How Drug Tests Work

Track fans may be aware of the news of a failed drug test by Bernard Lagat, generally regarded as a great guy. Lagat denies taking EPO, while sportswriters are ready to condemn immediately. It might be useful to look at how the numbers work.
It’s hard to find accurate measures of the effectiveness of the EPO test. The test creators claim extraordinary specificity (only finds EPO) and sensitivity (no “false positives” – a finding that EPO is present when in fact it is not) in 3500 cases. However, other authors are more conservative (and realistic) in accuracy claims. To get a feel for the numbers, let’s say the test is 99.5% accurate.And for discussion, let’s say one in two thousand athletes actually use EPO. (No-one knows the real number of users.)
Suppose 10,000 athletes get tested. If an athlete gets a positive test for EPO (which is 99.5% accurate, remember), what is the real likelihood he or she is taking EPO?
All 5 athletes taking EPO are caught.
That 0.5% of 10,000 results in 50 athletes who aren’t taking EPI being “caught.”
So a total of 55 athletes have a positive test. Being caught means you have a 1-in 11 chance of being a cheater. Said another way, you have a 91% chance of being falsely accused.
As I said above, I don’t know the real numbers. But a positive test for a drug doesn’t mean someone has taken the drug. If the numbers above are right, in fact, it would mean about a 90% chance of not taking the drug.
All this assumes no human error – no mislabeled or mistakenly switched samples, no contamination in the lab, everything goes exactly perfectly.
Please don’t judge until all the evidence is in. (9/6)

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