passed. 
thetaH0 
The null hypothesis value,
default is
For testing a rate in one sample, a value 
directionUpper 
Logical. Specifies the direction of the alternative,
only applicable for onesided testing; default is 
pi1 
A numeric value or vector that represents the assumed event rate in the treatment group,
default is 
pi2 
A numeric value that represents the assumed event rate in the control group, default is 
lambda1 
The assumed hazard rate in the treatment group, there is no default.

lambda2 
The assumed hazard rate in the reference group, there is no default.

median1 
The assumed median survival time in the treatment group, there is no default. 
median2 
The assumed median survival time in the reference group, there is no default. Must be a positive numeric of length 1. 
hazardRatio 
The vector of hazard ratios under consideration. If the event or hazard rates in both treatment groups are defined, the hazard ratio needs not to be specified as it is calculated, there is no default. Must be a positive numeric of length 1. 
kappa 
A numeric value > 0. A 
piecewiseSurvivalTime 
A vector that specifies the time intervals for the piecewise
definition of the exponential survival time cumulative distribution function 
allocation1 
The number how many subjects are assigned to treatment 1 in a
subsequent order, default is 
allocation2 
The number how many subjects are assigned to treatment 2 in a
subsequent order, default is 
eventTime 
The assumed time under which the event rates are calculated, default is 
accrualTime 
The assumed accrual time intervals for the study, default is

accrualIntensity 
A numeric vector of accrual intensities, default is the relative
intensity 
accrualIntensityType 
A character value specifying the accrual intensity input type.
Must be one of 
dropoutRate1 
The assumed dropout rate in the treatment group, default is 
dropoutRate2 
The assumed dropout rate in the control group, default is 
dropoutTime 
The assumed time for dropout rates in the control and the
treatment group, default is 
maxNumberOfSubjects 

plannedEvents 

minNumberOfEventsPerStage 
When performing a data driven sample size recalculation,
the numeric vector 
maxNumberOfEventsPerStage 
When performing a data driven sample size recalculation,
the numeric vector 
conditionalPower 
If 
thetaH1 
If specified, the value of the alternative under which the conditional power or sample size recalculation calculation is performed. Must be a numeric of length 1. 
maxNumberOfIterations 
The number of simulation iterations, default is 
maxNumberOfRawDatasetsPerStage 
The number of raw datasets per stage that shall
be extracted and saved as 
longTimeSimulationAllowed 
Logical that indicates whether long time simulations
that consumes more than 30 seconds are allowed or not, default is 
seed 
The seed to reproduce the simulation, default is a random seed. 
calcEventsFunction 
Optionally, a function can be entered that defines the way of performing the sample size
recalculation. By default, event number recalculation is performed with conditional power and specified

showStatistics 
Logical. If 
At given design the function simulates the power, stopping probabilities, conditional power, and expected
sample size at given number of events, number of subjects, and parameter configuration.
It also simulates the time when the required events are expected under the given
assumptions (exponentially, piecewise exponentially, or Weibull distributed survival times
and constant or nonconstant piecewise accrual).
Additionally, integers allocation1
and allocation2
can be specified that determine the number allocated
to treatment group 1 and treatment group 2, respectively.
More precisely, unequal randomization ratios must be specified via the two integer arguments allocation1
and
allocation2
which describe how many subjects are consecutively enrolled in each group, respectively, before a
subject is assigned to the other group. For example, the arguments allocation1 = 2
, allocation2 = 1
,
maxNumberOfSubjects = 300
specify 2:1 randomization with 200 subjects randomized to intervention and 100 to
control. (Caveat: Do not use allocation1 = 200
, allocation2 = 100
, maxNumberOfSubjects = 300
as this would imply that the 200 intervention subjects are enrolled prior to enrollment of any control subjects.)
conditionalPower
The definition of thetaH1
makes only sense if kMax
> 1
and if conditionalPower
, minNumberOfEventsPerStage
, and
maxNumberOfEventsPerStage
are defined.
Note that numberOfSubjects
, numberOfSubjects1
, and numberOfSubjects2
in the output
are the expected number of subjects.
calcEventsFunction
This function returns the number of events at given conditional power and conditional critical value for specified
testing situation. The function might depend on variables
stage
,
conditionalPower
,
thetaH0
,
plannedEvents
,
eventsPerStage
,
minNumberOfEventsPerStage
,
maxNumberOfEventsPerStage
,
allocationRatioPlanned
,
conditionalCriticalValue
,
The function has to contain the threedots argument '...' (see examples).
Returns a SimulationResults
object.
The following generics (R generic functions) are available for this object:
names()
to obtain the field names,
print()
to print the object,
summary()
to display a summary of the object,
plot()
to plot the object,
as.data.frame()
to coerce the object to a data.frame
,
as.matrix()
to coerce the object to a matrix
.
The first element of the vector piecewiseSurvivalTime
must be equal to 0
.
piecewiseSurvivalTime
can also be a list that combines the definition of the
time intervals and hazard rates in the reference group.
The definition of the survival time in the treatment group is obtained by the specification
of the hazard ratio (see examples for details).
accrualTime
is the time period of subjects' accrual in a study.
It can be a value that defines the end of accrual or a vector.
In this case, accrualTime
can be used to define a nonconstant accrual over time.
For this, accrualTime
is a vector that defines the accrual intervals.
The first element of accrualTime
must be equal to 0
and, additionally,
accrualIntensity
needs to be specified.
accrualIntensity
itself is a value or a vector (depending on the
length of accrualTime
) that defines the intensity how subjects
enter the trial in the intervals defined through accrualTime
.
accrualTime
can also be a list that combines the definition of the accrual time and
accrual intensity (see below and examples for details).
If the length of accrualTime
and the length of accrualIntensity
are the same
(i.e., the end of accrual is undefined), maxNumberOfSubjects > 0
needs to be specified
and the end of accrual is calculated.
In that case, accrualIntensity
is the number of subjects per time unit, i.e., the absolute accrual intensity.
If the length of accrualTime
equals the length of accrualIntensity  1
(i.e., the end of accrual is defined), maxNumberOfSubjects
is calculated if the absolute accrual intensity is given.
If all elements in accrualIntensity
are smaller than 1, accrualIntensity
defines
the relative intensity how subjects enter the trial.
For example, accrualIntensity = c(0.1, 0.2)
specifies that in the second accrual interval
the intensity is doubled as compared to the first accrual interval. The actual (absolute) accrual intensity
is calculated for the calculated or given maxNumberOfSubjects
.
Note that the default is accrualIntensity = 0.1
meaning that the absolute accrual intensity
will be calculated.
The summary statistics "Simulated data" contains the following parameters: median range; mean +/sd
$show(showStatistics = FALSE)
or $setShowStatistics(FALSE)
can be used to disable
the output of the aggregated simulated data.
Example 1:
simulationResults < getSimulationSurvival(maxNumberOfSubjects = 100, plannedEvents = 30)
simulationResults$show(showStatistics = FALSE)
Example 2:
simulationResults < getSimulationSurvival(maxNumberOfSubjects = 100, plannedEvents = 30)
simulationResults$setShowStatistics(FALSE)
simulationResults
getData()
can be used to get the aggregated simulated data from the
object as data.frame
. The data frame contains the following columns:
iterationNumber
: The number of the simulation iteration.
stageNumber
: The stage.
pi1
: The assumed or derived event rate in the treatment group.
pi2
: The assumed or derived event rate in the control group.
hazardRatio
: The hazard ratio under consideration (if available).
analysisTime
: The analysis time.
numberOfSubjects
: The number of subjects under consideration when the
(interim) analysis takes place.
eventsPerStage1
: The observed number of events per stage
in treatment group 1.
eventsPerStage2
: The observed number of events per stage
in treatment group 2.
eventsPerStage
: The observed number of events per stage
in both treatment groups.
rejectPerStage
: 1 if null hypothesis can be rejected, 0 otherwise.
futilityPerStage
: 1 if study should be stopped for futility, 0 otherwise.
eventsNotAchieved
: 1 if number of events could not be reached with
observed number of subjects, 0 otherwise.
testStatistic
: The test statistic that is used for the test decision,
depends on which design was chosen (group sequential, inverse normal,
or Fisher combination test)'
logRankStatistic
: Zscore statistic which corresponds to a onesided
logrank test at considered stage.
hazardRatioEstimateLR
: The estimated hazard ratio, derived from the
logrank statistic.
trialStop
: TRUE
if study should be stopped for efficacy or futility or final stage, FALSE
otherwise.
conditionalPowerAchieved
: The conditional power for the subsequent stage of the trial for
selected sample size and effect. The effect is either estimated from the data or can be
user defined with thetaH1
.
getRawData()
can be used to get the simulated raw data from the
object as data.frame
. Note that getSimulationSurvival()
must called before with maxNumberOfRawDatasetsPerStage
> 0.
Click on the link of a generic in the list above to go directly to the help documentation of
the rpact
specific implementation of the generic.
Note that you can use the R function methods
to get all the methods of a generic and
to identify the object specific name of it, e.g.,
use methods("plot")
to get all the methods for the plot
generic.
There you can find, e.g., plot.AnalysisResults
and
obtain the specific help documentation linked above by typing ?plot.AnalysisResults
.
# Fixed sample size with minimum required definitions, pi1 = (0.3,0.4,0.5,0.6) and
# pi2 = 0.3 at event time 12, and accrual time 24
getSimulationSurvival(
pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3, eventTime = 12,
accrualTime = 24, plannedEvents = 40, maxNumberOfSubjects = 200,
maxNumberOfIterations = 10
)
## Not run:
# Increase number of simulation iterations
getSimulationSurvival(
pi1 = seq(0.3, 0.6, 0.1), pi2 = 0.3, eventTime = 12,
accrualTime = 24, plannedEvents = 40, maxNumberOfSubjects = 200,
maxNumberOfIterations = 50
)
# Determine necessary accrual time with default settings if 200 subjects and
# 30 subjects per time unit can be recruited
getSimulationSurvival(
plannedEvents = 40, accrualTime = 0,
accrualIntensity = 30, maxNumberOfSubjects = 200, maxNumberOfIterations = 50
)
# Determine necessary accrual time with default settings if 200 subjects and
# if the first 6 time units 20 subjects per time unit can be recruited,
# then 30 subjects per time unit
getSimulationSurvival(
plannedEvents = 40, accrualTime = c(0, 6),
accrualIntensity = c(20, 30), maxNumberOfSubjects = 200,
maxNumberOfIterations = 50
)
# Determine maximum number of Subjects with default settings if the first
# 6 time units 20 subjects per time unit can be recruited, and after
# 10 time units 30 subjects per time unit
getSimulationSurvival(
plannedEvents = 40, accrualTime = c(0, 6, 10),
accrualIntensity = c(20, 30), maxNumberOfIterations = 50
)
# Specify accrual time as a list
at < list(
"0  <6" = 20,
"6  Inf" = 30
)
getSimulationSurvival(
plannedEvents = 40, accrualTime = at,
maxNumberOfSubjects = 200, maxNumberOfIterations = 50
)
# Specify accrual time as a list, if maximum number of subjects need to be calculated
at < list(
"0  <6" = 20,
"6  <=10" = 30
)
getSimulationSurvival(plannedEvents = 40, accrualTime = at, maxNumberOfIterations = 50)
# Specify effect size for a twostage group sequential design with
# O'Brien & Fleming boundaries. Effect size is based on event rates
# at specified event time, directionUpper = FALSE needs to be specified
# because it should be shown that hazard ratio < 1
designGS < getDesignGroupSequential(kMax = 2)
getSimulationSurvival(
design = designGS,
pi1 = 0.2, pi2 = 0.3, eventTime = 24, plannedEvents = c(20, 40),
maxNumberOfSubjects = 200, directionUpper = FALSE, maxNumberOfIterations = 50
)
# As above, but with a threestage O'Brien and Fleming design with
# specified information rates, note that planned events consists of integer values
designGS2 < getDesignGroupSequential(informationRates = c(0.4, 0.7, 1))
getSimulationSurvival(
design = designGS2,
pi1 = 0.2, pi2 = 0.3, eventTime = 24,
plannedEvents = round(designGS2$informationRates * 40),
maxNumberOfSubjects = 200, directionUpper = FALSE,
maxNumberOfIterations = 50
)
# Effect size is based on event rate at specified event time for the reference
# group and hazard ratio, directionUpper = FALSE needs to be specified because
# it should be shown that hazard ratio < 1
getSimulationSurvival(
design = designGS, hazardRatio = 0.5,
pi2 = 0.3, eventTime = 24, plannedEvents = c(20, 40), maxNumberOfSubjects = 200,
directionUpper = FALSE, maxNumberOfIterations = 50
)
# Effect size is based on hazard rate for the reference group and
# hazard ratio, directionUpper = FALSE needs to be specified because
# it should be shown that hazard ratio < 1
getSimulationSurvival(
design = designGS,
hazardRatio = 0.5, lambda2 = 0.02, plannedEvents = c(20, 40),
maxNumberOfSubjects = 200, directionUpper = FALSE,
maxNumberOfIterations = 50
)
# Specification of piecewise exponential survival time and hazard ratios,
# note that in getSimulationSurvival only on hazard ratio is used
# in the case that the survival time is piecewise expoential
getSimulationSurvival(
design = designGS,
piecewiseSurvivalTime = c(0, 5, 10), lambda2 = c(0.01, 0.02, 0.04),
hazardRatio = 1.5, plannedEvents = c(20, 40), maxNumberOfSubjects = 200,
maxNumberOfIterations = 50
)
pws < list(
"0  <5" = 0.01,
"5  <10" = 0.02,
">=10" = 0.04
)
getSimulationSurvival(
design = designGS,
piecewiseSurvivalTime = pws, hazardRatio = c(1.5),
plannedEvents = c(20, 40), maxNumberOfSubjects = 200,
maxNumberOfIterations = 50
)
# Specification of piecewise exponential survival time for both treatment arms
getSimulationSurvival(
design = designGS,
piecewiseSurvivalTime = c(0, 5, 10), lambda2 = c(0.01, 0.02, 0.04),
lambda1 = c(0.015, 0.03, 0.06), plannedEvents = c(20, 40),
maxNumberOfSubjects = 200, maxNumberOfIterations = 50
)
# Specification of piecewise exponential survival time as a list,
# note that in getSimulationSurvival only on hazard ratio
# (not a vector) can be used
pws < list(
"0  <5" = 0.01,
"5  <10" = 0.02,
">=10" = 0.04
)
getSimulationSurvival(
design = designGS,
piecewiseSurvivalTime = pws, hazardRatio = 1.5,
plannedEvents = c(20, 40), maxNumberOfSubjects = 200,
maxNumberOfIterations = 50
)
# Specification of piecewise exponential survival time and delayed effect
# (response after 5 time units)
getSimulationSurvival(
design = designGS,
piecewiseSurvivalTime = c(0, 5, 10), lambda2 = c(0.01, 0.02, 0.04),
lambda1 = c(0.01, 0.02, 0.06), plannedEvents = c(20, 40),
maxNumberOfSubjects = 200, maxNumberOfIterations = 50
)
# Specify effect size based on median survival times
getSimulationSurvival(
median1 = 5, median2 = 3, plannedEvents = 40,
maxNumberOfSubjects = 200, directionUpper = FALSE,
maxNumberOfIterations = 50
)
# Specify effect size based on median survival
# times of Weibull distribtion with kappa = 2
getSimulationSurvival(
median1 = 5, median2 = 3, kappa = 2,
plannedEvents = 40, maxNumberOfSubjects = 200,
directionUpper = FALSE, maxNumberOfIterations = 50
)
# Perform recalculation of number of events based on conditional power for a
# threestage design with inverse normal combination test, where the conditional power
# is calculated under the specified effect size thetaH1 = 1.3 and up to a fourfold
# increase in originally planned sample size (number of events) is allowed.
# Note that the first value in minNumberOfEventsPerStage and
# maxNumberOfEventsPerStage is arbitrary, i.e., it has no effect.
designIN < getDesignInverseNormal(informationRates = c(0.4, 0.7, 1))
resultsWithSSR1 < getSimulationSurvival(
design = designIN,
hazardRatio = seq(1, 1.6, 0.1),
pi2 = 0.3, conditionalPower = 0.8, thetaH1 = 1.3,
plannedEvents = c(58, 102, 146),
minNumberOfEventsPerStage = c(NA, 44, 44),
maxNumberOfEventsPerStage = 4 * c(NA, 44, 44),
maxNumberOfSubjects = 800, maxNumberOfIterations = 50
)
resultsWithSSR1
# If thetaH1 is unspecified, the observed hazard ratio estimate
# (calculated from the logrank statistic) is used for performing the
# recalculation of the number of events
resultsWithSSR2 < getSimulationSurvival(
design = designIN,
hazardRatio = seq(1, 1.6, 0.1),
pi2 = 0.3, conditionalPower = 0.8, plannedEvents = c(58, 102, 146),
minNumberOfEventsPerStage = c(NA, 44, 44),
maxNumberOfEventsPerStage = 4 * c(NA, 44, 44),
maxNumberOfSubjects = 800, maxNumberOfIterations = 50
)
resultsWithSSR2
# Compare it with design without event size recalculation
resultsWithoutSSR < getSimulationSurvival(
design = designIN,
hazardRatio = seq(1, 1.6, 0.1), pi2 = 0.3,
plannedEvents = c(58, 102, 145), maxNumberOfSubjects = 800,
maxNumberOfIterations = 50
)
resultsWithoutSSR$overallReject
resultsWithSSR1$overallReject
resultsWithSSR2$overallReject
# Confirm that event size racalcuation increases the Type I error rate,
# i.e., you have to use the combination test
resultsWithSSRGS < getSimulationSurvival(
design = designGS2,
hazardRatio = seq(1),
pi2 = 0.3, conditionalPower = 0.8, plannedEvents = c(58, 102, 145),
minNumberOfEventsPerStage = c(NA, 44, 44),
maxNumberOfEventsPerStage = 4 * c(NA, 44, 44),
maxNumberOfSubjects = 800, maxNumberOfIterations = 50
)
resultsWithSSRGS$overallReject
# Set seed to get reproducable results
identical(
getSimulationSurvival(
plannedEvents = 40, maxNumberOfSubjects = 200,
seed = 99
)$analysisTime,
getSimulationSurvival(
plannedEvents = 40, maxNumberOfSubjects = 200,
seed = 99
)$analysisTime
)
# Perform recalculation of number of events based on conditional power as above.
# The number of events is recalculated only in the first interim, the recalculated number
# is also used for the final stage. Here, we use the user defind calcEventsFunction as
# follows (note that the last stage value in minNumberOfEventsPerStage and maxNumberOfEventsPerStage
# has no effect):
myCalcEventsFunction < function(...,
stage, conditionalPower, estimatedTheta,
plannedEvents, eventsOverStages,
minNumberOfEventsPerStage, maxNumberOfEventsPerStage,
conditionalCriticalValue) {
theta < max(1 + 1e12, estimatedTheta)
if (stage == 2) {
requiredStageEvents <
max(0, conditionalCriticalValue + qnorm(conditionalPower))^2 / log(theta)^2
requiredStageEvents < min(
max(minNumberOfEventsPerStage[stage], requiredStageEvents),
maxNumberOfEventsPerStage[stage]
) + eventsOverStages[stage  1]
} else {
requiredStageEvents < 2 * eventsOverStages[stage  1]  eventsOverStages[1]
}
return(requiredStageEvents)
}
resultsWithSSR < getSimulationSurvival(
design = designIN,
hazardRatio = seq(1, 2.6, 0.5),
pi2 = 0.3,
conditionalPower = 0.8,
plannedEvents = c(58, 102, 146),
minNumberOfEventsPerStage = c(NA, 44, 4),
maxNumberOfEventsPerStage = 4 * c(NA, 44, 4),
maxNumberOfSubjects = 800,
calcEventsFunction = myCalcEventsFunction,
seed = 1234,
maxNumberOfIterations = 50
)
## End(Not run)