You’ll often hear Phase I **dose-finding** trials referred to as **dose escalation** studies. This is because simple dose-finding methods can only explore in one direction: they can only escalate.

## Three-plus-three rule

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 [1].

## Deterministic thinking

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 [2].

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 three samples.

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 is toxic.

## Bayesian dose-finding

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.

## Related posts

[1] 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.

[2] 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 contradiction.

Dr. Cook,

Great article, I have a question for you, in the case of small populations, such as rare diseases or paediatrics, is there any way to apply Bayesian dose-finding?

Yes. Bayesian dose-finding methods are especially useful for rare diseases because a large portion of the population, maybe the entire population, is part of the study.

Conventional methods say to start with a sample in a clinical trial. The priority for treating this group is to learn as much as we ethically can, not to treat the patients in the trial as effectively as possible. We learn effectively in the trial so we can treat effectively in the population. But when the trial group and the population are synonymous, we need to mix learning and effective treatment, and Bayesian adaptive methods can do that.