Rolling continual reassessment method (CRM) for dose escalation

Examples

This vignette demonstrates how to implement a rolling continual reassessment method (CRM) for dose escalation using the crmPack package. This design is attractive when reducing the trial duration is a priority, as it allows enrolling new patients before the outcomes of previously enrolled patients are fully observed.

Author

Jiawen Zhu, Daniel Sabanés Bové

Published

February 13, 2026

Please note that for understanding this vignette easily, it is recommended to first read the methodology paper introducing the rolling CRM design. (Zhu et al. 2021)

Example 1: Recommend a dose for the next cohort

Setting up the data

library(crmPack)
data <- DataDA(
  x = c(0.1, 0.5, 1.5, 3, 6, 10, 10, 10),
  y = c(0, 0, 1, 1, 0, 0, 1, 0),
  ID = as.integer(1:8),
  cohort = as.integer(c(1, 2, 3, 4, 5, 6, 6, 6)),
  doseGrid =
    c(
      0.1, 0.5, 1.5, 3, 6,
      seq(from = 10, to = 80, by = 2)
    ),
  u = c(42, 30, 15, 5, 20, 25, 30, 60),
  t0 = rep(0, 8),
  Tmax = 60
)

emptydata <- DataDA(
  doseGrid = c(
    0.1, 0.5, 1, 1.5, 3, 6,
    seq(from = 10, to = 80, by = 2)
  ),
  Tmax = 60
)

Structure of the model class

npiece_ <- 10
Tmax_ <- 60

lambda_prior <- function(k) {
  npiece_ / (Tmax_ * (npiece_ - k + 0.5))
}

model <- DALogisticLogNormal(
  mean = c(-0.85, 1),
  cov = matrix(c(1, -0.5, -0.5, 1), nrow = 2),
  ref_dose = 56,
  npiece = npiece_,
  l = as.numeric(t(apply(as.matrix(c(1:npiece_), 1, npiece_), 2, lambda_prior))),
  c_par = 2
)

Obtain the posterior

options <- McmcOptions(
  burnin = 10,
  step = 2,
  samples = 1e2
)

set.seed(94)
samples <- mcmc(data, model, options)

Use ggmcmc to diagnose

library(ggmcmc)
alpha0samples <- get(samples, "alpha0")

print(ggs_traceplot(alpha0samples))

A trace plot for alpha0. It looks like skyscrapers ina big city, but there are only just over 200 samples in the chain.

print(ggs_autocorrelation(alpha0samples))

An auto correlation plot for aplha0. There is significant auto-correlation of 0.25 or more even at lags of 50. There is seasonality too, with three groups of negative auto-correlation and four of positive.

Plot the model fit

plot(samples, model, data, hazard = TRUE)

Two plots in a single row. The first shows the posterior mean and ci for the probability of toxicity by dose. The second shows 100 times the posterior hazard by time.

plot(samples, model, data, hazard = FALSE)

Two plots in a single row. Both show the posterior mean and ci for the probability of toxicity by dose on the y axis. In the first plot, the x axis is dose. In the second, it is time.

prior mean curve

emptydata <- DataDA(doseGrid = c(
  0.1, 0.5, 1.5, 3, 6,
  seq(from = 10, to = 80, by = 2)
), Tmax = 60)

Priorsamples <- mcmc(emptydata, model, options)

plot(Priorsamples, model, emptydata, hazard = FALSE)

Two plots in a single row. Both show the prior mean and ci for the probability of toxicity by dose on the y axis. In the first plot, the x axis is dose. In the second, it is time.

Escalation rules

Need to fill in (use the same rule in the section 8 of “using the package crmPack: introductory examples”)

myIncrements <- IncrementsRelative(
  intervals = c(0, 20),
  increments = c(1, 0.33)
)

nextMaxDose <- maxDose(myIncrements, data = data)

myNextBest <- NextBestNCRM(
  target = c(0.2, 0.35),
  overdose = c(0.35, 1),
  max_overdose_prob = 0.25
)

mySize1 <- CohortSizeRange(intervals = c(0, 30), cohort_size = c(1, 3))
mySize2 <- CohortSizeDLT(intervals = c(0, 1), cohort_size = c(1, 3))
mySize <- maxSize(mySize1, mySize2)

myStopping1 <- StoppingTargetProb(target = c(0.2, 0.35), prob = 0.5)
myStopping2 <- StoppingMinPatients(nPatients = 50)
myStopping <- (myStopping1 | myStopping2)

Recommended dose for the next cohort

doseRecommendation <- nextBest(myNextBest,
  doselimit = nextMaxDose,
  samples = samples,
  model = model,
  data = data
)

doseRecommendation$plot

Two graphs arranged in a single column. The upper graph shoes green lines of various heights that show the probability each dose is in the target toxicity range. There is a big arrow pointing to the bar at a dose of 0.5, that this is the recommended dose for the next cohort. The bars for other doses are higher, but they are not eligible for dosing because of the overdose rule illustrated in the second graph below. The lower graph as a similar series of red lines, indicating the probability that each dose is in the overdose range. There is a horizontal black dashed line at 25%, indicating that this is the highest acceptable probability of being in the overdose range. The red bars for doses above 0.5 all extend above 25%, indicating that their toxicity is unacceptable. The toxicity for doses of 0.1 and 0.5 lie below 25%.

doseRecommendation$value
#> [1] 3

Example 2: Run a simulation to evaluate operating characteristics

Set up safety window and `DADesign` to be completed

mysafetywindow <- SafetyWindowConst(c(6, 2), 7, 7)

design <- DADesign(
  model = model,
  increments = myIncrements,
  nextBest = myNextBest,
  stopping = myStopping,
  cohort_size = mySize,
  data = emptydata,
  safetyWindow = mysafetywindow,
  startingDose = 3
)

Set up true curves

myTruth <- probFunction(model, alpha0 = 2, alpha1 = 3)
curve(myTruth(x), from = 0, to = 100, ylim = c(0, 1))

A logistic dose response curverising from 0 at dose 0 to almost 100% for a dose of 100.


onset <- 15
exp_cond.cdf <- function(x) {
  1 - (pexp(x, 1 / onset, lower.tail = FALSE) - pexp(28, 1 / onset, lower.tail = FALSE)) / pexp(28, 1 / onset)
}

Perform the simulations

mySims <- simulate(design,
  args = NULL,
  truthTox = myTruth,
  truthSurv = exp_cond.cdf,
  trueTmax = 80,
  nsim = 2,
  seed = 819,
  mcmcOptions = options,
  firstSeparate = TRUE,
  deescalate = FALSE,
  parallel = FALSE
)

Interpret the simulation results

Use a similar way as section 9.2 in the “using the package crmPack: introductory examples” document

a <- summary(mySims, truth = myTruth)
b <- mySims@data[[1]]

plot(mySims)
plot(b)

Two graphs in a single column, summarising the results of a single simulated trial. The upper one plots patient number on the x axis and dose andministered on the y axis. Different symbols indicate whether or not each participant reported a toxicity. Sixteen patients were enrolled, four of which reported toxicities. The points rise and fall like waves in response to changes in the model's recommended dose. The lower one plots time on the x axis and patient number on the y axis. For each patient, a horizontal line runs from their enrolment time to the time at which they reported a toxicity, completed their safety evaluatiuon window or (at the end of the trial) were censored. Different coloured and shaped symbols at the right hand end of each line indicate whether or not the participant reported a toxicity.


mySims@stop_reasons[[2]]
#> [[1]]
#> [1] "Probability for target toxicity is 50 % for dose 36 and thus above the required 50 %"
#> 
#> [[2]]
#> [1] "Number of patients is 17 and thus below the prespecified minimum number 50"

References

Zhu, Jiawen, Daniel Sabanés Bové, Ziwei Liao, Ulrich Beyer, Godwin Yung, and Somnath Sarkar. 2021. “Rolling Continual Reassessment Method with Overdose Control: An Efficient and Safe Dose Escalation Design.” Contemporary Clinical Trials 107: 106436. https://doi.org/https://doi.org/10.1016/j.cct.2021.106436.

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