A probabilistic analysis of multiple-drug testing procedures in sports doping control

Athletes engaged in competition, particularly those involved in international competitions such as the Olympics, are increasingly being tested for a greater variety of banned substances; it is not unusual for tests to be conducted for 100 drugs and another 400 as metabolites. Previous studies related to the accuracy of drug testing processes have failed to properly consider the effects of testing for more than one drug. In order to identify appropriate indicators for the multiple-drug case, probability theory and accuracy concepts applicable to testing for multiple drugs are developed and applied to illustrative data. The probability that a drug-free individual will test positive for drug use is shown to be much higher than indicated by previous studies, and it is shown that an increase in the number of drugs tested for yields an approximately proportionate increase in the probability that a positive test result is erroneous. Therefore, while testing for one drug may result in a comfortably low rate of false accusations of drug use, testing for multiple drugs may well result in an unacceptably high rate. Finally, a set of empirical measures is suggested for use in cases of tests for multiple drugs; the measures will provide for comparability among laboratory proficiency studies.