It is always a pleasure to read David Colquhoun’s posts.
The most recent explains a simple statistical point that still escapes many health adminisitrators (and others). He describes two tests for Alzheimer’s disease. The first (which I will discuss) is actually a test for mild cognitive impairment (MCI), “a condition that may, but often isn’t, a precursor of Alzheimer’s disease”. This condition has prevalence 1% in the population; the new test has specificity 95% (so only 5% probability of a false positive) and sensitivity 80% (so 20% probability of a false negative). With the help of a tree diagram, he calculates that if the test were used for screening (as is proposed, apparently), 86% of people testing positive would not have the disease.
He is righteously (and rightly) indignant that everything from the journal’s press release to NHS Choices seems to ignore this, which as he says makes the test “worse than useless”.
This is a simple application of Bayes’ Theorem. I taught Probability to the first-year maths students for many years, and calculations like this were a standard example that I used.
How many times do you think Colquhoun mentioned Thomas Bayes (or Richard Price) in his article?
So this post is really a musing on the vagaries of fame in mathematics.