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Rolling CRM Example

Jiawen Zhu, Daniel Sabanes Bove

02 January 2019

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.

plot of chunk Diagnose-1 

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 of chunk Diagnose-2

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 of chunk Fit-1 

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.

plot of chunk Fit-2

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.

plot of chunk Prior

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)

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.

plot of chunk Truth 


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.

plot of chunk Interpret 


mySims@stop_reasons[[2]]
#> [[1]]
#> [1] "Probability for target toxicity is 68 % for dose 34 and thus above the required 50 %"
#> 
#> [[2]]
#> [1] "Number of patients is 17 and thus below the prespecified minimum number 50"

# nolint end

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