In dcnorris/DTAT: Dose Titration Algorithm Tuning: a framework for dose individualization

knitr::opts_chunk$set(echo = TRUE)
# Notwithstanding the advice offered in the package:htmlwidgets docs (see link),
# setting self_contained = TRUE (**) proved necessary for embedding the D3 viz.
# https://cran.r-project.org/web/packages/widgetframe/vignettes/widgetframe_and_knitr.html 
knitr::opts_chunk$set(widgetframe_self_contained = TRUE)  # **
knitr::opts_chunk$set(widgetframe_isolate_widgets = TRUE) # default = TRUE

library(r2d3)
library(widgetframe)
library(DTAT)

Precautionary Coherence and the '3+3/PC' Design

Perhaps you had been planning to conduct a phase 1 dose-finding trial using a dose-escalation design built upon any of the usual, one-size-fits-all methods such as the 3+3, CRM, EWOC, mTPI, BOIN, etc. But then somehow you stumbled upon [@norris_precautionary_2017], and learned:

• that dose-escalation designs are fundamentally unethical,
• that one-size-fits-all dosing is wasteful---see also [@norris_costing_2017],
• and a few modifications can convert the inveterate '3+3' dose-escalation design into an efficient '3+3/PC' dose-titration design that outperforms even the fancy 'model-based' methods.

In that case ... this vignette is for you. Here, we will work stepwise through the process of developing a 3+3/PC design, and simulating its performance under various scenarios.

Optimal-Dose Heterogeneity

Your first step in designing a dose-finding trial should be to articulate your expectations regarding the heterogeneity of optimal dosing in your patient population. In what follows, I'll assume we're working under a maximum tolerated dose (MTD) heuristic, so that we denote the optimal dose for individual i as MTD~i~ [@norris_dose_2017]. Formally, the most straightforward way to describe MTD~i~ heterogeneity is with a distribution:

# You might find it easiest to think in terms of CV and median:
CV <- 0.7    # coefficient of variation of MTDi
MTDi50 <- 75 # median MTDi (i.e., 50th percentile)
# Calculate the shape and scale parameters of a Gamma distribution
# that would exhibit the posited CV and median:
shape <- CV^-2
scale <- MTDi50/qgamma(0.5, shape=CV^-2)
# Plot:
MTDi <- 0:200
dens <- dgamma(MTDi, shape=shape, scale=scale)
xyplot(dens ~ MTDi, type = "l"
       , xlab = expression(MTD[i]*' [mg/kg]')
       , ylab = "density")

A density as plotted above has a natural intuitive appeal, in part because it shows clearly the central tendency of the distribution, as well as the rare individuals in the 'tails'. (To appreciate what motivates the particular choice of the Gamma distribution here, please see [@norris_costing_2017].) More directly useful than this density, however, is the corresponding cumulative distribution:

F <- pgamma(MTDi, shape=shape, scale=scale)
xyplot(F ~ MTDi, type = "l"
       , xlab = expression(MTD[i]*' [mg/kg]')
       , ylab = "Cumulative Distribution"
       , panel = function(...){
         panel.xyplot(...)
         panel.refline(h=0.5)
         panel.refline(v=MTDi50)
       })

Notice that the crosshairs let you read off the median MTD~i~ of 75 mg/kg we had posited. Before moving on, let me introduce one final modification to this cumulative distribution, which should look familiar to the oncology trialist:

F <- pgamma(MTDi, shape=shape, scale=scale)
xyplot((1-F) ~ MTDi, type = "l"
       , xlab = "Dose [mg/kg]"
       , ylab = "Fraction Tolerant")

From this curve, you can read off the fraction of your patient population that you anticipate will be able to tolerate any given dose. At the left-hand side of the plot, you have low doses that most patients tolerate. As you move to the right (increasing the dose), fewer patients will be able to tolerate it. For obvious reasons, [@norris_precautionary_2017] calls this a 'dose-survival curve'.

PC Rules

TODO: Give a quick review of the PC rules, but refer readers to the PC paper for details. In this section, it makes sense to decide what doses to try. Also give some indication about the origin [@simon_accelerated_1997] of the 40% rule.

Parameters of a 3+3/PC Trial

TODO: Introduce the DE object, and its parameters.

Simulating your 3+3/PC Trial

Wouldn't it be nice, if the 3+3/PC simulation automatically embedded easily in the HTML vignette?

# TODO: Drop this code in preference for simulating our actual case study.
x <- test.DE()

viz <- r2d3::r2d3(data=as_d3_data(x),
                  script=system.file("htmlwidgets/lib/main.js", package="DTAT"),
                  d3_version = 4, container = "div",
                  dependencies = system.file(paste("htmlwidgets/lib",
                                                   c("margins.js", "exx.js",
                                                     "ox-plot.js", "ds-plot.js"),
                                                   sep="/"), package="DTAT"))
frameWidget(viz, height='350')

References

dcnorris/DTAT documentation built on May 7, 2019, 10:45 p.m.