The Uniformly Minimum Variance Unbiased Estimator of Response Rate in a Two-Stage Design

二階段設計下反應率之均勻最小變異數不偏估計量

陳嘉民(Chia-Min Chen)

《中國統計學報》 53卷4期 (2015/12) Pp. 262-273

摘要

在賽門二階段設計中，若新藥療效不如預期，則試驗可能在第一階段即提前停止試驗。反之，當第二階段允許進行時，研究人員希望對療效反應率有準確的估計，以作為接下來的確認療效試驗中計算所需樣本數的資訊。在療效反應率的估計上，一般多是採用樣本比例或是最大概式估計量來估計。然而樣本比例會顯著高估療效反應率，反之，最大概式估計量則會出現輕微低估的現象。因此，在第二階段允許進行的情況下，本研究推導出療效反應率之均勻最小變異數不偏估計量，來完全消除估計上的偏差。雖然均勻最小變異數不偏估計量在效率上較樣本比例差，但是卻不像樣本比例存在明顯的偏差。

關鍵字

賽門二階段設計 ； 截斷二項分配 ； 均勻最小變異數不偏估計量

並列摘要

In a Simon's two-stage design, the trial may be terminated early for lack of drug efficacy at the first stage. When the second stage is allowed to continue, an accurate estimate of the response rate is needed for determining the sample size in the subsequent confirmatory trial. It is natural to use either a sample proportion or a maximum likelihood estimator to estimate the true response rate. However, the sample proportion will significantly overestimate the response rate and the maximum likelihood estimator has slight downward bias. Therefore, this paper derives a uniformly minimum variance unbiased estimator for the response rate when the trial continues to the second stage. Due to a trade-off with completely eliminating the bias, the proposed estimator is slightly less efficient than the sample proportion, which has a more significant positive bias.

並列關鍵字

Simon's two-stage designs ； truncated binomial distribution ； uniformly minimum variance unbiased estimator

參考文獻

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