Comparison of normal distribution–based and nonparametric decision limits on the GH‐2000 score for detecting growth hormone misuse (doping) in sport

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 or nominal FPR 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.