nbsamplesize: Sample Size for Negative Binomial Rate Ratio

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

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, [e-mail]

See Also

nbpower

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)

lrstat documentation built on Oct. 18, 2024, 9:06 a.m.