---
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
)
```

Alternatively we can also use `examine()` to look at possible trial outcomes.
Each cohort is reached assuming no additional DLTs in earlier cohorts. `DLTs`
is the hypothetical number of additional DLTs among the current cohort and
patients from earlier cohorts whose DLT windows are still open at the next
decision. Thus it can exceed the cohort size.

`DLT_scenario` identifies the allocation scenario: `"no additional DLTs"`,
`"late DLTs"` (earlier-enrolled eligible patients at their available follow-up
times), or `"early DLTs"` (later-enrolled eligible patients with early event
times). See `?examine` for the timing details.

`cohort` indexes the current cohort, continuing any indices already present in
the design data. `dose` is that cohort's dose. `DLT_cohorts` lists the cohort
indices of the additional hypothetical DLTs, separated by commas and sorted.
For example, `"1, 2, 2"` means one DLT in cohort 1 and two in cohort 2; `""`
means no additional DLTs. `DLT_time` lists their corresponding onset times,
relative to the start of each patient's cohort, in the same order. Previously
observed DLTs are excluded from both columns.

Each hypothetical scenario requires an MCMC fit. `maxNoIncrement` limits the
number of consecutive unchanged dose recommendations on the zero-DLT path
(default: 100); reaching this limit produces a warning.


``` r
set.seed(321)
examineTable <- examine(
  design,
  mcmcOptions = options
)
examineTable
#>    cohort       DLT_scenario dose DLTs   DLT_cohorts           DLT_time
#> 1       1 no additional DLTs    8    0                                 
#> 2       1          late DLTs    8    1             1                 21
#> 3       1         early DLTs    8    1             1                 15
#> 4       1          late DLTs    8    2          1, 1             21, 21
#> 5       1         early DLTs    8    2          1, 1              8, 15
#> 6       1          late DLTs    8    3       1, 1, 1         21, 21, 21
#> 7       1         early DLTs    8    3       1, 1, 1           1, 8, 15
#> 8       2 no additional DLTs   36    0                                 
#> 9       2          late DLTs   36    1             1                 42
#> 10      2         early DLTs   36    1             2                 15
#> 11      2          late DLTs   36    2          1, 1             42, 42
#> 12      2         early DLTs   36    2          2, 2              8, 15
#> 13      2          late DLTs   36    3       1, 1, 2         42, 42, 21
#> 14      2         early DLTs   36    3       2, 2, 2           1, 8, 15
#> 15      2          late DLTs   36    4    1, 1, 2, 2     42, 42, 21, 21
#> 16      2         early DLTs   36    4    1, 2, 2, 2       22, 1, 8, 15
#> 17      2          late DLTs   36    5 1, 1, 2, 2, 2 42, 42, 21, 21, 21
#> 18      2         early DLTs   36    5 1, 1, 2, 2, 2   22, 22, 1, 8, 15
#>    nextDose  stop increment
#> 1        36 FALSE       350
#> 2        48 FALSE       500
#> 3        38 FALSE       375
#> 4        20 FALSE       150
#> 5        14 FALSE        75
#> 6        12 FALSE        50
#> 7        10 FALSE        25
#> 8        50 FALSE        39
#> 9        32 FALSE       -11
#> 10       24 FALSE       -33
#> 11       30 FALSE       -17
#> 12       28 FALSE       -22
#> 13       16 FALSE       -56
#> 14       22 FALSE       -39
#> 15       14 FALSE       -61
#> 16       26 FALSE       -28
#> 17       16 FALSE       -56
#> 18       14 FALSE       -61
```