Chang M N, Wieand H S, Chang V T
Department of Statistics, University of Florida, Gainesville 32611.
Stat Med. 1989 May;8(5):563-70. doi: 10.1002/sim.4780080505.
Group sequential testing procedures have seen wide use in Phase II clinical trials. The sample proportion p of responders is the commonly used estimator for the binomial response probability p. It can be shown that p is the maximum likelihood estimator (MLE) of p. It is well known that MLE can be in general (Whitehead) and p in particular (Dupont) biased estimators, if ther computation follows a group sequential procedure. In this paper we numerically investigate the bias of p. We find that the magnitude of the bias of p is less than 0.025 in all cases we investigated. We apply the idea in Whitehead to propose a bias-adjusted estimator that reduces the bias substantially and reduces the mean square error as well in a certain range of p. We also evaluate the uniformly minimum variance unbiased (UMVU) estimator. If one does not mind a bias of 0.025, one may find the sample proportion a suitable estimator for p because of its simplicity and easy explanation. If one is concerned with bias, the bias-adjusted estimator may be a good choice.
序贯检验程序在II期临床试验中得到了广泛应用。响应者的样本比例p是二项式响应概率p常用的估计量。可以证明，p是p的最大似然估计量（MLE）。众所周知，如果计算遵循序贯检验程序，MLE一般（怀特黑德）尤其是p（杜邦）可能是有偏估计量。在本文中，我们对p的偏差进行了数值研究。我们发现在我们研究的所有情况下，p的偏差幅度均小于0.025。我们应用怀特黑德的思想提出了一种偏差调整估计量，该估计量在一定的p范围内能大幅减少偏差并降低均方误差。我们还评估了一致最小方差无偏（UMVU）估计量。如果不介意0.025的偏差，由于样本比例简单且易于解释，人们可能会发现它是p的合适估计量。如果关注偏差，偏差调整估计量可能是个不错的选择。
