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Log-Rank Test Simulation for MCPMod Design

Source: R/lrsim_mcpmod.R
lrsim_mcpmod.Rd

Simulate an MCPMod design using a Cox model. Analyses can be triggered either by the total number of events or by the pre-specified calendar time.

Usage

lrsim_mcpmod(
  M = 2,
  alpha = 0.05,
  hazardRatioH0s = 1,
  allocations = 1,
  accrualTime = 0,
  accrualIntensity = NA,
  piecewiseSurvivalTime = 0,
  stratumFraction = 1,
  lambdas = NULL,
  candidateHazardRatios = NULL,
  gammas = NULL,
  n = NA,
  followupTime = NA,
  fixedFollowup = FALSE,
  plannedEvents = NA,
  plannedTime = NA,
  maxNumberOfIterations = 1000,
  maxNumberOfRawDatasetsPerStage = 0,
  seed = 0,
  nthreads = 0
)

Arguments

M

Number of active treatment arms.

alpha

Significance level for the max test (1-sided).

hazardRatioH0s

Scalar or numeric vector of length \(M\). Hazard ratios under \(H_0\) for each active arm versus the common control. Defaults to 1 for superiority tests.

allocations

Integer or integer vector of length \(M + 1\). Number of subjects per arm within a randomization block.

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 \([3, \infty)\).

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 \([6, \infty)\). Defaults to 0 for exponential distribution.

stratumFraction

A vector of stratum fractions that sum to 1. Defaults to 1 for no stratification.

lambdas

List of length \(M + 1\) (one element per arm). Each element is a scalar or a numeric vector of event hazard rates for the corresponding arm.

candidateHazardRatios

Numeric matrix of dimension \(M \times T\) containing the candidate hazard ratios for the \(T\) candidate models.

gammas

List of length \(M + 1\) (one element per arm). Each element is a scalar or a numeric vector of dropout hazard rates for the corresponding arm.

n

Planned total sample size across all active arms and control.

followupTime

Follow-up time for the last enrolled subject.

fixedFollowup

Whether a fixed follow-up design is used. Defaults to FALSE for variable follow-up.

plannedEvents

Planned total number of events to trigger the analysis. Leave missing when using calendar-time planning.

plannedTime

Planned calendar time for the analysis. Leave missing when using event-based planning.

maxNumberOfIterations

Number of Monte Carlo replications.

maxNumberOfRawDatasetsPerStage

Number of subject-level raw datasets to retain.

seed

Random seed for reproducibility.

nthreads

Number of threads for parallel simulation. Use 0 to accept the default RcppParallel behavior.

Value

An S3 object of class "lrsim_mcpmod" with components overview, sumdata1, sumdata2, and optionally rawdata.

Examples

if (FALSE) { # \dontrun{
# Define candidate dose-response models
# (negative sign models decreasing dose-response for hazard)
f_emax <- function(d, ED50) { -d / (ED50 + d) }
f_exponential <- function(d, delta) { -exp(d / delta) + 1 }
f_linear <- function(d) { -d }
f_logistic <- function(d, ED50, delta) {
  -1 / (1 + exp((ED50 - d) / delta))
}
f_betamod <- function(d, delta1, delta2, D) {
  -dbeta(d / D, delta1 + 1, delta2 + 1)
}

# Log hazard parameters
b0 <- log(log(2) / 0.5)  # placebo: median survival 0.5 years
b1 <- log(0.6) + b0       # optimal dose: HR = 0.6 vs. placebo

# Rescale candidate models to match hazard rates
f1 <- function(dose) {
  a0 <- f_emax(0, 50); a1 <- f_emax(100, 50)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_emax(dose, 50)
}
f2 <- function(dose) {
  a0 <- f_exponential(0, 22.756); a1 <- f_exponential(100, 22.756)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_exponential(dose, 22.756)
}
f3 <- function(dose) {
  a0 <- f_emax(0, 6.25); a1 <- f_emax(100, 6.25)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_emax(dose, 6.25)
}
f4 <- function(dose) {
  a0 <- f_logistic(0, 40.3287, 6.9764)
  a1 <- f_logistic(100, 40.3287, 6.9764)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_logistic(dose, 40.3287, 6.9764)
}
f5 <- function(dose) {
  a0 <- f_linear(0); a1 <- f_linear(100)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_linear(dose)
}
f6 <- function(dose) {
  a0 <- f_betamod(0, 0.7489, 1.0485, 120)
  dstar <- 0.7489 * 120 / (0.7489 + 1.0485)
  a1 <- f_betamod(dstar, 0.7489, 1.0485, 120)
  slope <- (b1 - b0) / (a1 - a0)
  intercept <- b0 - slope * a0
  intercept + slope * f_betamod(dose, 0.7489, 1.0485, 120)
}

f <- list(f1, f2, f3, f4, f5, f6)
doselevels <- c(5, 25, 50, 100)

# Run the simulations (each candidate model is the true model in one scenario)
sims <- lapply(1:6, function(i) {
  lrsim_mcpmod(
    M = 4, alpha = 0.05, accrualIntensity = 360,
    lambdas = as.list(exp(f[[i]](c(doselevels, 0)))),
    candidateHazardRatios = exp(sapply(f, function(ff) ff(doselevels) - ff(0))),
    gammas = list(0, 0, 0, 0, 0),
    n = 300, plannedEvents = 242,
    maxNumberOfIterations = 1000,
    maxNumberOfRawDatasetsPerStage = 10,
    seed = 314159
  )
})

sapply(sims, function(s) s$overview$overallReject)
} # }