Sports medicine clinicians and researchers should all be familiar with the concepts of false positives and false negatives. Research to test a hypothesis about a link between, say, a risk factor and a disease can potentially be wrong in either of two ways. The findings might falsely show a link when in reality one does not exist (a type I or α error), or they might fail to show a link when there really is one (a type II or β error).1 2 Hopefully most of the time, if studies are well conducted, the likelihood of both of these errors is reduced.

Similar errors in both directions can potentially occur in drug testing in sport, although the nature of false positives and false negatives is somewhat different from that in other clinical testing. The rigorous methods of collection and the use of “A” and “B” samples mean that many sources of potential laboratory error are minimised. The false positive and false negative phenomena in doping may be better referenced to the athlete’s intent to cheat using performance-enhancing drugs. An athlete who takes a so-called “undetectable” anabolic steroid is a true “drug cheat”, but one who might produce a “false-negative” drug test because the structure of the undetectable drug is not yet known by the testing authorities. By comparison, the athlete who inadvertently takes a banned drug (particularly one with minimal performance-enhancing potential) not to cheat, but to treat a legitimate medical condition, may test positive in a doping test. Such a result may be considered a “false positive” with respect to intent to cheat using a performance-enhancing drug, even though the testing process was accurate in finding the drug in the athlete’s system.

Intent to cheat is so difficult to prove or disprove that WADA takes a pragmatic approach and enforces strict liability for all positive tests.3 Strict liability means that denying intention to cheat is not relevant if the results of a drug test are positive. If the excuse of lack of intention was generally accepted, most true cheats would deny intent and many would escape prosecution as a result. History suggests, though, that there are some drug suspensions which were probably false positives with respect to intent to cheat. Perhaps the first such case was Rick DeMont of the USA, who lost a swimming gold medal after apparently being prescribed ephedrine by his team doctor to treat asthma at the Munich Olympics in 1972. A similar case saw Andrea Raducan of Romania stripped of her Olympic gold medal in gymnastics in 2000 after a positive test for pseudoephedrine, apparently taken as a medication to treat a cold.

Babette Pluim has recently highlighted cases of suspected false positives from the sport of tennis.4 Alarmingly, it was calculated that as many as 68% of the doping charges in tennis over the previous 5 years were false positives.4 Glucocorticoids were one of the major classes responsible for the suspected false positive cases. Because glucocorticoids are extremely commonly used in general medicine and have not been shown to enhance performance in humans,4 it can be strongly argued, using Bayes’ theorem, that this drug class is particularly likely to produce false positive results.

Bayes’ theorem, developed centuries ago by an English clergyman, is a formula to calculate “positive predictive value” (the likelihood that a positive test actually represents a true positive).1 The numerator is the number of true positive cases with the denominator being the sum of both true positive and false positive cases. One of the principles of Bayes’ theorem is that the likelihood of a positive result being a true positive is proportional to the prevalence of the condition being tested for in the sample population. The principles of Bayes’ theorem are used for screening in other areas of medicine, like cancer detection.5 Mammograms, for example, are recommended for postmenopausal women, but not for younger women. This is because breast lesions detected by mammogram in older women are somewhat likely to be malignant (because the prevalence of breast cancer is relatively high). By comparison, breast lesions in younger women are extremely likely to be benign (because the prevalence of breast cancer is very low). It is generally calculated by screening experts that a mammogram performed in a young woman is much more likely to cause harm (by falsely identifying a suspicious lesion which is, in fact, benign) than it is to lead to benefit (by identifying a suspicious lesion which is a true malignancy).5 As women get older and breast cancer becomes more likely, then the value of screening tests, such as mammograms, increases. In sports medicine, Bayes’ theorem has been used to argue against routine ECG screening of asymptomatic young athletes.6

Bayes’ theorem as it applies to drug testing can be demonstrated by considering a theoretical population of 10 000 elite athletes and two theoretical drugs which we can call “G” and “A”. Drug “G” is a glucocorticoid and is commonly used to treat medical conditions such as asthma and sinus congestion. Therapeutic use exemption (TUE) is available for athletes who have been prescribed the drug legitimately by a doctor. Because its performance-enhancing effects are not well documented, it is banned and it is also easy to detect in urine, cheats rarely choose to use this drug. Drug “A” is a synthetic anabolic steroid that is strongly performance-enhancing and is only manufactured underground, so virtually never prescribed by medical practitioners. TUEs are not ever granted for drug “A”. However, it is potentially a contaminant of supplements made in countries with poor drug regulations, so that a false positive with respect to intent to cheat is very rare but possible. Table 1 shows hypothetical numbers out of the 10 000 athletes with the two drugs in their system at the time of testing, and the positive predictive value of the drug testing. Using Bayes’ theorem to calculate positive predictive value, it can be shown that most positive tests to drug “A” are true positives with respect to intent to cheat, whereas most positive tests to drug “G” are in fact inadvertent positives with no intent to cheat.

Can Bayes’ theorem assist us in determining which drugs should be on the banned list? Since WADA enforces strict liability, it makes sense that drugs which are on the banned list should have a user profile somewhat similar to drug “A”. If a drug has a user profile similar to drug “G” then, by enforcing strict liability, WADA would need to suspend many potentially innocent (albeit careless) athletes in order to punish a small number of true cheats. Therefore a drug with a profile similar to “G” probably should not be on the banned list, or, if it is, strict liability should not apply.

There are some drugs which are currently on the banned list with a profile most similar to drug “G”. They are commonly used in medicine and have minimal or dubious performance enhancement qualities.3 4 Glucocorticoids are the best example but some mild stimulants, such as β₂-agonists, would also be far more likely to have legitimate (as opposed to illegitimate) use. Because of their common use in the medical treatment of athletes, WADA does permit use of such drugs by the TUE process. However, Bayes’ theorem suggests that any athlete who tests positive to a glucocorticoid is more likely to have legitimately used this drug for a medical condition than for any attempt to cheat, irrespective of whether a TUE was completed/accepted or not. It is easy to think of fairly common scenarios where such a use might occur: e.g. an athlete who has asthma might borrow a puffer from a friend which contains a banned glucocorticoid; or alternatively he or she may be prescribed such a medication by a medical practitioner who is unaware of the WADA code. Are there drug cheats who attempt to use glucocorticoids to enhance performance? Perhaps, but they are probably rare, particularly given that well-informed drug cheats would try to avoid drugs that they know are banned and regularly tested for. Glucocorticoids are catabolic agents and probably lead to performance detriment in most sports if they are used over the medium to long term.3 Even if there is a small (and currently unproven) performance-enhancing effect of these drugs in the short term and therefore the potential for misuse, there is certainly also a huge pool of legitimate medical use. Bayes’ theorem therefore suggests that a positive test for these drugs is more likely to be a case of legitimate or inadvertent use than a case of true cheating.

Bayes’ theorem can therefore be used to argue either that drugs such as glucocorticoids should not be on the banned list, or, if they remain on the banned list, that strict liability should not apply to these drugs. Currently the three criteria to consider when placing a drug on the banned list are: (1) that the substance is performance-enhancing; (2) that there are health risks to the athlete with use of the substance; (3) that use of the substance violates the spirit of sport. Perhaps a further criterion should be added: (4) that the presence of the substance in an athlete’s sample is more likely to represent a case of attempted cheating than of genuine medical use.

Ever increasing resources are being devoted to the problem of false negatives – that is, trying to catch more actual cheats and stop them avoiding detection and sanction. Perhaps if drugs which are more commonly found in the systems of legitimate competitors than drug cheats were removed from the banned list, this would allow a greater degree of resources to be devoted to the drugs that are more likely to represent true cases of cheating.