Sample Size for Negative Binomial Rate Ratio

Obtains the needed accrual duration given power and follow-up time, the needed follow-up time given power and accrual duration, or the needed absolute accrual rates given power, accrual duration, follow-up duration, and relative accrual rates in a two-group negative binomial design.

Usage

nbsamplesize(
  beta = 0.2,
  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_,
  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 = FALSE,
  spendingTime = NA_real_,
  rounding = TRUE,
  nullVariance = FALSE
)

Arguments

beta: Type II error. Defaults to 0.2.
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, "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.
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 \([3, \infty)\).
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.
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 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.
rounding: Whether to round up sample size. Defaults to 1 for sample size rounding.
nullVariance: Whether to calculate the variance for log rate ratio under the null hypothesis.

Value

A list of two components:

resultsUnderH1: An S3 class nbpower object under the alternative hypothesis.
resultsUnderH0: An S3 class nbpower object under the null hypothesis.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples