“Many randomized studies in small patient populations and studies in early research (such as Phase I and Phase II trials) have small to moderate numbers of patients. In such studies the use of simple randomization or blocking on only one or two factors can easily result in imbalance between treatment groups with respect to one or more potentially prognostic variables. Baseline adaptive randomization methods (such as biased coin methods) can be used to virtually guarantee balance between treatment groups with respect to several covariates.”

This quote comes from the abstract of a paper by James Frane, and I couldn’t resist quoting it because he explains the issue so succinctly. The method he describes is an incredibly intuitive biased coin adaptive randomization that can accommodate multiple balancing factors—including continuous measures. After you randomize a few subjects, you start looking at the subject’s characteristics you’ve identified as important to balance.

Let’s take a simple example of age as the balancing factor and two treatment groups to randomize to. You calculate two p-values based on a t-test comparing the distribution of age between your two treatment groups. The first p-value is calculated based on putting the subject into the first treatment group and the second p-value is calculated based on putting the subject into the second treatment group. Now, you set your “biased coin” probability of randomization to treatment 1 to p1/(p1+p2). In our example, let’s assume that putting our subject in treatment group 1 results in a p-value comparing the age distributions of 0.15 and that putting s/he in treatment group 2 gives us a p-value of 0.52. We then randomize to treatment 1 with probability 0.15/(0.15+0.52)=0.22 and treatment 2 with probability 0.78.

I must confess to having a moment of backwards thinking because I’m so conditioned to thinking that a low p-value indicates “good” that I couldn’t understand why the higher probability went to the higher p-value. But in this case, we want balance, not difference, so bigger p-values are better.

Frane goes on to explain how this method can be applied for multiple balancing factors. Then he runs the method through a randomization test to show that this doesn’t affect your analysis results at the end of the study.

I love this article—it’s clear, concise and covers all the bases. I definitely recommend checking it out.

Frane, J W (1998) “A Method of Biased Coin Randomization, Its Implementation, and Its Validation” DIJ Vol 32, pp 423-432