This book is a good introduction, includes a lot of anecdote from different health care professionals across a range of different testing (including cancer and HIV), and mentions the research across different health care professionals.
Here's an extract: https://imgur.com/zO4zkl4
I'm reminded of Gerd Gigerenzer's book "Reckoning with risk". It's about medical testing, so forgive the language used:
> A condition exists. There is a test for that condition. The test is good, but not perfect. If someone has the condition there is a 90% chance they'll return positive. If someone does not have the condition there is a 1% chance they'll return positive. About 1% of the population have the condition. Bob has the test, and it comes back positive. What's the probability Bob has the condition?
Most people, even doctors who give these types of tests, get this wrong. The answer is about 50%, but most people put it much higher at 99% or 90%.
I think the Guardian reporting is irresponsible because the general public do not understand percentages, and any reporter using percentages is misleading (albeit inadvertantly) the public.
Here's a link to the book: https://www.amazon.co.uk/Reckoning-Risk-Learning-Live-Uncert...