The properties of entropy as a measure of randomness in a clinical trial

Abstract We study entropy as a measure of randomness in a sequential clinical trial. For any randomization design, we consider the well-known sequence of conditional treatment assignment probabilities, P n , which complements the random allocation proportion. We then use P n to formulate and prove a statement about conditions for the asymptotic mean entropy of a randomization design to achieve its optimum value. We compare both response-adaptive and non response adaptive randomization designs with respect to the asymptotic mean entropy, connecting the variance of P n to the asymptotic mean entropy under normality. Then we explore whether both P n , as well as the allocation proportion, may have zero asymptotic variance.