The short answer in many cases is “no”:
In one session, almost half the group of 160 gynaecologists responded that the woman’s chance of having cancer was nine in 10. Only 21% said that the figure was one in 10 – which is the correct answer. That’s a worse result than if the doctors had been answering at random.
The fact that 90% of women with breast cancer get a positive result from a mammogram doesn’t mean that 90% of women with positive results have breast cancer. The high false alarm rate, combined with the disease’s prevalence of 1%, means that roughly nine out of 10 women with a worrying mammogram don’t actually have breast cancer.
It’s a maths puzzle many of us would struggle with. That’s because, Gigerenzer says, setting probabilities out as percentages, although standard practice, is confusing. He campaigns for risks to be expressed using numbers of people instead, and if possible diagrams.
Graphic showing “false positives” in mammogram tests
Even so, Gigerenzer says, it’s surprising how few specialists understand the risk a woman with a positive mammogram result is facing – and worrying too. “We can only imagine how much anxiety those innumerate doctors instil in women,” he says. Research suggests that months after a mammogram false alarm, up to a quarter of women are still affected by the process on a daily basis.
Survival rates are another source of confusion for doctors, not to mention journalists, politicians and patients. These are not, as you might assume, simply the opposite of mortality rates – the proportion of the general population who die from a disease. They describe the health outcomes of people who have been diagnosed with a disease, over a period of time – often five years from the point of diagnosis. They don’t tell us about whether patients die from the disease afterwards.
The linked article is worth reading despite its implicit pro-NHS boosterism. See also this. The poor education in statistical analysis of doctors, lawyers, journalists and members of other influential groups in our society is a significant problem.
UPDATE: Gerd Gigerenzer’s Books