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The uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling

机译：逆向抽样下病例对照研究中优势比的一致最小方差无偏估计

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摘要

The stated goal of this paper is to propose the uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling design. The problem of estimating odds ratio plays a central role in case–control studies. However, the traditional sampling schemes appear inadequate when the expected frequencies of not exposed cases and exposed controls can be very low. In such a case, it is convenient to use the inverse sampling design, which requires that random drawings shall be continued until a given number of relevant events has emerged. In this paper we prove that a uniformly minimum variance unbiased estimator of odds ratio does not exist under usual binomial sampling, while the standard odds ratio estimator is uniformly minimum variance unbiased under inverse sampling. In addition, we compare these two sampling schemes by means of large-sample theory and small-sample simulation.
机译：本文的既定目标是在逆向抽样设计下的病例对照研究中提出比值比的均匀最小方差无偏估计。估计优势比的问题在病例对照研究中起着核心作用。但是，当未暴露的病例和暴露的对照的预期频率可能非常低时，传统的采样方案似乎不足。在这种情况下，使用反采样设计会很方便，因为它要求继续进行随机绘制，直到出现给定数量的相关事件为止。在本文中，我们证明了在通常的二项式抽样中不存在比值比均匀最小方差无偏估计量，而在反采样下，标准比值比估计量是均匀性最小方差无偏量。另外，我们通过大样本理论和小样本仿真比较了这两种采样方案。

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