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Group Sequential Design for Equivalence in Two-Sample Risk Ratio

Source: R/getDesignProportions.R
getDesignRiskRatioEquiv.Rd

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

Usage

getDesignRiskRatioEquiv(
  beta = NA_real_,
  n = NA_real_,
  riskRatioLower = NA_real_,
  riskRatioUpper = NA_real_,
  pi1 = NA_real_,
  pi2 = NA_real_,
  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.

riskRatioLower

The lower equivalence limit of risk ratio.

riskRatioUpper

The upper equivalence limit of risk ratio.

pi1

The assumed probability for the active treatment group.

pi2

The assumed probability for the control group.

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 designRiskRatioEquiv 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.

    • riskRatioLower: The lower equivalence limit of risk ratio.

    • riskRatioUpper: The upper equivalence limit of risk ratio.

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

    • pi2: The assumed probability for the control group.

    • riskRatio: The risk ratio.

  • 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.

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

    • efficacyRiskRatioUpper: The efficacy boundaries on the risk ratio 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 the active treatment versus control.

    • rounding: Whether to round up sample size.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


(design1 <- getDesignRiskRatioEquiv(
  beta = 0.2, n = NA, riskRatioLower = 0.8,
  riskRatioUpper = 1.25, pi1 = 0.12, pi2 = 0.12,
  kMax = 3, alpha = 0.05, typeAlphaSpending = "sfOF"))
#>                                                                                          
#> Group-sequential design with 3 stages for equivalence in two-sample risk ratio           
#> Lower limit for risk ratio: 0.8, upper limit for risk ratio: 1.25                        
#> Proportion on treatment: 0.12, proportion on control: 0.12, risk ratio: 1                
#> Overall power: 0.8, overall alpha: 0.05, attained under H10: 0.05, under H20: 0.05       
#> Max information: 175.23, expected under H1: 162.63, under H10: 174.48, under H20: 174.48 
#> Max # subjects: 5140, expected under H1: 4770.6, under H10: 5118.2, under H20: 5118.2    
#> Allocation ratio: 1, variance of standardized test statistic:                            
#> Alpha spending: Lan-DeMets O'Brien-Fleming                                               
#>                                                                                          
#>                                        Stage 1 Stage 2 Stage 3
#> Information rate                       0.333   0.667   1.000  
#> Boundary for each 1-sided test (Z)     3.200   2.141   1.695  
#> Cumulative rejection                   0.0000  0.2157  0.8000 
#> Cumulative alpha for each 1-sided test 0.0007  0.0164  0.0500 
#> Cumulative alpha attained under H10    0.0000  0.0127  0.0500 
#> Cumulative alpha attained under H20    -0.0000 0.0127  0.0500 
#> Number of subjects                     1713.0  3427.0  5140.0 
#> Boundary for lower limit (risk ratio)  1.216   0.975   0.909  
#> Boundary for upper limit (risk ratio)  0.822   1.025   1.100  
#> Boundary for each 1-sided test (p)     0.0007  0.0161  0.0451 
#> Information                            58.40   116.83  175.23