CRM

O’Quigley, Pepe, and Fisher (1990) introduced the classic continual reassessment method (CRM) and it has been implemented in many software packages since. One of the most popular R implementations is the dfcrm package by Cheung (2013). Let’s fit a model using dfcrm.

The very least information we need to provide is a dose-toxicity skeleton, and our target toxicity level:

skeleton <- c(0.05, 0.1, 0.25, 0.4, 0.6)
target <- 0.25

We use these to create a model-fitting object:

library(escalation)
model <- get_dfcrm(skeleton = skeleton, target = target)

The model can then be fit to outcomes. The escalation package uses the outcome syntax introduced for phase I trials in Brock (2019) and for seamless phase I/II trials in Brock et al. (2017). Let’s assume we have treated 3 patients at dose-level 2 and none of them experienced toxicity. We represent this using the outcome string 2NNN. Fitting the model to the set of outcomes invokes the dose-selection algorithm:

fit <- model %>% fit('2NNN')

and the fit object will tell you the dose recommended by the CRM model to be administered next:

fit %>% recommended_dose()

## [1] 4

The model advocates skipping straight from dose 2 to dose 4. Clinicians are unlikely to feel comfortable with this. We can respecify the model to expressly not skip doses in escalation:

model <- get_dfcrm(skeleton = skeleton, target = target) %>% 
  dont_skip_doses(when_escalating = TRUE)

We have taken the original dfcrm model and added an extra module to prevent skipping doses in escalation. Refitting the new model to the same outcomes gives:

fit <- model %>% fit('2NNN')
fit %>% recommended_dose()

## [1] 3

We see that the ensemble now decides to select dose 3. We can ask the trial design whether it wants to keep recruting patients:

fit %>% continue()

## [1] TRUE

Naturally it wants to continue because dfcrm does not implement any stopping rules. However, we can easily add some. Let us say that we want to stop once the model has evaluated 18 patients, or at least 9 at the dose being recommended, whichever occurs first. We specify this model by adding more behaviours:

model <- get_dfcrm(skeleton = skeleton, target = target) %>% 
  dont_skip_doses(when_escalating = TRUE) %>% 
  stop_at_n(n = 18) %>% 
  stop_when_n_at_dose(dose = 'recommended', n = 9)

Let’s fit this model to some more patients to see how this trial plays out:

fit <- model %>% fit('2NNN 3TTN')
fit %>% recommended_dose()

## [1] 2

fit %>% continue()

## [1] TRUE

After seeing two-in-three patients in the second cohort experience toxicity at dose 3, the design understandably wants to de-escalate. Let’s do that:

fit <- model %>% fit('2NNN 3TTN 2TNN')
fit %>% recommended_dose()

## [1] 2

fit %>% continue()

## [1] TRUE

The third cohort yielded one-in-three tox at dose 2. The design wants to continue at dose 2 so let’s do that:

fit <- model %>% fit('2NNN 3TTN 2TNN 2NNT')
fit %>% recommended_dose()

## [1] 2

fit %>% continue()

## [1] FALSE

Notice that the call to continue() now returns FALSE. The design wants to stop now and recommend dose 2. It does this because it has seen 9 patients at the recommended dose. We can see the number of patients treated at each of the five doses under investigation:

fit %>% n_at_dose()

## [1] 0 9 3 0 0

Our stopping criteria have been met. We can verify that dose 2 is indeed the dose with posterior expected toxicity rate closest to our target of 25%:

fit %>% mean_prob_tox()

## [1] 0.1845713 0.2728713 0.4575229 0.5964102 0.7496662

BOIN

escalate also implements the BOIN dose-finding design by Liu and Yuan (2015) via the BOIN R-package (Yuan and Liu 2018).

In contrast to CRM, BOIN does not require a dose-toxicity skeleton. In its simplest case, it requires merely the number of doses under investigation and our target toxicity level:

target <- 0.25
model <- get_boin(num_doses = 5, target = target)

As before, we can fit the model to some observed outcomes:

fit <- model %>% fit('2NNN')
fit %>% recommended_dose()

## [1] 3

fit %>% continue()

## [1] TRUE

The BOIN dose selector natively implements stopping rules, as described by Liu & Yuan. For instance, if the bottom dose is too toxic, the design will advise the trial halts:

fit <- model %>% fit('2NTN 1TTT')
fit %>% recommended_dose()

## [1] NA

fit %>% continue()

## [1] FALSE

Nevertheless, as with the CRM examples above, our BOIN selector can be adorned with various behaviours to tailor stopping and skipping. In fact, we can add the exact same behaviours as before because all escalation objects support exactly the same interface. This makes the package completely modular. We are building the design we want from pieces of Lego:

model <- get_boin(num_doses = 5, target = target) %>% 
  dont_skip_doses(when_escalating = TRUE) %>% 
  stop_at_n(n = 18) %>% 
  stop_when_n_at_dose(dose = 'recommended', n = 9)

fit <- model %>% fit('2NNN 3TTN 2TNN 2NNT')
fit %>% recommended_dose()

## [1] 2

fit %>% continue()

## [1] FALSE

fit %>% mean_prob_tox()

## [1]   NA 0.23 0.66   NA   NA

Notice that the posterior toxicity estimate is similar to the CRM model at dose 2, but ultimately different because the two approaches use different model forms. BOIN does not estimate the tox rate at doses that have not been administered.

Initial escalation plans

Another dose-selection mechanism supported by escalation is the concept of an initial escalation plan. These can be used at the start of a trial to show how escalation should proceed initially. As soon as the realised outcomes diverge from the prespecified path, or the path reaches the end, a secondary model takes over.

For instance, let us assume we would like to treat one patient per dose so long as no toxicity is seen, in order to facilitate fast escalation. When toxicity is seen, or dose five is reached, we would like to hand control to a CRM model. We can write:

model <- follow_path('1N 2N 3N 4N 5N') %>% 
  get_dfcrm(skeleton = skeleton, target = target)

So long as the idealised path is realised, it continues:

model %>% 
  fit('1N') %>% 
  recommended_dose()

## [1] 2

model %>% 
  fit('1N 2N') %>% 
  recommended_dose()

## [1] 3

But if the path is deviated from, the secondary model takes over:

model %>% 
  fit('1N 2N 3T') %>% 
  recommended_dose()

## [1] 2

Also, when the initial path is completed, the secondary model continues:

model %>% 
  fit('1N 2N 3N 4N 5N') %>% 
  recommended_dose()

## [1] 5