Exact statistical calculation of the uncertainty term in the decision limits of the GH-2000 score for growth hormone misuse (doping) detection:

The GH-2000 score has been developed as a powerful and unique technique for the detection of growth hormone misuse by sportsmen and women. The score depends upon the measurement of two growth hormone sensitive markers, insulin-like growth factor-I and the amino-terminal pro-peptide of type III collagen. It also includes a term to adjust for the age of the athlete. Decision limits for the GH-2000 score have been developed and are incorporated into the guidelines of the World Anti-Doping Agency. These decision limits are derived by setting a 1 in 10,000 false-positive rate rule. As these decision limits are estimated from samples of GH-2000 scores, they carry uncertainty. In previous work, this uncertainty has been addressed by establishing an upper 95% confidence interval for the true decision limits based on a normal approximation which has been shown to be appropriate if sample sizes are large (such as 1000 and above). Here, we show that these approximations, whether reasonable or not, can be entirely av...