nbsamplesizeequiv {lrstat}

Sample size for equivalence in negative binomial rate ratio

Description

Obtains the sample size for equivalence in negative binomial rate ratio.

Usage

nbsamplesizeequiv(
  beta = 0.2,
  kMax = 1L,
  informationRates = NA_real_,
  criticalValues = NA_real_,
  alpha = 0.05,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  rateRatioLower = NA_real_,
  rateRatioUpper = NA_real_,
  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,
  interval = as.numeric(c(0.001, 240)),
  spendingTime = NA_real_,
  rounding = 1L,
  nullVariance = 0L
)

Arguments

beta

The type II error.

kMax

The maximum number of stages.

informationRates

The information rates. 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.

rateRatioLower

The lower equivalence limit of rate ratio.

rateRatioUpper

The upper equivalence limit of rate ratio.

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.

interval

The interval to search for the solution of accrualDuration, followupDuration, or the proportionality constant of accrualIntensity. Defaults to c(0.001, 240).

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

An S3 class nbpowerequiv object

Author(s)

Kaifeng Lu, [e-mail]

See Also

nbpowerequiv

Examples

# Example 1: Variable follow-up design and solve for follow-up time
nbsamplesizeequiv(beta = 0.1, kMax = 2, informationRates = c(0.5, 1),
                  alpha = 0.05, typeAlphaSpending = "sfOF",
                  rateRatioLower = 2/3, rateRatioUpper = 3/2,
                  accrualIntensity = 1956/1.25,
                  stratumFraction = c(0.2, 0.8),
                  kappa1 = c(3, 5),
                  kappa2 = c(2, 3),
                  lambda1 = c(0.125, 0.165),
                  lambda2 = c(0.135, 0.175),
                  gamma1 = -log(1-0.05),
                  gamma2 = -log(1-0.10),
                  accrualDuration = 1.25,
                  followupTime = NA, fixedFollowup = FALSE,
                  nullVariance = 1)

# Example 2: Fixed follow-up design and solve for accrual duration
nbsamplesizeequiv(beta = 0.2, kMax = 2, informationRates = c(0.5, 1),
                  alpha = 0.05, typeAlphaSpending = "sfOF",
                  rateRatioLower = 0.5, rateRatioUpper = 2,
                  accrualIntensity = 220/1.5,
                  kappa1 = 3, kappa2 = 3,
                  lambda1 = 8.4, lambda2 = 8.4,
                  gamma1 = 0, gamma2 = 0,
                  accrualDuration = NA,
                  followupTime = 0.5, fixedFollowup = TRUE)