lrsamplesize: Log-Rank Test Sample Size

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 time, and relative accrual rates in a two-group survival design.

Usage

lrsamplesize(
  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_,
  hazardRatioH0 = 1,
  allocationRatioPlanned = 1,
  accrualTime = 0L,
  accrualIntensity = NA_real_,
  piecewiseSurvivalTime = 0L,
  stratumFraction = 1L,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  gamma1 = 0L,
  gamma2 = 0L,
  accrualDuration = NA_real_,
  followupTime = NA_real_,
  fixedFollowup = 0L,
  rho1 = 0,
  rho2 = 0,
  estimateHazardRatio = 1L,
  typeOfComputation = "direct",
  interval = as.numeric(c(0.001, 240)),
  spendingTime = NA_real_,
  rounding = 1L
)

Value

A list of two components:

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

Arguments

beta: Type II error. Defaults to 0.2.
kMax: The maximum number of stages.
informationRates: The information rates in terms of number of events for the conventional log-rank test and in terms of the actual information for weighted log-rank tests. 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.
hazardRatioH0: Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 for superiority test.
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.
lambda1: A vector of hazard rates for the event in each analysis time interval by stratum for the active treatment group.
lambda2: A vector of hazard rates for the event in each analysis time interval by stratum for the control group.
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.
rho1: The first parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
rho2: The second parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
estimateHazardRatio: Whether to estimate the hazard ratio from weighted Cox regression model and report the stopping boundaries on the hazard ratio scale.
typeOfComputation: The type of computation, either "direct" for the direct approximation method, or "schoenfeld" for the Schoenfeld method. Defaults to "direct". Can use "Schoenfeld" under proportional hazards and conventional log-rank test.
interval: The interval to search for the solution of accrualDuration, followupTime, or the proportionality constant of accrualIntensity. Defaults to c(0.001, 240). Adjustment may be needed for non-monotone relationship with study power.
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 and events. Defaults to 1 for sample size rounding.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

Run this code

# Piecewise accrual, piecewise exponential survival, and 5% dropout by
# the end of 1 year.

# Example 1: Obtains accrual duration given power and follow-up time

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = NA,
             followupTime = 18, fixedFollowup = FALSE)


# Example 2: Obtains follow-up time given power and accrual duration

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = 22,
             followupTime = NA, fixedFollowup = FALSE)


# Example 3: Obtains absolute accrual intensity given power,
# accrual duration, follow-up time, and relative accrual intensity

lrsamplesize(beta = 0.2, kMax = 2,
             informationRates = c(0.8, 1),
             alpha = 0.025, typeAlphaSpending = "sfOF",
             accrualTime = seq(0, 8),
             accrualIntensity = 26/9*seq(1, 9),
             piecewiseSurvivalTime = c(0, 6),
             lambda1 = c(0.0533, 0.0309),
             lambda2 = c(0.0533, 0.0533),
             gamma1 = -log(1-0.05)/12,
             gamma2 = -log(1-0.05)/12,
             accrualDuration = 22,
             followupTime = 18, fixedFollowup = FALSE)