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.
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, numSubintervals = 300L, estimateHazardRatio = 1L, typeOfComputation = "direct", interval = as.numeric(c(0.001, 240)), spendingTime = NA_real_, rounding = 1L ) Type II error. Defaults to 0.2.
The maximum number of stages.
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.
Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.
Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.
Upper boundaries on the z-test statistic scale for stopping for efficacy.
The significance level. Defaults to 0.025.
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".
The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".
The user defined alpha spending. Cumulative alpha spent up to each stage.
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.
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".
The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".
The user defined beta spending. Cumulative beta spent up to each stage.
Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 for superiority test.
Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
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).
A vector of accrual intensities. One for each accrual time interval.
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.
A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.
A vector of hazard rates for the event in each analysis time interval by stratum for the active treatment group.
A vector of hazard rates for the event in each analysis time interval by stratum for the control group.
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.
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.
Duration of the enrollment period.
Follow-up time for the last enrolled subject.
Whether a fixed follow-up design is used. Defaults to 0 for variable follow-up.
The first parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
The second parameter of the Fleming-Harrington family of weighted log-rank test. Defaults to 0 for conventional log-rank test.
Number of sub-intervals to approximate the mean and variance of the weighted log-rank test score statistic. Defaults to 300. Specify a larger number for better approximation.
Whether to estimate the hazard ratio from weighted Cox regression model and report the stopping boundaries on the hazard ratio scale.
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.
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.
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 .
Whether to round up sample size and events. Defaults to 1 for sample size rounding.
A list of two components:
# 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), stratumFraction = c(0.2, 0.8), lambda1 = c(0.0533, 0.0309, 1.5*0.0533, 1.5*0.0309), lambda2 = c(0.0533, 0.0533, 1.5*0.0533, 1.5*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), stratumFraction = c(0.2, 0.8), lambda1 = c(0.0533, 0.0309, 1.5*0.0533, 1.5*0.0309), lambda2 = c(0.0533, 0.0533, 1.5*0.0533, 1.5*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), stratumFraction = c(0.2, 0.8), lambda1 = c(0.0533, 0.0309, 1.5*0.0533, 1.5*0.0309), lambda2 = c(0.0533, 0.0533, 1.5*0.0533, 1.5*0.0533), gamma1 = -log(1-0.05)/12, gamma2 = -log(1-0.05)/12, accrualDuration = 22, followupTime = 18, fixedFollowup = FALSE)