Obtains the power and sample size for two-sample mean difference at the last time point from the mixed-model for repeated measures (MMRM) model.
getDesignMeanDiffMMRM(
beta = NA_real_,
meanDiffH0 = 0,
meanDiff = 0.5,
k = 1,
t = NA_real_,
covar1 = diag(k),
covar2 = NA_real_,
accrualTime = 0,
accrualIntensity = NA_real_,
piecewiseSurvivalTime = 0,
gamma1 = 0,
gamma2 = 0,
accrualDuration = NA_real_,
allocationRatioPlanned = 1,
normalApproximation = TRUE,
rounding = TRUE,
kMax = 1L,
informationRates = NA_real_,
efficacyStopping = NA_integer_,
futilityStopping = NA_integer_,
criticalValues = NA_real_,
alpha = 0.025,
typeAlphaSpending = "sfOF",
parameterAlphaSpending = NA_real_,
userAlphaSpending = NA_real_,
futilityBounds = NA_real_,
typeBetaSpending = "none",
parameterBetaSpending = NA_real_,
userBetaSpending = NA_real_,
spendingTime = NA_real_
)An S3 class designMeanDiffMMRM object with three
components:
overallResults: A data frame containing the following variables:
overallReject: The overall rejection probability.
alpha: The overall significance level.
attainedAlpha: The attained significance level, which is
different from the overall significance level in the presence of
futility stopping.
kMax: The number of stages.
theta: The parameter value.
information: The maximum information.
expectedInformationH1: The expected information under H1.
expectedInformationH0: The expected information under H0.
drift: The drift parameter, equal to
theta*sqrt(information).
inflationFactor: The inflation factor (relative to the
fixed design).
numberOfSubjects: The maximum number of subjects.
studyDuration: The maximum study duration.
expectedNumberOfSubjectsH1: The expected number of subjects
under H1.
expectedNumberOfSubjectsH0: The expected number of subjects
under H0.
expectedStudyDurationH1: The expected study duration
under H1.
expectedStudyDurationH0: The expected study duration
under H0.
accrualDuration: The accrual duration.
followupTime: The follow-up time.
fixedFollowup: Whether a fixed follow-up design is used.
meanDiffH0: The mean difference under H0.
meanDiff: The mean difference under H1.
byStageResults: A data frame containing the following variables:
informationRates: The information rates.
efficacyBounds: The efficacy boundaries on the Z-scale.
futilityBounds: The futility boundaries on the Z-scale.
rejectPerStage: The probability for efficacy stopping.
futilityPerStage: The probability for futility stopping.
cumulativeRejection: The cumulative probability for efficacy
stopping.
cumulativeFutility: The cumulative probability for futility
stopping.
cumulativeAlphaSpent: The cumulative alpha spent.
efficacyP: The efficacy boundaries on the p-value scale.
futilityP: The futility boundaries on the p-value scale.
information: The cumulative information.
efficacyStopping: Whether to allow efficacy stopping.
futilityStopping: Whether to allow futility stopping.
rejectPerStageH0: The probability for efficacy stopping
under H0.
futilityPerStageH0: The probability for futility stopping
under H0.
cumulativeRejectionH0: The cumulative probability for
efficacy stopping under H0.
cumulativeFutilityH0: The cumulative probability for futility
stopping under H0.
efficacyMeanDiff: The efficacy boundaries on the mean
difference scale.
futilityMeanDiff: The futility boundaries on the mean
difference scale.
numberOfSubjects: The number of subjects.
analysisTime: The average time since trial start.
settings: A list containing the following input parameters:
typeAlphaSpending: The type of alpha spending.
parameterAlphaSpending: The parameter value for alpha
spending.
userAlphaSpending: The user defined alpha spending.
typeBetaSpending: The type of beta spending.
parameterBetaSpending: The parameter value for beta spending.
userBetaSpending: The user defined beta spending.
spendingTime: The error spending time at each analysis.
allocationRatioPlanned: The allocation ratio for the active
treatment versus control.
accrualTime: A vector that specifies the starting time of
piecewise Poisson enrollment time intervals.
accrualIntensity: A vector of accrual intensities.
One for each accrual time interval.
piecewiseSurvivalTime: A vector that specifies the
starting time of piecewise exponential survival time intervals.
gamma1: The hazard rate for exponential dropout or
a vector of hazard rates for piecewise exponential dropout
for the active treatment group.
gamma2: The hazard rate for exponential dropout or
a vector of hazard rates for piecewise exponential dropout
for the control group.
k: The number of postbaseline time points.
t: The postbaseline time points.
covar1: The covariance matrix for the repeated measures
given baseline for the active treatment group.
covar2: The covariance matrix for the repeated measures
given baseline for the control group.
normalApproximation: The type of computation of the p-values.
If TRUE, the variance is assumed to be known, otherwise
the calculations are performed with the t distribution.
rounding: Whether to round up sample size.
The type II error.
The mean difference at the last time point under the null hypothesis. Defaults to 0.
The mean difference at the last time point under the alternative hypothesis.
The number of postbaseline time points.
The postbaseline time points.
The covariance matrix for the repeated measures given baseline for the active treatment group.
The covariance matrix for the repeated measures given baseline for the control group. If missing, it will be set equal to the covariance matrix for the active treatment group.
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.
The hazard rate for exponential dropout, or a vector of hazard rates for piecewise exponential dropout for the active treatment group.
The hazard rate for exponential dropout, or a vector of hazard rates for piecewise exponential dropout for the control group.
Duration of the enrollment period.
Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
The type of computation of the p-values.
If TRUE, the variance is assumed to be known, otherwise
the calculations are performed with the t distribution. The
degrees of freedom for the t-distribution is the total effective
sample size minus 2. The exact calculation using the t distribution
is only implemented for the fixed design.
Whether to round up sample size. Defaults to 1 for sample size rounding.
The maximum number of stages.
The information rates. Defaults to
(1:kMax) / kMax if left unspecified.
Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.
Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.
Upper boundaries on the z-test statistic scale for stopping for efficacy.
The significance level. Defaults to 0.025.
The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".
The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".
The user defined alpha spending. Cumulative alpha spent up to each stage.
Lower boundaries on the z-test statistic scale
for stopping for futility at stages 1, ..., kMax-1. Defaults to
rep(-6, kMax-1) if left unspecified. The futility bounds are
non-binding for the calculation of critical values.
The type of beta spending. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early futility stopping. Defaults to "none".
The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".
The user defined beta spending. Cumulative beta spent up to each stage.
A vector of length kMax for the error spending
time at each analysis. Defaults to missing, in which case, it is the
same as informationRates.
Kaifeng Lu, kaifenglu@gmail.com
# function to generate the AR(1) correlation matrix
ar1_cor <- function(n, corr) {
exponent <- abs(matrix((1:n) - 1, n, n, byrow = TRUE) - ((1:n) - 1))
corr^exponent
}
(design1 = getDesignMeanDiffMMRM(
beta = 0.2,
meanDiffH0 = 0,
meanDiff = 0.5,
k = 4,
t = c(1,2,3,4),
covar1 = ar1_cor(4, 0.7),
accrualIntensity = 10,
gamma1 = 0.02634013,
gamma2 = 0.02634013,
accrualDuration = NA,
allocationRatioPlanned = 1,
kMax = 3,
alpha = 0.025,
typeAlphaSpending = "sfOF"))
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