R: Sample size for negative binomial rate ratio

nbsamplesize {lrstat}

R Documentation

Sample size for negative binomial rate ratio

Description

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 = 0L,
  interval = as.numeric(c(0.001, 240)),
  spendingTime = NA_real_,
  rounding = 1L,
  nullVariance = 0L
)

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, 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

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(s)

Kaifeng Lu, kaifenglu@gmail.com

Examples

# Example 1: Obtains follow-up duration given power, accrual intensity,
# and accrual duration for variable follow-up

nbsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.5, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualIntensity = 1956/1.25,
             kappa1 = 5, kappa2 = 5,
             lambda1 = 0.0875, lambda2 = 0.125,
             gamma1 = 0, gamma2 = 0,
             accrualDuration = 1.25,
             followupTime = NA, fixedFollowup = FALSE)

# Example 2: Obtains accrual intensity given power, accrual duration, and
# follow-up duration for variable follow-up

nbsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.5, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualIntensity = 100,
             kappa1 = 5, kappa2 = 5,
             lambda1 = 0.0875, lambda2 = 0.125,
             gamma1 = 0, gamma2 = 0,
             accrualDuration = 1.25,
             followupTime = 2.25, fixedFollowup = FALSE)


# Example 3: Obtains accrual duration given power, accrual intensity, and
# follow-up duration for fixed follow-up

nbsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.5, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualIntensity = 1667,
             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 = NA,
             followupTime = 0.5, fixedFollowup = TRUE)

[Package lrstat version 0.2.5 Index]