Statistical illiteracy abounds in society, and nowhere is it more evident than in the screaming headlines this afternoon about “Floyd Landis’ failed drug test”. OK, so this statistical illiteracy is a pet peeve of mine, so let me scratch it here. Cyclists face a two-tier drug test, A and B. If you have an anomalous result in A, then you get a test on your backup B sample. On the night of his mind-boggling stage win in the Alps, Landis was tested (is it true that all stage winners are tested on the day? I think so). His ratio of testosterone/epitestosterone was high; they test for this because if you are testosterone doping (i.e., through patches etc.) it will mess up your ratio, which for most folks is normally around 1:1 but can be higher for endurance athletes. This year the UCI has changed the trigger ratio from 6:1 to 4:1.
Problem is, it’s a ratio (and you economists out there know the problem of drawing inferences about X and Y separately by looking at the ratio X/Y). According to the reports I’ve read this afternoon, Landis’ ratio was high not because of high testosterone; his testosterone was at normal levels, but his epitestosterone levels were extremely low. Epitestosterone cannot be turned into testosterone in the body. So it’s possible that the result is from too low a Y and not a too high X.
How can this be? Two of the things that can affect epitestosterone are alcohol and cortisone. We know that Landis had a beer the night before the stage because he was so upset at his bonking on that stage. We also know that Landis is legally taking cortisone shots for his half-dead hip.
If you want background information, see this American Statistical Assocation article on false positives in testosterone testing and other issues of testosterone testing. The article does a very nice job of discussing Bayes’ Rule and its importance in assessing probability of guilt, in the context of Mary Decker Slaney’s testosterone results at the 1996 US Olympic Trials; epitestosterone levels have a very high variance in women, particularly athletes (that’s why I know so much about this subject).
Two things boggle my mind on this. One is that the admittedly tainted sport of cycling has led to the media immediately leaping to the conclusion that Landis behaved illegally, when the correct inference to make from the data does not necessarily support that conclusion. At this point we cannot reject that conclusion, but it doesn’t sell stories to be statistically literate, does it? The other is that the UCI has publicized the results of the A test (although it was Landis’ team that identified him by name) before they have run the B test. That is unprofessional, and raises the criticism of the anti-American bias of French cycling. It would be better for the sport if riders did not attempt to enhance their performance illegally, and it would also be better for the sport if its organizers behaved with more professionalism and respect for statistical evidence.
If you want to keep up with this story in a non-histrionic and knowledgable place, I recommend tdf blog, which right now has several posts with very useful links (I got the ASA link from there).