Dose Titration Algorithm Tuning: a Framework for Dose Individualization in Drug Development

Description

Dose Titration Algorithm Tuning (DTAT) is a methodologic framework allowing dose individualization to be conceived as a continuous learning process that begins in early-phase clinical trials and continues throughout drug development, on into clinical practice. This package includes code that researchers may use to reproduce or extend key results of the DTAT research programme, plus tools for trialists to design and simulate a '3+3/PC' dose-finding study. Please see Norris (2017a) doi:10.12688/f1000research.10624.3 and Norris (2017c) doi:10.1101/240846.

Author(s)

David C. Norris

References

1. Norris DC. Dose Titration Algorithm Tuning (DTAT) should supersede ‘the’ Maximum Tolerated Dose (MTD) in oncology dose-finding trials. F1000Research. 2017;6:112. doi:10.12688/f1000research.10624.3. https://f1000research.com/articles/6-112/v3

2. Norris DC. Costing ‘the’ MTD. bioRxiv. August 2017:150821. doi:10.1101/150821. https://www.biorxiv.org/content/10.1101/150821v3

3. Norris DC. Precautionary Coherence Unravels Dose Escalation Designs. bioRxiv. December 2017:240846. doi:10.1101/240846. https://www.biorxiv.org/content/10.1101/240846v1

4. Norris DC. One-size-fits-all dosing in oncology wastes money, innovation and lives. Drug Discov Today. 2018;23(1):4-6. doi:10.1016/j.drudis.2017.11.008. https://www.sciencedirect.com/science/article/pii/S1359644617303586

5. Norris DC. Costing ‘the’ MTD ... in 2-D. bioRxiv. July 2018:370817. doi:10.1101/370817. https://www.biorxiv.org/content/10.1101/370817v1

An S4 class for simulating dose-titration study designs

Description

An S4 class for simulating dose-titration study designs

Slots

doses

A numeric vector of prospectively-determined discrete doses to trial.

units

A string indicating dose units, e.g. "mg/kg".

MTDi

A numeric vector of optimal doses for simulated study participants. Optionally a call to an ⁠r<distribution>(...)⁠ function which may be parsed to calculate the mtd_quantiles slot.

mtd_quantiles

A numeric vector of quantiles of the distribution from which the MTDi slot was simulated. Intended mainly to support visualization of this distribution, e.g. as an transparent overlay on the dose-survival plot. NULL in case MTDi is provided verbatim.

fractol

A numeric vector of probabilities for the simulated MTDi slot. Intended mainly to support visualization, e.g. plotting of 'MTD pointers' on the interactive dose-survival plot.

data

A data.frame with columns:

• id Participant identifier

• period DLT assessment period, numbered consecutively from 1

• dose Dose level, numbered consecutively starting from 1

• dlt A logical indicator: did this this participant experience a DLT during this period?

stop_esc

integer Period in which ‘stop rule’ was triggered

ds_conf_level

numeric Confidence level for confidence band around Kaplan-Meier estimate of the dose-survival curve.

dose_drop_threshold

numeric Threshold for triggering the ‘bypass rule’.

stop_esc_under

numeric Threshold for triggering the ‘stop rule’.

undo_esc_under

numeric Threshold for triggering the ‘rollback rule’.

POMP PK/PD model for docetaxel, combining Onoue et al (2016) with Friberg et al (2002)

Description

This function produces a POMP model combining docetaxel pharmacokinetics (PK) drawn from Table 2 of Onoue et al (2016) with myelosuppression dynamics drawn from Friberg et al (2002). This model enables simulation of neutrophil-guided dose titration of docetaxel, as done in Norris (2017).

Usage

Onoue.Friberg(
  N,
  cycle.length.days = 21,
  data = data.frame(time = c(seq(0, 1.95, 0.05), seq(2, cycle.length.days * 24, 1)), y =
    NA),
  delta.t = 0.1
)

Arguments

Value

No value is returned; rather, the function sets global variables in package environment DTAT::sim.

Author(s)

David C. Norris

References

1. Onoue H, Yano I, Tanaka A, Itohara K, Hanai A, Ishiguro H, et al. Significant effect of age on docetaxel pharmacokinetics in Japanese female breast cancer patients by using the population modeling approach. Eur J Clin Pharmacol. 2016 Jun;72(6):703-10. doi:10.1007/s00228-016-2031-3.

2. Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO. Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol. 2002 Dec 15;20(24):4713-21. doi:10.1200/JCO.2002.02.140.

3. Norris DC. Dose Titration Algorithm Tuning (DTAT) should supersede ‘the’ Maximum Tolerated Dose (MTD) in oncology dose-finding trials. F1000Research. 2017;6:112. doi:10.12688/f1000research.10624.3. https://f1000research.com/articles/6-112/v3

See Also

pomp, sim

Examples

# Reproduce the sim$pkpd model and sim$pop population from reference #3:
library(pomp)
Onoue.Friberg(N=25)
sim$pop # NB: this differs from pop of original paper...

# Whereas the present version of Onoue.Friberg() draws simulated populations
# using pomp::rprior(), to reproduce the original F1000Research paper [3] we
# re-draw sim$pop as originally & prosaically done (see https://osf.io/vwnqz/):
set.seed(2016)
N <- 25
dtx.mm <- 0.808 # molar mass (mg/µM) of docetaxel
sim$pop$Circ0 <- rlnorm(N, meanlog=log(5050), sdlog=0.42) # units=cells/mm^3
sim$pop$MTT <- rlnorm(N, meanlog=log(89.3), sdlog=0.16)  # mean transit time
sim$pop$gamma <- rlnorm(N, meanlog=log(0.163), sdlog=0.039) # feedback factor
sim$pop$Emax <- rlnorm(N, meanlog=log(83.9), sdlog=0.33)
sim$pop$EC50 <- rlnorm(N, meanlog=log(7.17*dtx.mm), sdlog=0.50)
# PK params from 2-compartment docetaxel model of Onoue et al (2016)
sim$pop$CL <- rlnorm(N, meanlog=log(32.6), sdlog=0.295)
sim$pop$Q  <- rlnorm(N, meanlog=log(5.34), sdlog=0.551)
sim$pop$Vc <- rlnorm(N, meanlog=log(5.77), sdlog=0.1) # Onoue gives no CV% for V1
sim$pop$Vp <- rlnorm(N, meanlog=log(11.0), sdlog=0.598) # Called 'V2' in Onoue
sim$pop$kTR=4/sim$pop$MTT

# Now we run the sim$pkpd model, separately for each of N simultated individuals:
allout <- data.frame() # accumulator for N individual ODE solutions
for (id in 1:sim$N) {
  out <- trajectory(sim$pkpd,
                    params=c(sim$pop[sim$pop$id==id, -which(names(sim$pop) %in% c('id','MTT'))]
                             , sigma=0.05, dose=100, duration=1),
                    format="data.frame")
  # drop 'traj' and shift 'time' to first column
  out <- out[,c('time',setdiff(colnames(out),c('time','traj')))]
  out$id <- paste("id",id,sep="")
  allout <- rbind(allout, out)
}

library(Hmisc)
allout <- upData(allout
                 , id = ordered(id, levels=paste("id",1:sim$N,sep=""))
                 , units=c(Prol="cells/mm^3", Tx.1="cells/mm^3",
                           Tx.2="cells/mm^3", Tx.3="cells/mm^3",
                           Circ="cells/mm^3",
                           Cc="ng/mL", Cp="ng/mL",
                           time="hours"), print=FALSE)

library(tidyr)
cout <- gather(allout, key="Series", value="Concentration"
, Cc, Cp
, factor_key = TRUE)

label(cout$Concentration) <- "Drug Concentration"

# Figure 1 from reference [3]:
library(RColorBrewer)
xYplot(Concentration ~ time | id, group=Series
       , data=cout, subset=time<6
       , layout=c(5,NA)
       , type='l', as.table=TRUE
       , label.curves=FALSE
       , par.settings=list(superpose.line=list(lwd=2,col=brewer.pal(4,"PRGn")[c(1,4)]))
       , scales=list(y=list(log=TRUE, lim=c(10^-3,10^1)))
       , auto.key=list(points=FALSE, lines=TRUE, columns=2))

mout <- gather(allout, key="Series", value="ANC"
, Prol, Tx.1, Tx.2, Tx.3, Circ
, factor_key = TRUE)

mout <- upData(mout
               , time = time/24
               , units = c(time="days")
               , print = FALSE)

# Figure 3 from citation [3]:
xYplot(ANC ~ time | id, group=Series
       , data=mout
       , layout=c(5,5)
       , type='l', as.table=TRUE
       , label.curves=FALSE
       , par.settings=list(superpose.line=list(lwd=2,col=brewer.pal(11,"RdYlBu")[c(1,3,4,8,10)]))
       , scales=list(y=list(log=TRUE, lim=c(100,15000), at=c(200, 500, 1000, 2000, 5000, 10000)))
       , auto.key=list(points=FALSE, lines=TRUE, columns=5))

Convert a DE object to JSON

Description

Convert a DE object to JSON

Usage

## S4 method for signature 'DE'
as_d3_data(x, ...)

Arguments

Simulated ‘3+3/PC’ dose-titration study from bioRxiv paper no. 240846

Description

This is a length-10 list of data frames, summarizing the simulated trial from this paper, at the end of periods 1, 2, ..., 10. This structure reflects an awkward S3 implementation that package DTAT v0.3 reimplemented using S4. This data set is retained to support regression tests.

Format

A length-10 list of data frames, each with the following columns:

id

Participant identifier

period

DLT assessment period, numbered consecutively from 1

dose

Dose level, numbered consecutively starting from 1

dlt

A logical indicator: did this this participant experience a DLT during this period?

Details

A stop.esc attribute is attached to data frames in this list, indicating when escalation stopped during the simulated trial.

References

Norris DC. Precautionary Coherence Unravels Dose Escalation Designs. bioRxiv. December 2017:240846. doi:10.1101/240846. https://www.biorxiv.org/content/10.1101/240846v1

Examples

data(de.bioRxiv.240846)
# Demonstrate that the new S4 3+3/PC implementation reproduces the
# simulated trial from the paper:
set.seed(2017)
CV <- 0.7; mean_mtd <- 1.0
shape <- CV^-2; scale <- mean_mtd/shape
trial <- new("DE", doses=0.25 * 1.4^(0:6),
             MTDi=rgamma(24, shape=shape, scale=scale),
             units="mg")
trial <- titration(trial, periods=10)
stopifnot(all(trial@data == de.bioRxiv.240846[[10]]))
stopifnot(trial@stop_esc == attr(de.bioRxiv.240846[[10]],'stop.esc'))

Calculate a dose-survival curve from a dose titration study, adding a confidence band

Description

The 'dose-survival curve' is nothing other than an empirical cumulative distribution for MTDi in the sampled population. The term 'survival' is suggested in part by our application of the Kaplan-Meier estimator to interval-censored toxicity information.

Usage

dose.survfit(de, method = "rothman", avoid.degeneracy = TRUE, conf.level = 0.8)

Arguments

Details

TODO: Describe details of degeneracy avoidance, once these have stabilized.

Value

An object of class survfit.

Author(s)

David C. Norris

See Also

dose.survival, km.ci

Examples

CV <- 0.7; mean_mtd <- 1.0
shape <- CV^-2; scale <- mean_mtd/shape
trial <- new("DE", doses=0.25 * 1.4^(0:6),
             MTDi=rgamma(24, shape=shape, scale=scale),
             units="mg")
trial <- titration(trial, periods=10)
sf <- dose.survfit(trial@data)
summary(sf)

Extract interval-censored dose tolerance data from a dose titration study

Description

Constructs a Surv object from a dose-escalation experiment, using interval-censoring constructs of type='interval2'.

Usage

dose.survival(de)

Arguments

Value

A Surv object of type='interval2'

Author(s)

David C. Norris

See Also

dose.survfit

Examples

CV <- 0.7; mean_mtd <- 1.0
shape <- CV^-2; scale <- mean_mtd/shape
trial <- new("DE", doses=0.25 * 1.4^(0:6),
             MTDi=rgamma(24, shape=shape, scale=scale),
             units="mg")
trial <- titration(trial, periods=10)
dose.survival(trial@data)

Extract the dose-survival curve, with its upper and lower confidence band limits

Description

This utility function simply makes the results of dose.survfit available in the convenient form of a list.

Usage

ds.curve(de, ...)

Arguments

Value

A list with components surv, upper and lower, each containing a vector that can be indexed by dose level.

Author(s)

David C. Norris

See Also

dose.survfit

Examples

CV <- 0.7; mean_mtd <- 1.0
shape <- CV^-2; scale <- mean_mtd/shape
trial <- new("DE", doses=0.25 * 1.4^(0:6),
             MTDi=rgamma(24, shape=shape, scale=scale),
             units="mg")
trial <- titration(trial, periods=10)
ds.curve(trial@data)

Precomputed neutrophil-guided chemotherapy dose titration for 1000 simulated subjects.

Description

This dataset is provided to support fast reproduction of a forthcoming pharmacoeconomic paper that includes examination of the empirical distribution of MTDi in N=1000 simulated subjects.

Format

A data frame showing end-of-cycle state of neutrophil-guided dose titration for 1000 simulated subjects, across 10 cycles of chemotherapy.

cycle

Cycle number 1..10

id

Subject identifiers; an ordered factor with levels id1 < ... < id1000

Cc

Central-compartment drug concentration

Cp

Peripheral-compartment drug concentration

Prol

Progenitor cells in proliferating compartment of Friberg et al. (2002) model

Tx.1

Transit compartment 1

Tx.2

Transit compartment 1

Tx.3

Transit compartment 1

Circ

Concentration (cells/mm^3) of circulating neutrophils

dose

Dose of 1-hour infusion administered this cycle

CircMin

Neutrophil nadir (cells/mm^3)

tNadir

Time (days) of neutrophil nadir

scaled.dose

Fourth root of dose

time

Time (weeks) of dose administration

Details

Running the examples interactively, you can verify the reproducibility of this dataset. (That demo is included in a donttest block to spare the CRAN servers.)

References

1. Norris DC. Dose Titration Algorithm Tuning (DTAT) should supersede ‘the’ Maximum Tolerated Dose (MTD) in oncology dose-finding trials. F1000Research. 2017;6:112. doi:10.12688/f1000research.10624.3. https://f1000research.com/articles/6-112/v3

2. Norris DC. Costing ‘the’ MTD. bioRxiv. August 2017:150821. doi:10.1101/150821. https://www.biorxiv.org/content/10.1101/150821v3

Examples

data(dtat1000)
# 1. Extract the N final doses, assuming convergence by the tenth course
MTD_i <- with(dtat1000, dose[time==27])
MTD_i <- MTD_i[MTD_i < 5000] # Exclude few outliers
# 2. Do a kernel density plot
library(Hmisc)
library(latticeExtra)
hist <- histogram(~MTD_i, breaks=c(0,100,200,300,400,600,900,1500,2500,4000,5000)
                  , xlab=expression(MTD[i]))
approx <- data.frame(mtd_i=seq(0, 5000, 10))
approx <- upData(approx,
                 gamma = dgamma(mtd_i, shape=1.75, scale=200))
dist <- xyplot(gamma ~ mtd_i, data=approx, type='l', col='black', lwd=2)
library(grid)
hist + dist
grid.text(expression(MTD[i] %~%
                     paste("Gamma(", alpha==1.75, ", ", beta==1/200,")"))
         , x=unit(0.5,"npc")
         , y=unit(0.75,"npc")
         )
## A very long repro, which a user of this package may well wish to verify
## by running the examples interactively, although it takes many minutes
## to compute.  (Enclosed in a dontest block to avoid overburdening CRAN.)

# Demonstrate close reproduction of original titration (the titration takes many minutes!)
set.seed(2016)
library(pomp)
Onoue.Friberg(N=1000)
# This titration may take an hour to run ...
chemo <- titrate(doserange = c(50, 3000),
                 dta=newton.raphson(dose1 = 100,
                                    omega = 0.75,
                                    slope1 = -2.0,
                                    slopeU = -0.2)
)

dtat1k <- upData(chemo$course
                , time = 3*(cycle-1)
                , labels = c(time="Time")
                , units = c(time="weeks")
                , print = FALSE)

c10dose1k <- subset(dtat1k, cycle==10)$scaled.dose
c10dose1000 <- subset(dtat1000, cycle==10)$scaled.dose
stopifnot(0.999 < cor(c10dose1k, c10dose1000))

A dose titration algorithm (DTA) 'factory' based on the Newton-Raphson heuristic

Description

This higher-order ('factory') function produces a simple dose titration algorithm for neutrophil-guided chemotherapy dosing.

Usage

newton.raphson(dose1, omega, slope1, slopeU)

Arguments

Details

This function manifests the core concept of Dose Titration Algorithm Tuning by delivering an objectively realized 'DTA'. It therefore enables a variety of DTAs to be implemented and compared.

Value

A dose titration function that advises dose for next cycle of chemotherapy.

Author(s)

David C. Norris

See Also

titrate

Plot a DE object as an interactive htmlwidget

Description

Plot a DE object as an interactive htmlwidget

Usage

## S4 method for signature 'DE,missing'
plot(x, y, ..., devtree = FALSE)

Arguments

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

• r2d3 as_d3_data

Run Shiny apps included in package DTAT

Description

Run Shiny apps included in package DTAT

Usage

runDTATapp(app)

Arguments

Value

Invoked for side effect. Runs the named Shiny app.

Examples

if(interactive()){
runDTATapp("Sim33PC")
runDTATapp("TheCost")
}

Power-law scaling for doses

Description

Implement an inverse power-law scaling for drug dose.

Usage

scaled(dose, a = 4)

Arguments

Value

A rescaled vector of doses

Author(s)

David C. Norris

A seq method supporting custom-scaled plot axes.

Description

This provides a seq method for class function, supporting a natural axis scaling idiom.

Usage

## S3 method for class ''function''
seq(scalefun, from, to, length.out, digits = NULL, ...)

Arguments

Value

A numeric vector that (not considering the effect of any rounding applied), becomes an arithmetic sequence after application of scalefun to it. The initial and final elements of that vector are from and to.

Author(s)

David C. Norris

Examples

# Provide evenly-spaced length-6 sequence from 100 to 1000,
# evenly spaced on a fourth-root scale:
seq(function(dose, a=4.0) dose^(1/a), from=100, to=1000, length.out=6, digits=0)

Environment for simulation global variables.

Description

To simplify the code of package DTAT, as well as client tasks, this exported environment contains a handful of global variables useful for the simulations.

Details

Global variables maintained within environment sim are:

1. pkpd: The population PK/PD model to be simulated.

2. pop: A sample drawn from the population model.

3. N: Restricts simulation to first N subjects in pop.

4. params.default: Default parameters.

Examples

# Even when nrow(pop) is large, one may easily restrict
# time-consuming simulations to pop[1:N,], as follows:
sim$N <- 25
# Now perform simulation work
## Not run: 
titrate(...)

## End(Not run)

Perform neutrophil-guided dose titration of a chemotherapy drug.

Description

This is included in package DTAT mainly for archival purposes, with the aim to document a reproduction of Figure 5 from the 2017 F1000Research paper (referenced below), using a clearer and more general software design than is found in the online code supplement available at https://osf.io/vwnqz/.

Usage

titrate(draw.days = NULL, Ncycles = 10, doserange = c(50, 500), dta = NULL)

Arguments

Value

A list with 2 components:

Author(s)

David C. Norris

References

Norris DC. Dose Titration Algorithm Tuning (DTAT) should supersede ‘the’ Maximum Tolerated Dose (MTD) in oncology dose-finding trials. F1000Research. 2017;6:112. doi:10.12688/f1000research.10624.3. https://f1000research.com/articles/6-112/v3

Examples

if(interactive()){
# Reproduce Figure 5 from the F1000Research paper (run time > 10 s).
# 1. Set up sim$pop & sim$pkpd by running the repro for Figures 1 & 3:
example(topic="Onoue.Friberg", package="DTAT", ask=FALSE)
# 2. Do the neutrophil-nadir-guided dose titration:
chemo <- titrate(doserange = c(50, 3000),
                 dta=newton.raphson(dose1 = 50,
                                    omega = 0.75,
                                    slope1 = -2.0,
                                    slopeU = -0.2)
                 )
library(latticeExtra)
newton <- chemo$course
new.ts <- chemo$anc.ts
anc.tics <- c(200,500,1500,4000,10000)
right <- xYplot(ANC ~ time | id, data=new.ts
                , as.table=TRUE, type="l"
                , layout=c(5,5)
                , scales=list(y=list(log=TRUE, lim=c(100,1.5e4)
                                     , at=anc.tics
                                     , lab=as.character(anc.tics)),
                              x=list(at=seq(0,30,3)))
)
newton <- upData(newton
                 , time = 3*(cycle-1)
                 , labels = c(time="Time")
                 , units = c(time="weeks")
                 , print = FALSE)
dose.tics <- c(50, 200, 600, 1500, 3000)
left <- xYplot(scaled.dose ~ time | id, data=newton
               , as.table=TRUE, type='p', pch='+', cex=1.5
               , layout=c(5,5)
               , scales=list(y=list(lim=DTAT:::scaled(c(30,3200))
                                    , at=DTAT:::scaled(dose.tics)
                                    , lab=as.character(dose.tics)),
                             x=list(lim=c(-1,31)
                                    , at=seq(0,30,3)
                                    , lab=c('0','','6','','12','','18','','24','','30')))
)
update(doubleYScale(left, right, add.ylab2=TRUE)
       , par.settings = simpleTheme(col=brewer.pal(4,"PRGn")[c(4,1)])
)
}

Simulate a ‘3+3/PC’ dose-titration trial

Description

Simulate a ‘3+3/PC’ dose-titration trial

Usage

titration(x, periods, ...)

## S4 method for signature 'DE,numeric'
titration(x, periods, ...)

Arguments

References

Norris DC. Precautionary Coherence Unravels Dose Escalation Designs. bioRxiv. December 2017:240846. doi:10.1101/240846. https://www.biorxiv.org/content/10.1101/240846v1