Statistical rationale for a 3+3 design

Question

I am starting to learn about design of experiments for clinical trials and in particular I am interested in understanding the statistical rationale for the 3+3 design used for dose escalation in Phase I of a clinical trial.

Basically, this is what a 3+3 design is:

1) Treat group of 3 patents sequentially, starting with the minimum dose

2) Escalate the dosage if no toxicity is observed in all 3 patients; otherwise an additional 3 patients are treated at the same dose level

3) If 1/6 patients has toxicity, escalate; if 2/6 patients have toxicity, declare the current dose as the maximum tolerable dose (MTD); if more that 2/6 patients have toxicity, use the lower dose as the MTD

The idea seems very basic to me, but I cannot understand why this seems like a good idea (i.e., 3 people seems like a very small sample size) and if there is any statistical rationale to this idea. Anyt thoughts on this?

Answer 1

I am not an expert in this, but, on top of Hansen et al in Cancer Control 2014, recommended above by Matthew Lau, there are some other interesting papers or guidances which provide the background on the 3 + 3 design, references to papers highlighting some of its limitations, and suitable alternatives:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2684552/pdf/djp079.pdf

http://www.fda.gov/downloads/biologicsbloodvaccines/guidancecomplianceregulatoryinformation/guidances/vaccines/ucm278673.pdf

https://www.mdanderson.org/education-and-research/departments-programs-and-labs/departments-and-divisions/division-of-quantitative-sciences/lectures-and-seminars/yingyuan-biostatgr-may2013.pdf

See for instance table 2 from Le Tourneau et al, J Natl Cancer Inst 2009:

Intriguingly, it appears that the 3 + 3 rule is derived at least in part by Fibonacci sequence as reported in the 13th Century:

https://en.wikipedia.org/wiki/Fibonacci_number

Answer 2

The answer isn't as much about statistics as it is about common sense. If you're working with people, the number one concern should be safety. When trying out a new drug, or testing a substance to the maximum possible level until toxicity is detected, you don't want to be injecting hundreds of people. You want to keep the group small. Once you have reasonable assurance that a dose is safe, you can increase the group. This is where the statistics part comes in (i.e. bigger population is better for generalization). If toxicity is detected, the group is increased but at the same dosage to either confirm the original findings or show that it is in fact safe to continue the trial at a higher dosage.

But to start with a big group of people when the initial dose could already cause toxicity in the human body would be irresponsible.