R: Power and sample size for a generic group sequential design

getDesign {lrstat}

R Documentation

Power and sample size for a generic group sequential design

Description

Obtains the maximum information and stopping boundaries for a generic group sequential design assuming a constant treatment effect, or obtains the power given the maximum information and stopping boundaries.

Usage

getDesign(
  beta = NA_real_,
  IMax = NA_real_,
  theta = NA_real_,
  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_,
  varianceRatio = 1
)

Arguments

`beta`	The type II error.
`IMax`	The maximum information. Either `beta` or `IMax` should be provided while the other one should be missing.
`theta`	The parameter value.
`kMax`	The maximum number of stages.
`informationRates`	The information rates. Fixed prior to the trial. Defaults to `(1:kMax) / kMax` if left unspecified.
`efficacyStopping`	Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.
`futilityStopping`	Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.
`criticalValues`	Upper boundaries on the z-test statistic scale for stopping for efficacy.
`alpha`	The significance level. Defaults to 0.025.
`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.
`futilityBounds`	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.
`typeBetaSpending`	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".
`parameterBetaSpending`	The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".
`userBetaSpending`	The user defined beta spending. Cumulative beta 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`.
`varianceRatio`	The ratio of the variance under H0 to the variance under H1.

Value

An S3 class design 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).
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.
- efficacyTheta: The efficacy boundaries on the parameter scale.
- futilityTheta: The futility boundaries on the parameter scale.
- 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.
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.
- varianceRatio: The ratio of the variance under H0 to the variance under H1.

Author(s)

Kaifeng Lu, kaifenglu@gmail.com

References

Christopher Jennison, Bruce W. Turnbull. Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC: Boca Raton, 2000, ISBN:0849303168

Examples


# Example 1: obtain the maximum information given power
(design1 <- getDesign(
  beta = 0.2, theta = -log(0.7),
  kMax = 2, informationRates = c(0.5,1),
  alpha = 0.025, typeAlphaSpending = "sfOF",
  typeBetaSpending = "sfP"))

# Example 2: obtain power given the maximum information
(design2 <- getDesign(
  IMax = 72.5, theta = -log(0.7),
  kMax = 3, informationRates = c(0.5, 0.75, 1),
  alpha = 0.025, typeAlphaSpending = "sfOF",
  typeBetaSpending = "sfP"))

[Package lrstat version 0.2.6 Index]