Wednesday, 6 April 2011

Science: Numbers Game

Will you a quiz for me today? Of course you will. Here goes then...

If you take a HIV blood test which is 99% accurate and the result comes positive (i.e. you are HIV positive), how likely are you to actually still be happily HIV negative assuming there is around 2% of people who actually are HIV positive (i.e. really positive, not just tested positive)? Of course, the reality is much brighter - provided you live in a place like US which has incidence of HIV positive people between 0.2 and 0.4%. Sadly, if you live in sub-Saharan Africa you may be looking at double digits. But anyway... I've given you enough time to work out the original problem now, so out with the answers! And no, it is not 99%. You may well be surprised that the answer is 33.1%. If you don't believe me the good people at Intuitor have worked it out for you. Just hop over there and have a look. It even has pictures. In colour, too. So, now that you (hopefully) believe me (and them) what should you do if you want an HIV test? Is it still worth doing? Of course it is. What you need to do if you tested positive is to repeat it, and if you want to be really sure, repeat it again. Every time you do that you slash your likelihood of a false positive considerably.

So, as you hopefully now realise, not everything is as it seems, but science wins every time...

PS
Some assumptions made above: you do not belong to a known high risk group (e.g. intravenous drug user, having unprotected sex with a stranger), and that probability of false positive is the same as the probability of the false negative. The former considerably decreases probability of a false positive as the incidence grows from 2% to something much, much higher. The latter not so much because the difference in probabilities is usually not too great. Either way, if you know the incidence rates in your group and more details about the test procedure, you just plug different numbers into Intuitor calculation, and Bob's your Uncle. However, the result you get is very, very unlikely to be the headline 99%...