# Simulation study example

#### Ziwei Liao, Daniel Sabanés Bové

#### 02 January 2019

## Simulation setting

Here the simulation study setting is defined.

    id <- 1
    onset <- 3
    a0 <- 2
    a1 <- 3
    refDose <- 56

    # True dose-DLT relationship
    myTruth <- function(dose) {
      StandLogDose <- log(dose / refDose)
      plogis(a0 + a1 * StandLogDose)
    }

    # The conditional CDF of the PEM
    if (onset == 30) {
      onset <- 15
      exp_cond_cdf <- function(x) {
        (pexp(42 - x, 1 / onset, lower.tail = FALSE) - pexp(t_max, 1 / onset, lower.tail = FALSE)) / pexp(t_max, 1 / onset)
      }
    } else {
      exp_cond_cdf <- function(x) {
        1 - (pexp(x, 1 / onset, lower.tail = FALSE) - pexp(t_max, 1 / onset, lower.tail = FALSE)) / pexp(t_max, 1 / onset)
      }
    }

## Design definition

Here the the dose escalation designs are defined: in this example the TITE-CRM is used. Similarly the code can be adapted for the rolling-CRM which is implemented in `DALogisticLogNormal`. Note that another alternative is `TITELogisticLogNormalSub` which is a submodel of `LogisticLogNormalSub`, which uses again the subtraction of the reference dose from the dose level in the regression model.

    library(crmPack)
    t_max <- 42

    model <- TITELogisticLogNormal(
      mean = c(1.33, 1.49),
      cov = matrix(c(1.826, 0.0209, 0.0209, 0.0245), nrow = 2),
      ref_dose = refDose
    )

    myIncrements <- IncrementsRelative(
      intervals = c(0, 20),
      increments = c(10, 3)
    )

    myNextBest <- NextBestMTD(
      target = 0.3,
      derive =
        function(mtd_samples) {
          mean(mtd_samples)
        }
    )

    myStopping <- StoppingMinPatients(nPatients = 48)

    mySize <- CohortSizeConst(size = 3)

    emptydata <- DataDA(doseGrid = seq(from = 2, to = 50, by = 2), Tmax = t_max)

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

    design <- DADesign(
      model = model,
      increments = myIncrements,
      nextBest = myNextBest,
      stopping = myStopping,
      cohort_size = mySize,
      data = emptydata,
      safetyWindow = mysafetywindow,
      startingDose = 8
    )

## Simulation run

In order to obtain stable results, increase the simulation parameters appropriately (step, samples, nsim).

    options <- McmcOptions(
      burnin = 20,
      step = 1,
      samples = 50
    )
    mySims <- simulate(design,
      args = NULL,
      truthTox = myTruth,
      truthSurv = exp_cond_cdf,
      trueTmax = 42,
      nsim = 10,
      seed = 819,
      mcmcOptions = options,
      parallel = FALSE
    )