Saturday, November 20, 2010

The trouble with screening

A math problem:

There exists a deadly condition that arises sporadically affecting 1% of the population. There exists a blood test for it that is 95% accurate i.e. 5% false positives and 5% false negatives (rarely are these numbers the same: more false negatives for pregnancy tests than false positives, for example). You have recently tested positive for this condition. How scared should you be? What are the chances you really have this condition?


The last number.

You have 1000 random people. Only 10 of them truly have the disease. Of the 990 people who don't have the disease, 49 test positive falsely. Altogether, about 60/1000 test positive. Your chances of being a true positive therefore is around 1 in 6.

Of course we are assuming no bias meaning you are not in subgroup more at risk for this condition. We also have to assume that early detection will influence the course of the disease otherwise there is no point in screening.

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