Minimizing selection bias in randomized trials: A Nash equilibrium approach to optimal randomization

Randomized trials can be compromised by selection bias, particularly when enrollment is sequential and previous assignments are unmasked. In such contexts, an appropriate randomization procedure minimizes selection bias while satisfying the need for treatment balance. This paper presents optimal randomization mechanisms based on non-cooperative game theory and the statistics of selection bias. For several different clinical trial examples, we examine subgame-perfect Nash equilibrium, which dictates a probability distribution on suitable assignment sequences. We find that optimal procedures do not involve discrete uniform distributions, because minimizing predictability is not equivalent to minimizing selection bias.