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The Continual Reassessment Method (CRM)
was published in 1990.
It is the most frequently used
model-based design in oncology.
The assignment of doses
is very similar to the up-and-down designs,
in the sense that we can escalate,
deescalate or repeat the dose
for the next cohort of patients.
Patients can be assigned
one at a time or in groups.
We need to specify the total sample size.
It's usually 18-24,
if we have maybe four dose levels or five.
The dose assignment for the next cohort
or the next patient is determined based
on a parsimonious model.
It is also referred to as the working model.
In the initial escalation,
sometimes this working model
tells us to assign high doses right away.
However, because of ethical constraints,
we do not skip doses
in the initial escalation.
Escalation starts
at the lowest dose level
and then it goes to dose level
2, 3, and 4, etc...
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So consider an example
where we have six dose levels selected,
what is our CRM working model?
There are several ways to specify the model.
Here, I will consider the so-called
'power model' as in the original 1990 paper.
This power model can be specified
as a constant for each dose level.
So we need six constants.
So these constants
should be specified in advance.
And then the model for toxicity probability
is such that the probability of toxicity,
given the parameter "a"
that is estimated, is equal to the constant
corresponding to a dose to the power of "a".
One can use the maximum
likelihood methods to estimate "a",
or one can use the Bayesian methods.
If we use a Bayesian variant of the CRM,
then we need to specify
the prior for the parameter "a".
For example, for this power model,
we can specify the exponential prior for "a."
