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, Pn, which complements the random allocation proportion. We then use Pn 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 Pn to the asymptotic mean entropy under normality. Then we explore whether both Pn, as well as the allocation proportion, may have zero asymptotic variance.
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