nbpower {lrstat}

Power for negative binomial rate ratio

Description

Estimates the power for negative binomial rate ratio test.

Usage

nbpower(
  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_,
  rateRatioH0 = 1,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  kappa1 = NA_real_,
  kappa2 = NA_real_,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  followupTime = NA_real_,
  fixedFollowup = 0L,
  spendingTime = NA_real_,
  studyDuration = NA_real_,
  nullVariance = 0L
)

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".

rateRatioH0

Rate ratio under the null hypothesis.

allocationRatioPlanned

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

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, Inf).

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, Inf). Defaults to 0 for exponential distribution.

stratumFraction

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

kappa1

The dispersion parameter (reciprocal of the shape parameter of the gamma mixing distribution) for the active treatment group by stratum.

kappa2

The dispersion parameter (reciprocal of the shape parameter of the gamma mixing distribution) for the control group by stratum.

lambda1

The rate parameter of the negative binomial distribution for the active treatment group by stratum.

lambda2

The rate parameter of the negative binomial distribution for the control group by stratum.

gamma1

The hazard rate for exponential dropout, a vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for the active treatment group.

gamma2

The hazard rate for exponential dropout, a vector of hazard rates for piecewise exponential dropout applicable for all strata, or a vector of hazard rates for dropout in each analysis time interval by stratum for the control group.

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 0 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.

nullVariance

Whether to calculate the variance for log rate ratio under the null hypothesis.

Value

An S3 class nbpower object with 4 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.

  • rateRatioH0: The rate ratio under the null hypothesis.

  • rateRatio: The rate ratio.

• 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.

  • efficacyRateRatio: The efficacy boundaries on the rate ratio scale.

  • futilityRateRatio: The futility boundaries on the rate ratio 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, allocationRatioPlanned, accrualTime, accuralIntensity, piecewiseSurvivalTime, kappa1, kappa2, lambda1, lambda2, gamma1, gamma2, spendingTime, and nullVariance.

• byTreatmentCounts: A list containing the following counts by treatment group:

  • numberOfEvents1: The number of events by stage for the treatment group.

  • numberOfDropouts1: The number of dropouts by stage for the treatment group.

  • numberOfSubjects1: The number of subjects by stage for the treatment group.

  • exposure1: The exposure by stage for the treatment group.

  • numberOfEvents2: The number of events by stage for the control group.

  • numberOfDropouts2: The number of dropouts by stage for the control group.

  • numberOfSubjects2: The number of subjects by stage for the control group.

  • exposure2: The exposure by stage for the control group.

  • expectedNumberOfEvents1: The expected number of events for the treatment group.

  • expectedNumberOfDropouts1: The expected number of dropouts for the treatment group.

  • expectedNumberOfSubjects1: The expected number of subjects for the treatment group.

  • expectedExposure1: The expected exposure for the treatment group.

  • expectedNumberOfEvents2: The expected number of events for control group.

  • expectedNumberOfDropouts2: The expected number of dropouts for the control group.

  • expectedNumberOfSubjects2: The expected number of subjects for the control group.

  • expectedExposure2: The expected exposure for the control group.

Author(s)

Kaifeng Lu, [e-mail]

See Also

nbstat

Examples

# Example 1: Variable follow-up design

nbpower(kMax = 2, informationRates = c(0.5, 1),
        alpha = 0.025, typeAlphaSpending = "sfOF",
        accrualIntensity = 1956/1.25,
        stratumFraction = c(0.2, 0.8),
        kappa1 = 5, kappa2 = 5,
        lambda1 = c(0.7*0.125, 0.75*0.25),
        lambda2 = c(0.125, 0.25),
        gamma1 = 0, gamma2 = 0,
        accrualDuration = 1.25,
        followupTime = 2.75, fixedFollowup = FALSE,
        nullVariance = 1)

# Example 2: Fixed follow-up design

nbpower(kMax = 2, informationRates = c(0.5, 1),
        alpha = 0.025, typeAlphaSpending = "sfOF",
        accrualIntensity = 220/1.5,
        kappa1 = 3, kappa2 = 3,
        lambda1 = 0.5*8.4, lambda2 = 8.4,
        gamma1 = 0, gamma2 = 0,
        accrualDuration = 1.5,
        followupTime = 0.5, fixedFollowup = TRUE)