---
title: "Simulation study example"
author: "Ziwei Liao, Daniel Sabanés Bové"
date: "02 January 2019"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Simulation study example}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteDepends{crmPack}
  \usepackage[utf8]{inputenc}
---

<!-- simulations.Rmd is generated from simulations.Rmd.orig Please edit that file -->



## Simulation setting

Here the simulation study setting is defined.


``` r
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.


``` r
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).


``` r
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
)
```