This week, cyclist Floyd Landis admitted to taking performance enhancing drugs, ending a long and expensive legal battle to clear his name and earn back his title as winner of the 2006 Tour de France. In 2008 Nature published a commentary by Donald Berry, the head of the Division of Quantitative Sciences at MD Anderson Cancer Center in Houston, Texas, unpacking what he saw as statistical weakness in the way that Landis’ positive drug tests during the 2006 Tour were analyzed.

Part of Berry’s arguments centre around what’s known as the Prosecutor’s fallacy, which concludes guilt based on an event, such as a positive drug test, because it has a low probability of happening for someone who hasn’t been taking drugs. This subverts Bayesian statistics, he says, which require that a measure of prior probability be calculated in. In doping cases this prior probability is essentially assumed to be 50% — the athlete is as likely to be doping as not. Prior probability comes from factors outside of the laboratory, essentially corroborating evidence, and without a good estimate, tests require extremely good measures of sensitivity and specificity so that one can be confident of the false positive rate. Berry contended these measures had not been well determined. Forensic sciences can often suffer similar problems (see our recent special on the subject).

Berry says he wasn’t particularly surprised by Landis’ admission, but that it doesn’t change the argument about prior probability, nor does it alter his conclusion about lab test procedures. What it does do, he says, is change the prior probability of Landis’ guilt to close to 100%, he says. Landis also alleged that several other riders had been doping. In an email Berry noted a theoretical problem this causes: “An issue is what Landis’s claim that ‘everybody did it’ means about the prior probability for other cyclists, such as Lance Armstrong. On its face it means that the prior probability is 100% for everyone and therefore no other evidence is necessary and no amount of evidence to the contrary could change it.” But, he adds, many have questioned the veracity of Landis’ claim given his long denial about his own use. Armstrong, a seven time Tour de France winner, among others, has denied using drugs.

Image: “velooooooo-vi” from foxtongue via Flickr under creative commons.