“Math is hard. Let’s Go Shopping!” Barbie
Each of our patients has to make decisions about their heath based on their assessment of the risks and benefits of proposed treatments. Will I take this course of tablets? Will I give up smoking? Will I have that operation?
To assist patients, doctors provide information about treatment options, based on their knowledge of medicine, the particular circumstances of the patient, clinical studies, and their own experience. But doctors are hampered in their ability to communicate risk in an understandable way by their own ‘statistical innumeracy’ and by the inadequate ‘mind tools’ they have been taught to deal with statistical probabilities.
So argues psychologist Gerd Gigerenzer , who has performed many studies on the miscommunication of risk. In his book ‘Reckoning with Risk’, Prof Gigerenzer argues that we can overcome innumeracy using three kinds of mind tools:
i) Franklin’s law (‘in this world nothing is certain but death and taxes’) to overcome the illusion of certainty;
ii) devices for communicating risk intelligibly;
iii) the use of natural frequencies for turning clouded thinking into insight.
To illustrate, the Prof conducted a study on 48 experienced physicians. He supplied them with information concerning asymptomatic woman aged 40-50 who participate in mammographic screening. Half were given the information in traditional conditional probabilities:
The probability that one of these woman has breast cancer is 0.8%. If a woman has breast cancer the probability is 90% that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7% that she will have a positive mammogram.
Your patient has a positive mammogram. What is the probability that she actually has breast cancer?
Given information presented in this form, only two physicians reasoned correctly (I’ll keep you in temporary suspense as regards the correct answer). One third concluded that the probability of breast cancer given a positive mammogram was 90%. The median estimate was 70%. The answers were highly inconsistent.
Prof Gigerenzer eschews percentages and probabilities in favour of ‘natural frequencies’. The other 24 physicians were given the information in ‘Natural Frequencies’ form.
Eight out of every 1000 woman have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don’t have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?
It is now (comparatively) easy to see what the answer is. (Work it out before you continue reading!)
77 woman will test positive, but only 7 of these will actually have breast cancer, which is 1 in 11, or 9% – much lower than the estimate provided by the majority of the ‘probabilities’ group. In the natural frequency group, the majority of the physicians responded with the correct answer, or close to it. Only five of the physicians (hopeless cases?) concluded that the chance of having breast cancer given a positive mammogram was above 50%.
The professor offers many other cases where good numeric representation is a key to effective thinking.
When prescribing Prozac to patients, considerable anxiety arose when they were told by their psychiatrist that 30-50% would develop a sexual problem. He was surprised that many did not question him further about this. It transpired that many patients thought that something would go awry in 30-50% of their sexual encounters! When the same risks were presented differently – ‘of every 10 patients to whom I prescribe Prozac, 3-5 will develop a sexual problem’ – patients understood and then asked appropriate questions to determine a course of action if they were one of those group. Compliance is aided by accurate communication.
Using natural frequencies assists decision making by patients. For example, in otitis media without systemic symptoms in children over two, we can inform parents that of every 20 children with ear aches like their child has, 19 will get better just as quickly without antibiotics. It makes good sense to them to delay treatment, especially given that of every 12 kids we give antibiotics to, one will get a significant side effect.
Pharmaceutical marketing is rife with the use of conditional probabilities, especially in relation to relative risk. The West of Scotland Coronary Prevention Study was presented in a press release as showing a 22% reduction of the risk of death if people with high cholesterol (>6.5) took Pravastatin. The majority of people interpret this as meaning that if 1000 people with high cholesterol take Pravastatin, 220 of these people can be prevented from dying from a heart attack. In fact, Pravastatin reduced the number of deaths per 1000 from 41 to 32 over the five years of the study. Different presentations of the same data have different effects on our decision making.
1) There is an absolute risk reduction with Pravachol of 9 in 1000, which is 0.9%
2) There is a relative risk reduction with Pravachol of 9/41 = 22%
3) The number of people who must be treated to save one life (the NNT) is 111.
These findings are still significant, but presenting information in different forms will lead to a different response from our patients. In many cases, where the actual incidence of an adverse outcome is very low, the discrepancy can be outstanding. Dr Chris Cate, gives an example on his EBM website concerning reports of DVT on new OCP treatments. “Switching users of third generation OCP pills to a second generation equivalent will result in an impressive sounding Relative Risk Reduction for DVT of 40%, but as the risk of DVT is so low the Absolute Risk Reduction is only 0.0001 giving an NNT of 10,000 women needing to be changed to prevent a single DVT in one year.” It is true that buying two tickets in lotto doubles your chance of winning – however, you’ve still got Buckley’s.
At the beginning of the last century, HG Wells is reported to have predicted “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”. In this century, Prof Gigerenzer challenges our innumeracy, encouraging us to ‘dare to know’ through the habit of sound statistical thinking. He advises us to insist on receiving appropriate numeric representation and to develop the tools to communicate risk accurately to our patients.
Gigerenzer, G ‘Reckoning the Risk’, 2002, Penguin Books
Glasziou PP, Hayem M, Del Mar CB. Antibiotic versus placebo for acute otitis media in children (Cochrane Review). In: The Cochrane Library, Issue 4, 1998. Oxford: Update Software As reported at Antibiotics for Acute OM in children – CAT
Dr Chris Cate’s EBM Website – http://www.nntonline.net