getDesignPairedMeanRatioEquiv: Group Sequential Design for Equivalence in Paired Mean Ratio

Description

Obtains the power given sample size or obtains the sample size given power for a group sequential design for equivalence in paired mean ratio.

Usage

getDesignPairedMeanRatioEquiv(
  beta = NA_real_,
  n = NA_real_,
  pairedRatioLower = NA_real_,
  pairedRatioUpper = NA_real_,
  pairedRatio = 1,
  CV = 1,
  normalApproximation = TRUE,
  rounding = TRUE,
  kMax = 1L,
  informationRates = NA_real_,
  alpha = 0.05,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  spendingTime = NA_real_
)

Value

An S3 class designPairedMeanRatioEquiv object with three components:

overallResults: A data frame containing the following variables:
- overallReject: The overall rejection probability.
- alpha: The significance level for each of the two one-sided tests. Defaults to 0.05.
- attainedAlpha: The attained significance level under H0.
- kMax: The number of stages.
- information: The maximum information.
- expectedInformationH1: The expected information under H1.
- expectedInformationH0: The expected information under H0.
- numberOfSubjects: The maximum number of subjects.
- expectedNumberOfSubjectsH1: The expected number of subjects under H1.
- expectedNumberOfSubjectsH0: The expected number of subjects under H0.
- pairedRatioLower: The lower equivalence limit of paired ratio.
- pairedRatioUpper: The upper equivalence limit of paired ratio.
- pairedRatio: The paired ratio under the alternative hypothesis.
- CV: The coefficient of variation for paired ratios.
byStageResults: A data frame containing the following variables:
- informationRates: The information rates.
- efficacyBounds: The efficacy boundaries on the Z-scale for each of the two one-sided tests.
- rejectPerStage: The probability for efficacy stopping.
- cumulativeRejection: The cumulative probability for efficacy stopping.
- cumulativeAlphaSpent: The cumulative alpha for each of the two one-sided tests.
- cumulativeAttainedAlpha: The cumulative alpha attained under H0.
- efficacyP: The efficacy bounds on the p-value scale for each of the two one-sided tests.
- information: The cumulative information.
- numberOfSubjects: The number of subjects.
- efficacyPairedRatioLower: The efficacy boundaries on the paired ratio scale for the one-sided null hypothesis on the lower equivalence limit.
- efficacyPairedRatioUpper: The efficacy boundaries on the paired ratio scale for the one-sided null hypothesis on the upper equivalence limit.
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.
- spendingTime: The error spending time at each analysis.
- 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. The exact calculation using the t distribution is only implemented for the fixed design.
- rounding: Whether to round up sample size.

Arguments

beta: The type II error.
n: The total sample size.
pairedRatioLower: The lower equivalence limit of paired ratio.
pairedRatioUpper: The upper equivalence limit of paired ratio.
pairedRatio: The paired ratio under the alternative hypothesis.
CV: The coefficient of variation for paired ratio.
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. The exact calculation using the t distribution is only implemented for the fixed design.
rounding: Whether to round up sample size. Defaults to 1 for sample size rounding.
kMax: The maximum number of stages.
informationRates: The information rates. Fixed prior to the trial. Defaults to (1:kMax) / kMax if left unspecified.
alpha: The significance level for each of the two one-sided tests. Defaults to 0.05.
typeAlphaSpending: 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".
parameterAlphaSpending: The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".
userAlphaSpending: The user defined alpha spending. Cumulative alpha spent up to each stage.
spendingTime: 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.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

Run this code


# Example 1: group sequential trial power calculation
(design1 <- getDesignPairedMeanRatioEquiv(
  beta = 0.1, n = NA, pairedRatioLower = 0.8, pairedRatioUpper = 1.25,
  pairedRatio = 1, CV = 0.35,
  kMax = 4, alpha = 0.05, typeAlphaSpending = "sfOF"))

# Example 2: sample size calculation for t-test
(design2 <- getDesignPairedMeanRatioEquiv(
  beta = 0.1, n = NA, pairedRatioLower = 0.8, pairedRatioUpper = 1.25,
  pairedRatio = 1, CV = 0.35,
  normalApproximation = FALSE, alpha = 0.05))

Run the code above in your browser using DataLab