getDesignRiskDiffEquiv {lrstat}

Group sequential design for equivalence in two-sample risk difference

Description

Obtains the power given sample size or obtains the sample size given power for a group sequential design for equivalence in two-sample risk difference.

Usage

getDesignRiskDiffEquiv(
  beta = NA_real_,
  n = NA_real_,
  riskDiffLower = NA_real_,
  riskDiffUpper = NA_real_,
  pi1 = NA_real_,
  pi2 = NA_real_,
  nullVariance = FALSE,
  allocationRatioPlanned = 1,
  rounding = TRUE,
  kMax = 1L,
  informationRates = NA_real_,
  criticalValues = 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.

riskDiffLower

The lower equivalence limit of risk difference.

riskDiffUpper

The upper equivalence limit of risk difference.

pi1

The assumed probability for the active treatment group.

pi2

The assumed probability for the control group.

nullVariance

Whether to use the variance under the null or the empirical variance under the alternative.

allocationRatioPlanned

Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.

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.

criticalValues

Upper boundaries on the z-test statistic scale for stopping for efficacy.

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 designRiskDiffEquiv 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.

  • attainedAlphaH10: The attained significance level under H10.

  • attainedAlphaH20: The attained significance level under H20.

  • kMax: The number of stages.

  • information: The maximum information.

  • expectedInformationH1: The expected information under H1.

  • expectedInformationH10: The expected information under H10.

  • expectedInformationH20: The expected information under H20.

  • numberOfSubjects: The maximum number of subjects.

  • expectedNumberOfSubjectsH1: The expected number of subjects under H1.

  • expectedNumberOfSubjectsH10: The expected number of subjects under H10.

  • expectedNumberOfSubjectsH20: The expected number of subjects under H20.

  • riskDiffLower: The lower equivalence limit of risk difference.

  • riskDiffUpper: The upper equivalence limit of risk difference.

  • pi1: The assumed probability for the active treatment group.

  • pi2: The assumed probability for the control group.

  • riskDiff: The risk difference.

• 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.

  • cumulativeAttainedAlphaH10: The cumulative alpha attained under H10.

  • cumulativeAttainedAlphaH20: The cumulative alpha attained under H20.

  • efficacyP: The efficacy bounds on the p-value scale for each of the two one-sided tests.

  • information: The cumulative information.

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

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

  • 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.

  • nullVariance: Whether to use the variance under the null or the empirical variance under the alternative.

  • varianceRatioH10: The ratio of the variance under H10 to the variance under H1.

  • varianceRatioH20: The ratio of the variance under H20 to the variance under H1.

  • varianceRatioH12: The ratio of the variance under H10 to the variance under H20.

  • varianceRatioH21: The ratio of the variance under H20 to the variance under H10.

  • allocationRatioPlanned: Allocation ratio for the active treatment versus control.

  • rounding: Whether to round up sample size.

Author(s)

Kaifeng Lu, [e-mail]

Examples

(design1 <- getDesignRiskDiffEquiv(
  beta = 0.2, n = NA, riskDiffLower = -0.1,
  riskDiffUpper = 0.1, pi1 = 0.12, pi2 = 0.12,
  nullVariance = 1,
  kMax = 3, alpha = 0.05, typeAlphaSpending = "sfOF"))