getDesignMeanDiffXOEquiv: Group Sequential Design for Equivalence in Mean Difference in...

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Group Sequential Design for Equivalence in Mean Difference in 2x2 Crossover

Description

Obtains the power given sample size or obtains the sample size given power for a group sequential design for equivalence in mean difference in 2x2 crossover.

Usage

getDesignMeanDiffXOEquiv(
  beta = NA_real_,
  n = NA_real_,
  meanDiffLower = NA_real_,
  meanDiffUpper = NA_real_,
  meanDiff = 0,
  stDev = 1,
  allocationRatioPlanned = 1,
  normalApproximation = TRUE,
  rounding = TRUE,
  kMax = 1L,
  informationRates = NA_real_,
  alpha = 0.05,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  spendingTime = NA_real_
)

Arguments

beta	The type II error.
n	The total sample size.
meanDiffLower	The lower equivalence limit of mean difference.
meanDiffUpper	The upper equivalence limit of mean difference.
meanDiff	The mean difference under the alternative hypothesis.
stDev	The standard deviation for within-subject random error.
allocationRatioPlanned	Allocation ratio for sequence A/B versus sequence B/A. Defaults to 1 for equal randomization.
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.

Value

An S3 class designMeanDiffXOEquiv 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.

  • 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.

  • meanDiffLower: The lower equivalence limit of mean difference.

  • meanDiffUpper: The upper equivalence limit of mean difference.

  • meanDiff: The mean difference under the alternative hypothesis.

  • stDev: The standard deviation for within-subject random error.

• 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 probability for efficacy stopping under H0.

  • efficacyMeanDiffLower: The efficacy boundaries on the mean difference scale for the one-sided null hypothesis on the lower equivalence limit.

  • efficacyMeanDiffUpper: The efficacy boundaries on the mean difference scale for the one-sided null hypothesis on the upper equivalence limit.

  • 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.

• 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.

  • allocationRatioPlanned: Allocation ratio for sequence A/B versus sequence B/A.

  • 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.

Author(s)

Kaifeng Lu, [e-mail]

Examples

# Example 1: group sequential trial power calculation
(design1 <- getDesignMeanDiffXOEquiv(
  beta = 0.1, n = NA, meanDiffLower = -1.3, meanDiffUpper = 1.3,
  meanDiff = 0, stDev = 2.2,
  kMax = 4, alpha = 0.05, typeAlphaSpending = "sfOF"))

# Example 2: sample size calculation for t-test
(design2 <- getDesignMeanDiffXOEquiv(
  beta = 0.1, n = NA, meanDiffLower = -1.3, meanDiffUpper = 1.3,
  meanDiff = 0, stDev = 2.2,
  normalApproximation = FALSE, alpha = 0.05))

lrstat documentation built on Oct. 18, 2024, 9:06 a.m.