You’ll often hear Phase I dose-finding
trials referred to as dose
studies. This is because simple dose-finding methods can
only explore in one direction: they can only escalate.
The most common dose finding method is the 3+3
rule. There are
countless variations on this theme, but the basic idea is that you give
a dose of an experimental drug to three people. If all three are OK, you
go up a dose next time. If two out of three are OK, you give that dose
again. If only one out of three is OK, you stop .
The 3+3 algorithm implicitly assumes deterministic thinking, at least in
part. The assumption is that if three out of three patients respond
well, we know
the dose is safe .
If you increase the dose level and the next three patients experience
adverse events, you stop the trial. Why? Because you know
that the new
dose is dangerous, and you know
the previous dose was safe. You can
only escalate because you assume you have complete knowledge based on
But if we treat three patients at a particular dose level and none have
an adverse reaction we do not know
for certain that the dose level
is safe, though we may have sufficient confidence in its safety to try
the next dose level. Similarly, if we treat three patients at a dose and
all have an adverse reaction, we do not know for certain that the dose
A Bayesian dose-finding method estimates toxicity probabilities given
the data available. It might decide at one point that a dose appears
safe, then reverse its decision later based on more data. Similarly, it
may reverse an initial assessment that a dose is unsafe.
A dose-finding method based on posterior probabilities of toxicity is
not strictly a dose escalation
method because it can explore in two
directions. It may decide that the next dose level to explore is higher
or lower than the current level.
Starting at the lowest dose
In Phase I studies of chemotherapeutics, you conventionally start at the
lowest dose. This makes sense. These are toxic agents, and you naturally
want to start at a dose you have reason to believe isn’t too toxic. (NB:
I say “too toxic” because chemotherapy is toxic. You hope that it’s
toxic to a tumor without being too toxic for the patient host.)
But on closer inspection maybe you shouldn’t start at the lowest dose.
Suppose you want to test 100 mg, 200 mg, and 300 mg of some agent. Then
100 mg is the lowest dose, and it’s ethical to start at 100 mg. Now what
if we add a dose of 50 mg to the possibilities? Did the 100 mg dose
suddenly become unethical as a starting dose?
If you have reason to believe that 100 mg is a tolerable dose, why not
start with that dose, even if you add a lower dose in case you’re wrong?
This makes sense if you think of dose-finding, but not if you think only
in terms of dose escalation. If you can only escalate, then it’s
impossible to ever give a dose below the starting dose.
I have heard, but I haven’t been able to confirm, that the 3+3
method has its origin in a method proposed by John Tukey during WWII for
testing bombs. When testing a mechanical system, like a bomb, there is
much less uncertainty than when testing a drug in a human. In a
mechanical setting, you may have a lot more confidence from three
samples than you would in a medical setting.
How do you explain the situation where one out of three has an
adverse reaction? Is the dose safe or not? Here you naturally switch to
probabilistic thinking because deterministic thinking leads to a