Bayes’ Theorem and drugs in sport.

I’ll preface this by saying both that IANAS* and that I’m not suggesting this is why so many athletes seem baffled by a positive test I just thought it was interesting and definitely worth thinking about…

The short story is that if a drug test is less than 100% accurate and the actual prevalence of the drug use in the population is very low then false positives will outweigh true positives and the probability of a positive test being an actual drug user may be very low indeed. A second test will increase the probability of a positive test being a true positive but only if the two tests are conditionally independent i.e. there isn’t some factor other than the presence of the drug that leads to the positive.

A (fairly) simple explanation of this here: https://towardsdatascience.com/bayes-theorem-for-medical-test-f1fb12b579c6
https://towardsdatascience.com/multiple-bayesian-tests-in-row-2e4ad8fb5055

I’m not aware of any athlete challenging a positive test on this basis but it looks like it’s got legs if only as a way of muddying the waters which is a pretty common tactic.

I always assumed that B sample tests were to reduce the likelihood of procedural errors and potential contamination but I now wonder if this is the main reason for them?

The other thing I’m wondering is that without knowing the true prevalence of drug use in the tested population it’s very difficult to interpret a result and how on earth does one establish the true prevalence of such a clandestine activity as doping?

Discuss… 🙂

*I Am Not A Statistician so if you are please feel free to chime in.

And a video which explains it visually:

One would hope that this well understood statistical phenomenon is you know well understood.

For some reason I prefer this video

You’d really need to know what the sensitivity and specificity of the doping test were before you could draw similar conclusions

One would hope that this well understood statistical phenomenon is you know well understood.

I’d certainly assume it’s well understood by those designing the testing. Once you get outwith that sphere to those administrating the process and the subjects I wouldn’t be so sure and by the time you get to the general public I’d say most don’t understand it!

All the stuff about COVID testing will have helped public understanding to a degree, it’s how I came to find out about it.