In the general introductory CRM vignette, we introduced the different
flavours of the Continual Reassessment Method (CRM) implmented in
trialr. In this vignette, we demonstrate some visualisation
methods that will be useful for conveying inferences to investigators
and the wider research community.
The following visualisation methods are applicable in all
trialr variants of the CRM because they rely only on the
prob_tox parameters that are estimated by all CRM
For illustration, let us assume that we have treated 6 patients at 3 dose-levels:
<- '2NN 3NN 4TT'outcomes
and that we are using the empiric CRM with the following prior to target the dose with Prob(DLT) closest to 25%:
<- c(0.05, 0.15, 0.25, 0.4, 0.6) skeleton <- 0.25target
To access the Stan implementations of the CRM, we must load
and to fit the data to the model, we run:
<- stan_crm(outcomes, skeleton = skeleton, target = target, fit beta_sd = sqrt(1.34), seed = 123) fit
Recall that we set the random number generator seed in demonstrations for reproducibility. You may or may not choose to do this in a real analysis.
We saw before that dose-level 2 is closest to our target toxicity rate of 25%. However, we will probably like to convey this information to the research world in a visually-appealing manner. This is simple with access to the posterior samples.
For ease of plotting with
ggplot2, we recompose the
posterior samples to a tall “tidy” format using
library(dplyr) library(tidybayes) <- fit %>% prob_tox_samp_tall gather_draws(prob_tox[dose]) %>% rename(prob_dlt = .value) %>% ungroup
The tidy data looks like this:
## # A tibble: 10 × 6 ## dose .chain .iteration .draw .variable prob_dlt ## <int> <int> <int> <int> <chr> <dbl> ## 1 1 1 1 1 prob_tox 0.00833 ## 2 1 1 2 2 prob_tox 0.000414 ## 3 1 1 3 3 prob_tox 0.0104 ## 4 1 1 4 4 prob_tox 0.0800 ## 5 1 1 5 5 prob_tox 0.00109 ## 6 1 1 6 6 prob_tox 0.00109 ## 7 1 1 7 7 prob_tox 0.177 ## 8 1 1 8 8 prob_tox 0.146 ## 9 1 1 9 9 prob_tox 0.194 ## 10 1 1 10 10 prob_tox 0.498
Boxplots would be a traditional way of visualising the distributions of the probability of toxicity at each dose:
library(ggplot2) %>% prob_tox_samp_tall ggplot(aes(x = dose, y = prob_dlt, group = dose)) + geom_boxplot() + ylim(0, 1) + labs(title = 'Boxplot of Prob(DLT) under CRM')
However, boxplots give only limited information on the distributions. For instance, it might be tempting to assume that the probability of toxicity is normally distributed at each dose-level. The boxplots suggest some wide tails. This inference is much more clear, however, using a violin-plot:
%>% prob_tox_samp_tall ggplot(aes(x = dose, y = prob_dlt, group = dose)) + geom_violin(fill = 'orange') + ylim(0, 1) + labs(title = 'Violin plot of Prob(DLT) under CRM')
If you are a fan of post-punk UK music (and you have installed the
package), you may however prefer to show this information using a ridge
plot, aka a joyplot
library(ggridges) %>% prob_tox_samp_tall mutate(dose = factor(dose)) %>% ggplot(aes(x = prob_dlt, y = dose, fill = dose)) + geom_density_ridges() + theme(legend.position = 'none') + labs(title = 'Joyplot of Prob(DLT) under CRM') + theme(legend.position = 'bottom')
Hopefully none of us would try to claim these posterior probabilities
of toxicity are normally distributed under this model. Assuming
normality has been one method for performing posterior inference with
CRM models in the non-MCMC setting. With the posterior samples provided
rstan, we do not need to assume.
We will naturally want to visualise quantities beyond just the
probability of toxicity. We learned in the introductory CRM vignette
that with the full Bayesian CRM provided by
rstan, we can calculate the probability that each dose is
the maximum tolerable dose (MTD).
We can visualise the MCMC candidates for the dose-toxicity curve on one plot. Colouring them by the MTD candidate they propose (i.e. using a single colour for all the curves that suggest dose-level 1 is the maximum tolerable dose, etc), we get an idea of uncertainty still in this trial:
%>% prob_tox_samp_tall group_by(.draw) %>% summarise(mtd = dose[which.min(abs(prob_dlt - target))]) %>% mutate(mtd = factor(mtd)) -> mtd_candidates %>% prob_tox_samp_tall left_join(mtd_candidates, by = '.draw') %>% filter(.draw <= 200) %>% ggplot(aes(x = dose, y = prob_dlt, group = .draw)) + geom_line(aes(col = mtd), alpha = 0.5) + geom_hline(yintercept = target, col = 'red', linetype = 'dashed') + labs(title = 'The identify of the MTD is still shrouded in mystery', y = 'Prob(DLT)', col = 'MTD') + theme(legend.position = 'bottom')
We used just 200 curves above to avoid saturating the plot. We can visualise that data rather more bluntly:
%>% mtd_candidates count(mtd) %>% mutate(prob_mtd = n / sum(n)) %>% ggplot(aes(x = mtd, y = prob_mtd, fill = mtd)) + geom_col() + labs(x = 'MTD') + theme(legend.position = 'bottom')
In this interim stage, each of the first four doses could plausibly be the MTD, but the top dose looks unlikely. This information was not readily available from some of the above plots of the probabilities of toxicity.
We might also like to visualise the probability that the toxicity rate at each dose exceeds our target toxicity rate.
%>% fit gather_draws(prob_tox[dose]) %>% group_by(dose) %>% summarise(prob_too_toxic = mean(.value > target)) %>% ggplot(aes(x = dose, y = prob_too_toxic, fill = dose)) + geom_col() + scale_fill_gradient(low="green", high="red") + labs(title = 'Posterior probability that each dose is too toxic', y = 'Prob(DLT risk > target)', fill = 'Probability dose is too toxic') + theme(legend.position = 'bottom')
Based on our prior and the data assembled thus far, dose-levels 4 and 5 look quite likely to be overdoses.
There are many vignettes illustrating the CRM and other dose-finding
trialr. Be sure to check them out.
is an R package that provides a grammar for specifying dose-finding
clinical trials. For instance, it is common for trialists to say
something like ‘I want to use this published design… but I want it to
stop once \(n\) patients have been
treated at the recommended dose’ or ‘…but I want to prevent dose
skipping’ or ‘…but I want to select dose using a more risk-averse metric
than merely closest-to-target’.
escalation work together to
achieve these goals.
trialr provides model-fitting
escalation, including the CRM methods
escalation then provides additional classes
to achieve all of the above custom behaviours, and more.
escalation also provides methods for running simulations
and calculating dose-paths. Simulations are regularly used to appraise
the operating characteristics of adaptive clinical trial designs.
Dose-paths are a tool for analysing and visualising all possible future
trial behaviours. Both are provided for a wide array of dose-finding
designs, with or without custom behaviours like those identified above.
There are many examples in the
escalation vignettes at https://cran.r-project.org/package=escalation.