This paper is motivated by the GH-2000 biomarker test, though the discussion is applicable to other diagnostic tests. The GH-2000 biomarker test has been developed as a powerful technique to detect growth hormone misuse by athletes, based on the GH-2000 score. Decision limits on the GH-2000 score have been developed and incorporated into the guidelines of the World Anti-Doping Agency (WADA). These decision limits are constructed, however, under the assumption that the GH-2000 score follows a normal distribution. As it is difficult to affirm the normality of a distribution based on a finite sample, nonparametric decision limits, readily available in the statistical literature, are viable alternatives. In this paper, we compare the normal distribution-based and nonparametric decision limits. We show that the decision limit based on the normal distribution may deviate significantly from the nominal confidence level 1 - α or nominal FPR γ when the distribution of the GH-2000 score departs only slightly from the normal distribution. While a nonparametric decision limit does not assume any specific distribution of the GH-2000 score and always guarantees the nominal confidence level and FPR, it requires a much larger sample size than the normal distribution-based decision limit. Due to the stringent FPR of the GH-2000 biomarker test used by WADA, the sample sizes currently available are much too small, and it will take many years of testing to have the minimum sample size required, in order to use the nonparametric decision limits. Large sample theory about the normal distribution-based and nonparametric decision limits is also developed in this paper to help understanding their behaviours when the sample size is large.

中文翻译：

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GH-2000 分数基于正态分布和非参数决策限的比较，用于检测运动中生长激素滥用（兴奋剂）

本文的动机是 GH-2000 生物标志物测试，尽管该讨论适用于其他诊断测试。GH-2000 生物标志物测试已被开发为一种强大的技术，可根据 GH-2000 分数检测运动员是否滥用生长激素。GH-2000 分数的决定限制已经制定并纳入世界反兴奋剂机构 (WADA) 的指导方针。然而，这些决策限是在 GH-2000 分数服从正态分布的假设下构建的。由于难以基于有限样本确定分布的正态性，因此在统计文献中很容易获得的非参数决策限是可行的替代方案。在本文中，我们比较了基于正态分布和非参数决策限。我们表明，当 GH-2000 分数的分布仅略微偏离正态分布时，基于正态分布的决策限制可能会显着偏离名义置信水平 1 - α 或名义 FPR γ。虽然非参数决策限制不假设 GH-2000 分数的任何特定分布，并且始终保证名义置信水平和 FPR，但它需要比基于正态分布的决策限制大得多的样本量。由于 WADA 使用的 GH-2000 生物标志物测试的严格 FPR，目前可用的样本量太小，需要多年的测试才能达到所需的最小样本量，以便使用非参数决策限.