Performs simulation for two-endpoint three-arm group
sequential trials based on weighted log-rank test. The first
kMaxe1 looks are driven by the total number of PFS events in Arm A
and Arm C combined, and the subsequent looks are driven by the total
number of OS events in Arm A and Arm C combined. Alternatively,
the analyses can be planned to occur at specified calendar times.
lrsim2e3a(
kMax = NA_integer_,
kMaxe1 = NA_integer_,
hazardRatioH013e1 = 1,
hazardRatioH023e1 = 1,
hazardRatioH012e1 = 1,
hazardRatioH013e2 = 1,
hazardRatioH023e2 = 1,
hazardRatioH012e2 = 1,
allocation1 = 1L,
allocation2 = 1L,
allocation3 = 1L,
accrualTime = 0L,
accrualIntensity = NA_real_,
piecewiseSurvivalTime = 0L,
stratumFraction = 1L,
rho = 0,
lambda1e1 = NA_real_,
lambda2e1 = NA_real_,
lambda3e1 = NA_real_,
lambda1e2 = NA_real_,
lambda2e2 = NA_real_,
lambda3e2 = NA_real_,
gamma1e1 = 0L,
gamma2e1 = 0L,
gamma3e1 = 0L,
gamma1e2 = 0L,
gamma2e2 = 0L,
gamma3e2 = 0L,
accrualDuration = NA_real_,
followupTime = NA_real_,
fixedFollowup = 0L,
rho1 = 0,
rho2 = 0,
plannedEvents = NA_integer_,
plannedTime = NA_real_,
maxNumberOfIterations = 1000L,
maxNumberOfRawDatasetsPerStage = 0L,
seed = NA_integer_
)A list with 2 components:
sumdata: A data frame of summary data by iteration and stage:
iterationNumber: The iteration number.
eventsNotAchieved: Whether the target number of events
is not achieved for the iteration.
stageNumber: The stage number, covering all stages even if
the trial stops at an interim look.
analysisTime: The time for the stage since trial start.
accruals1: The number of subjects enrolled at the stage for
the active treatment 1 group.
accruals2: The number of subjects enrolled at the stage for
the active treatment 2 group.
accruals3: The number of subjects enrolled at the stage for
the control group.
totalAccruals: The total number of subjects enrolled at
the stage.
endpoint: The endpoint (1 or 2) under consideration.
events1: The number of events at the stage for
the active treatment 1 group.
events2: The number of events at the stage for
the active treatment 2 group.
events3: The number of events at the stage for
the control group.
totalEvents: The total number of events at the stage.
dropouts1: The number of dropouts at the stage for
the active treatment 1 group.
dropouts2: The number of dropouts at the stage for
the active treatment 2 group.
dropouts3: The number of dropouts at the stage for
the control group.
totalDropouts: The total number of dropouts at the stage.
logRankStatistic13: The log-rank test Z-statistic
comparing the active treatment 1 to the control for the endpoint.
logRankStatistic23: The log-rank test Z-statistic
comparing the active treatment 2 to the control for the endpoint.
logRankStatistic12: The log-rank test Z-statistic
comparing the active treatment 1 to the active treatment 2
for the endpoint.
rawdata (exists if maxNumberOfRawDatasetsPerStage is a
positive integer): A data frame for subject-level data for selected
replications, containing the following variables:
iterationNumber: The iteration number.
stageNumber: The stage under consideration.
analysisTime: The time for the stage since trial start.
subjectId: The subject ID.
arrivalTime: The enrollment time for the subject.
stratum: The stratum for the subject.
treatmentGroup: The treatment group (1, 2, or 3) for
the subject.
survivalTime1: The underlying survival time for
event endpoint 1 for the subject.
dropoutTime1: The underlying dropout time for
event endpoint 1 for the subject.
timeUnderObservation1: The time under observation
since randomization for event endpoint 1 for the subject.
event1: Whether the subject experienced event endpoint 1.
dropoutEvent1: Whether the subject dropped out for
endpoint 1.
survivalTime2: The underlying survival time for
event endpoint 2 for the subject.
dropoutTime2: The underlying dropout time for
event endpoint 2 for the subject.
timeUnderObservation2: The time under observation
since randomization for event endpoint 2 for the subject.
event2: Whether the subject experienced event endpoint 2.
dropoutEvent2: Whether the subject dropped out for
endpoint 2.
The maximum number of stages.
Number of stages with timing determined by PFS events.
Ranges from 0 (none) to kMax.
Hazard ratio under the null hypothesis for arm 1 vs arm 3 for endpoint 1 (PFS). Defaults to 1 for superiority test.
Hazard ratio under the null hypothesis for arm 2 vs arm 3 for endpoint 1 (PFS). Defaults to 1 for superiority test.
Hazard ratio under the null hypothesis for arm 1 vs arm 2 for endpoint 1 (PFS). Defaults to 1 for superiority test.
Hazard ratio under the null hypothesis for arm 1 vs arm 3 for endpoint 2 (OS). Defaults to 1 for superiority test.
Hazard ratio under the null hypothesis for arm 2 vs arm 3 for endpoint 2 (OS). Defaults to 1 for superiority test.
Hazard ratio under the null hypothesis for arm 1 vs arm 2 for endpoint 2 (OS). Defaults to 1 for superiority test.
Number of subjects in Arm A in a randomization block. Defaults to 1 for equal randomization.
Number of subjects in Arm B in a randomization block. Defaults to 1 for equal randomization.
Number of subjects in Arm C in a randomization block. Defaults to 1 for equal randomization.
A vector that specifies the starting time of
piecewise Poisson enrollment time intervals. Must start with 0, e.g.,
c(0, 3) breaks the time axis into 2 accrual intervals:
[0, 3) and [3, Inf).
A vector of accrual intensities. One for each accrual time interval.
A vector that specifies the starting time of
piecewise exponential survival time intervals. Must start with 0, e.g.,
c(0, 6) breaks the time axis into 2 event intervals:
[0, 6) and [6, Inf).
Defaults to 0 for exponential distribution.
A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.
The correlation coefficient for the standard bivariate normal random variables used to generate time to disease progression and time to death using the inverse CDF method.
A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and endpoint 1 (PFS).
A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and endpoint 1 (PFS).
A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and endpoint 1 (PFS).
A vector of hazard rates for the event in each analysis time interval by stratum for arm 1 and endpoint 2 (OS).
A vector of hazard rates for the event in each analysis time interval by stratum for arm 2 and endpoint 2 (OS).
A vector of hazard rates for the event in each analysis time interval by stratum for arm 3 and endpoint 2 (OS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 1 and endpoint 1 (PFS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 2 and endpoint 1 (PFS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 3 and endpoint 1 (PFS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 1 and endpoint 2 (OS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 2 and endpoint 2 (OS).
The hazard rate for exponential dropout. A vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for arm 3 and endpoint 2 (OS).
Duration of the enrollment period.
Follow-up time for the last enrolled subject.
Whether a fixed follow-up design is used. Defaults to 0 for variable follow-up.
The first parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
The second parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
The planned cumulative total number of PFS events at
Look 1 to Look kMaxe1 for Arms A and C combined and the planned
cumulative total number of OS events at Look kMaxe1+1 to Look
kMax for Arms A and C combined.
The calendar times for the analyses. To use calendar
time to plan the analyses, plannedEvents should be missing.
The number of simulation iterations. Defaults to 1000.
The number of raw datasets per stage to extract.
The seed to reproduce the simulation results. The seed from the environment will be used if left unspecified.
Kaifeng Lu, kaifenglu@gmail.com
sim1 = lrsim2e3a(
kMax = 3,
kMaxe1 = 2,
allocation1 = 2,
allocation2 = 2,
allocation3 = 1,
accrualTime = c(0, 8),
accrualIntensity = c(10, 28),
piecewiseSurvivalTime = 0,
rho = 0,
lambda1e1 = log(2)/12*0.60,
lambda2e1 = log(2)/12*0.70,
lambda3e1 = log(2)/12,
lambda1e2 = log(2)/30*0.65,
lambda2e2 = log(2)/30*0.75,
lambda3e2 = log(2)/30,
accrualDuration = 30.143,
plannedEvents = c(186, 259, 183),
maxNumberOfIterations = 500,
maxNumberOfRawDatasetsPerStage = 1,
seed = 314159)
head(sim1$sumdata)
head(sim1$rawdata)
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