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)

## Loading required package: ggplot2

## Registered S3 method overwritten by 'crmPack':
##   method       from  
##   print.gtable gtable

## Type crmPackHelp() to open help browser
## Type crmPackExample() to open example

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)

## Loading required package: dplyr

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

## Loading required package: tidyr

## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

alpha0samples <- get(samples, "alpha0")

print(ggs_traceplot(alpha0samples))

print(ggs_autocorrelation(alpha0samples))

Plot the model fit

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

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

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)

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

doseRecommendation$value

## [1] 0.1

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))

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, # piece_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)

mySims@stop_reasons[[2]]

## [[1]]
## [1] "Probability for target toxicity is 60 % for dose 20 and thus above the required 50 %"
## 
## [[2]]
## [1] "Number of patients is 20 and thus below the prespecified minimum number 50"

# nolint end