nbstat1: Negative Binomial Rate Ratio by Stratum

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

Negative Binomial Rate Ratio by Stratum

Description

Obtains the number of subjects accrued, number of events, number of dropouts, number of subjects reaching the maximum follow-up, total exposure, rate and variance for log rate in each group, rate ratio and variance for log rate ratio by stratum at a given calendar time.

Usage

nbstat1(
  time = 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,
  nullVariance = 0L
)

Arguments

time	The calendar time for data cut.
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.
nullVariance	Whether to calculate the variance for log rate ratio under the null hypothesis.

Value

A list with two components:

• resultsUnderH1: A data frame containing the following variables:

  • stratum: The stratum.

  • time: The calendar time since trial start.

  • subjects: The number of enrolled subjects.

  • nevents: The total number of events.

  • nevents1: The number of events in the active treatment group.

  • nevents2: The number of events in the control group.

  • ndropouts: The total number of dropouts.

  • ndropouts1: The number of dropouts in the active treatment group.

  • ndropouts2: The number of dropouts in the control group.

  • nfmax: The total number of subjects reaching maximum follow-up.

  • nfmax1: The number of subjects reaching maximum follow-up in the active treatment group.

  • nfmax2: The number of subjects reaching maximum follow-up in the control group.

  • exposure: The total exposure time.

  • exposure1: The exposure time for the active treatment group.

  • exposure2: The exposure time for the control group.

  • rateRatio: The rate ratio of the active treatment group versus the control group.

  • vlogRate1: The variance for the log rate parameter for the active treatment group.

  • vlogRate2: The variance for the log rate parameter for the control group.

  • vlogRR: The variance of log rate ratio.

• resultsUnderH0 when nullVariance = TRUE: A data frame with the following variables:

  • stratum: The stratum.

  • time: The analysis time since trial start.

  • lambda1H0: The restricted maximum likelihood estimate of the event rate for the active treatment group.

  • lambda2H0: The restricted maximum likelihood estimate of the event rate for the control group.

  • rateRatioH0: The rate ratio under H0.

  • vlogRate1H0: The variance for the log rate parameter for the active treatment group under H0.

  • vlogRate2H0: The variance for the log rate parameter for the control group under H0.

  • vlogRRH0: The variance of log rate ratio under H0.

  • lambda1: The true event rate for the active treatment group.

  • lambda2: The true event rate for the control group.

  • rateRatio: The true rate ratio.

• resultsUnderH0 when nullVariance = FALSE: A data frame with the following variables:

  • stratum: The stratum.

  • time: The analysis time since trial start.

  • rateRatioH0: The rate ratio under H0.

  • lambda1: The true event rate for the active treatment group.

  • lambda2: The true event rate for the control group.

  • rateRatio: The true rate ratio.

Author(s)

Kaifeng Lu, [e-mail]

Examples

# Example 1: Variable follow-up design

nbstat1(time = 2,
       accrualIntensity = 1956/1.25,
       kappa1 = 5,
       kappa2 = 5,
       lambda1 = 0.7*0.125,
       lambda2 = 0.125,
       gamma1 = 0,
       gamma2 = 0,
       accrualDuration = 1.25,
       followupTime = 2.75)

# Example 2: Fixed follow-up design

nbstat1(time = 1.8,
       accrualIntensity = 220/1.5,
       stratumFraction = c(0.2, 0.8),
       kappa1 = 3,
       kappa2 = 3,
       lambda1 = c(0.5*8.4, 0.7*10.2),
       lambda2 = c(8.4, 10.2),
       gamma1 = 0.05,
       gamma2 = 0.05,
       accrualDuration = 1.5,
       followupTime = 0.5,
       fixedFollowup = 1,
       nullVariance = 1)

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