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)
}
}Time-to-event continual reassessment method (TITE-CRM) example
Examples
This short vignette demonstrates how to implement a time-to-event continual reassessment method (TITE-CRM) for dose escalation using the
crmPack package.
Simulation setting
Here the simulation study setting is defined.
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 (burnin, 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
)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.
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 40 0
#> 9 2 late DLTs 40 1 1 42
#> 10 2 early DLTs 40 1 2 15
#> 11 2 late DLTs 40 2 1, 1 42, 42
#> 12 2 early DLTs 40 2 2, 2 8, 15
#> 13 2 late DLTs 40 3 1, 1, 2 42, 42, 21
#> 14 2 early DLTs 40 3 2, 2, 2 1, 8, 15
#> 15 2 late DLTs 40 4 1, 1, 2, 2 42, 42, 21, 21
#> 16 2 early DLTs 40 4 1, 2, 2, 2 22, 1, 8, 15
#> 17 2 late DLTs 40 5 1, 1, 2, 2, 2 42, 42, 21, 21, 21
#> 18 2 early DLTs 40 5 1, 1, 2, 2, 2 22, 22, 1, 8, 15
#> 19 3 no additional DLTs 36 0
#> 20 3 late DLTs 36 1 2 42
#> 21 3 early DLTs 36 1 3 15
#> 22 3 late DLTs 36 2 2, 2 42, 42
#> 23 3 early DLTs 36 2 3, 3 8, 15
#> 24 3 late DLTs 36 3 2, 2, 3 42, 42, 21
#> 25 3 early DLTs 36 3 3, 3, 3 1, 8, 15
#> 26 3 late DLTs 36 4 2, 2, 3, 3 42, 42, 21, 21
#> 27 3 early DLTs 36 4 2, 3, 3, 3 22, 1, 8, 15
#> 28 3 late DLTs 36 5 2, 2, 3, 3, 3 42, 42, 21, 21, 21
#> 29 3 early DLTs 36 5 2, 2, 3, 3, 3 22, 22, 1, 8, 15
#> 30 4 no additional DLTs 26 0
#> 31 4 late DLTs 26 1 3 42
#> 32 4 early DLTs 26 1 4 15
#> 33 4 late DLTs 26 2 3, 3 42, 42
#> 34 4 early DLTs 26 2 4, 4 8, 15
#> 35 4 late DLTs 26 3 3, 3, 4 42, 42, 21
#> 36 4 early DLTs 26 3 4, 4, 4 1, 8, 15
#> 37 4 late DLTs 26 4 3, 3, 4, 4 42, 42, 21, 21
#> 38 4 early DLTs 26 4 3, 4, 4, 4 22, 1, 8, 15
#> 39 4 late DLTs 26 5 3, 3, 4, 4, 4 42, 42, 21, 21, 21
#> 40 4 early DLTs 26 5 3, 3, 4, 4, 4 22, 22, 1, 8, 15
#> 41 5 no additional DLTs 46 0
#> 42 5 late DLTs 46 1 4 42
#> 43 5 early DLTs 46 1 5 15
#> 44 5 late DLTs 46 2 4, 4 42, 42
#> 45 5 early DLTs 46 2 5, 5 8, 15
#> 46 5 late DLTs 46 3 4, 4, 5 42, 42, 21
#> 47 5 early DLTs 46 3 5, 5, 5 1, 8, 15
#> 48 5 late DLTs 46 4 4, 4, 5, 5 42, 42, 21, 21
#> 49 5 early DLTs 46 4 4, 5, 5, 5 22, 1, 8, 15
#> 50 5 late DLTs 46 5 4, 4, 5, 5, 5 42, 42, 21, 21, 21
#> 51 5 early DLTs 46 5 4, 4, 5, 5, 5 22, 22, 1, 8, 15
#> nextDose stop increment
#> 1 40 FALSE 400
#> 2 20 FALSE 150
#> 3 24 FALSE 200
#> 4 22 FALSE 175
#> 5 20 FALSE 150
#> 6 24 FALSE 200
#> 7 16 FALSE 100
#> 8 36 FALSE -10
#> 9 28 FALSE -30
#> 10 44 FALSE 10
#> 11 12 FALSE -70
#> 12 28 FALSE -30
#> 13 16 FALSE -60
#> 14 32 FALSE -20
#> 15 12 FALSE -70
#> 16 22 FALSE -45
#> 17 24 FALSE -40
#> 18 14 FALSE -65
#> 19 26 FALSE -28
#> 20 34 FALSE -6
#> 21 44 FALSE 22
#> 22 40 FALSE 11
#> 23 36 FALSE 0
#> 24 26 FALSE -28
#> 25 42 FALSE 17
#> 26 26 FALSE -28
#> 27 30 FALSE -17
#> 28 26 FALSE -28
#> 29 24 FALSE -33
#> 30 46 FALSE 77
#> 31 42 FALSE 62
#> 32 36 FALSE 38
#> 33 38 FALSE 46
#> 34 32 FALSE 23
#> 35 34 FALSE 31
#> 36 32 FALSE 23
#> 37 30 FALSE 15
#> 38 30 FALSE 15
#> 39 24 FALSE -8
#> 40 26 FALSE 0
#> 41 50 FALSE 9
#> 42 40 FALSE -13
#> 43 50 FALSE 9
#> 44 36 FALSE -22
#> 45 38 FALSE -17
#> 46 38 FALSE -17
#> 47 42 FALSE -9
#> 48 32 FALSE -30
#> 49 36 FALSE -22
#> 50 36 FALSE -22
#> 51 36 FALSE -22