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.

我们研究熵作为顺序临床试验中随机性的度量。对于任何随机化设计，我们考虑众所周知的条件治疗分配概率序列，${磷}_n$，它补充了随机分配比例。然后我们使用${磷}_n$制定并证明有关随机化设计的渐近平均熵达到其最佳值的条件的陈述。我们比较了关于渐近平均熵的响应自适应和非响应自适应随机化设计，连接方差${磷}_n$到正态下的渐近平均熵。然后我们探讨两者是否${磷}_n$，以及分配比例，可能具有零渐近方差。