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Power for One-Sample Negative Binomial Rate

Source: R/RcppExports.R
nbpower1s.Rd

Estimates the power, stopping probabilities, and expected sample size in a one-group negative binomial design.

Usage

nbpower1s(
  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_,
  lambdaH0 = NA_real_,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  kappa = NA_real_,
  lambda = NA_real_,
  gamma = 0L,
  accrualDuration = NA_real_,
  followupTime = NA_real_,
  fixedFollowup = FALSE,
  spendingTime = NA_real_,
  studyDuration = NA_real_
)

Arguments

kMax

The maximum number of stages.

informationRates

The information rates. 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, 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".

lambdaH0

The rate parameter of the negative binomial distribution under the null hypothesis.

accrualTime

A vector that specifies the starting time of piecewise Poisson enrollment time intervals. Must start with 0, e.g., c(0, 3) breaks the time axis into 2 accrual intervals: \([0, 3)\) and \([3, \infty)\).

accrualIntensity

A vector of accrual intensities. One for each accrual time interval.

piecewiseSurvivalTime

A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: \([0, 6)\) and \([6, \infty)\). Defaults to 0 for exponential distribution.

stratumFraction

A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.

kappa

The dispersion parameter (reciprocal of the shape parameter of the gamma mixing distribution) of the negative binomial distribution by stratum.

lambda

The rate parameter of the negative binomial distribution under the alternative hypothesis by stratum.

gamma

The hazard rate for exponential dropout or a vector of hazard rates for piecewise exponential dropout by stratum. Defaults to 0 for no dropout.

accrualDuration

Duration of the enrollment period.

followupTime

Follow-up time for the last enrolled subject.

fixedFollowup

Whether a fixed follow-up design is used. Defaults to FALSE for variable follow-up.

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.

studyDuration

Study duration for fixed follow-up design. Defaults to missing, which is to be replaced with the sum of accrualDuration and followupTime. If provided, the value is allowed to be less than the sum of accrualDuration and followupTime.

Value

An S3 class nbpower1s object with 3 components:

  • overallResults: A data frame containing the following variables:

    • overallReject: The overall rejection probability.

    • alpha: The overall significance level.

    • numberOfEvents: The total number of events.

    • numberOfDropouts: The total number of dropouts.

    • numbeOfSubjects: The total number of subjects.

    • exposure: The total exposure.

    • studyDuration: The total study duration.

    • information: The maximum information.

    • expectedNumberOfEvents: The expected number of events.

    • expectedNumberOfDropouts: The expected number of dropouts.

    • expectedNumberOfSubjects: The expected number of subjects.

    • expectedExposure: The expected exposure.

    • expectedStudyDuration: The expected study duration.

    • expectedInformation: The expected information.

    • accrualDuration: The accrual duration.

    • followupTime: The follow-up duration.

    • fixedFollowup: Whether a fixed follow-up design is used.

    • kMax: The number of stages.

    • lambdaH0: The rate parameter of the negative binomial distribution under the null hypothesis.

    • lambda: The overall rate parameter of the negative binomial distribution under the alternative hypothesis.

  • 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.

    • numberOfEvents: The number of events.

    • numberOfDropouts: The number of dropouts.

    • numberOfSubjects: The number of subjects.

    • exposure: The exposure.

    • analysisTime: The average time since trial start.

    • efficacyRate: The efficacy boundaries on the rate scale.

    • futilityRate: The futility boundaries on the rate 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.

  • settings: A list containing the following input parameters: typeAlphaSpending, parameterAlphaSpending, userAlphaSpending, typeBetaSpending, parameterBetaSpending, accrualTime, accuralIntensity, piecewiseSurvivalTime, stratumFraction, kappa, lambda, gamma, and spendingTime.

See also

nbstat

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

# Example 1: Variable follow-up design

nbpower1s(kMax = 2, informationRates = c(0.5, 1),
          alpha = 0.025, typeAlphaSpending = "sfOF",
          lambdaH0 = 0.125, accrualIntensity = 500,
          stratumFraction = c(0.2, 0.8),
          kappa = c(3, 5), lambda = c(0.0875, 0.085),
          gamma = 0, accrualDuration = 1.25,
          followupTime = 2.75, fixedFollowup = FALSE)
#>                                                                             
#> Group-sequential design with 2 stages for one-sample negative binomial rate 
#> Rate under H0: 0.125, rate under H1: 0.0855                                 
#> Stratum fraction: 0.2 0.8, event rate: 0.0875 0.085, dispersion: 3 5        
#> Overall power: 0.9152, overall significance level (1-sided): 0.025          
#> Maximum # events: 180.4, expected # events: 146.3                           
#> Maximum # dropouts: 0, expected # dropouts: 0                               
#> Maximum # subjects: 625, expected # subjects: 625                           
#> Maximum exposure: 2109.4, expected exposure: 1711                           
#> Maximum information: 77.27, expected information: 66.69                     
#> Total study duration: 4, expected study duration: 3.4                       
#> Accrual duration: 1.2, follow-up duration: 2.8, fixed follow-up: FALSE      
#> Alpha spending: Lan-DeMets O'Brien-Fleming, beta spending: None             
#>                                                                             
#>                          Stage 1 Stage 2
#> Information rate         0.500   1.000  
#> Efficacy boundary (Z)    2.963   1.969  
#> Cumulative rejection     0.2738  0.9152 
#> Cumulative alpha spent   0.0015  0.0250 
#> Number of events         55.9    180.4  
#> Number of dropouts       0.0     0.0    
#> Number of subjects       625.0   625.0  
#> Exposure                 654.2   2109.4 
#> Analysis time            1.7     4.0    
#> Efficacy boundary (rate) 0.0776  0.0999 
#> Efficacy boundary (p)    0.0015  0.0245 
#> Information              38.63   77.27  

# Example 2: Fixed follow-up design

nbpower1s(kMax = 2, informationRates = c(0.5, 1),
          alpha = 0.025, typeAlphaSpending = "sfOF",
          lambdaH0 = 8.4, accrualIntensity = 40,
          kappa = 3, lambda = 0.5*8.4,
          gamma = 0, accrualDuration = 1.5,
          followupTime = 0.5, fixedFollowup = TRUE)
#>                                                                             
#> Group-sequential design with 2 stages for one-sample negative binomial rate 
#> Rate under H0: 8.4, rate under H1: 4.2                                      
#> Dispersion: 3                                                               
#> Overall power: 0.8198, overall significance level (1-sided): 0.025          
#> Maximum # events: 126, expected # events: 112.7                             
#> Maximum # dropouts: 0, expected # dropouts: 0                               
#> Maximum # subjects: 60, expected # subjects: 55.4                           
#> Maximum exposure: 30, expected exposure: 26.8                               
#> Maximum information: 17.26, expected information: 15.73                     
#> Total study duration: 2, expected study duration: 1.8                       
#> Accrual duration: 1.5, follow-up duration: 0.5, fixed follow-up: TRUE       
#> Alpha spending: Lan-DeMets O'Brien-Fleming, beta spending: None             
#>                                                                             
#>                          Stage 1 Stage 2
#> Information rate         0.500   1.000  
#> Efficacy boundary (Z)    2.963   1.969  
#> Cumulative rejection     0.1771  0.8198 
#> Cumulative alpha spent   0.0015  0.0250 
#> Number of events         50.7    126.0  
#> Number of dropouts       0.0     0.0    
#> Number of subjects       34.1    60.0   
#> Exposure                 12.1    30.0   
#> Analysis time            0.9     2.0    
#> Efficacy boundary (rate) 3.0641  5.2299 
#> Efficacy boundary (p)    0.0015  0.0245 
#> Information              8.63    17.26