cancer is another disease for which we have good data. In the U.S. and
European countries doctors advise men aged 40 to 50 to take a PSA test.
This is a prostate cancer test that is very simple, requiring just a
bit of blood, and so many people do it. The interesting thing is that
most of the men I've talked to have no idea of the benefits and costs
of this test. It's an example of decision-making based on trusting your
doctor or on rumors. But interestingly, if you read about the test on
the Internet in independent medical societies like Cochran.com, or read
the reports of various physicians' agencies who give recommendations
for screening, then you find out that the benefits and costs of prostate
cancer screening are roughly the following: Mortality reduction is the
usual goal of medical testing, yet there's no proof that prostate cancer
screening reduces mortality. On the other hand there is proof that,
if we distinguish between people who do not have prostate cancer and
those who do, there is a good likelihood that it will do harm. The test
produces a number of false positives. If you do it often enough there's
a good chance of getting a high level on the test, a so-called positive
result, even though you don't have cancer. It's like a car alarm that
goes off all the time.
very puzzling that in a country where a 12-year-old knows baseball statistics,
adults don't know the simplest statistics about tests, diseases, and
the consequences that may cause them serious damage. Why is this? One
reason, of course, is that the cost benefit computations for doctors
are not the same as for patients. One cannot simply accuse doctors of
knowing things or not caring about patients, but a doctor has to face
the possibility that if he or she doesn't advise someone to participate
in the PSA test and that person gets prostate cancer, then the patient
may turn up at his doorstep with a lawyer. The second thing is that
doctors are members of a community with professional pride, and for
many of them not detecting a cancer is something they don't want to
have on their records. Third, there are groups of doctors who have very
clear financial incentives to perform certain procedures. A good doctor
would explain this to a patient but leave the decision to the patient.
Many patients don't see this situation in which doctors find themselves,
but most doctors will recommend the test.
Thus, dealing with probabilities also relates to the issue of understanding the psychology of how we make rational decisions. According to decision theory, rational decisions are made according to the so-called expected utility calculus, or some variant thereof. In economics, for instance, the idea is that if you make an important decision whom to marry or what stock to buy, for example you look at all the consequences of each decision, attach a probability to these consequences, attach a value, and sum them up, choosing the optimal, highest expected value or expected utility. This theory, which is very widespread, maintains that people behave in this way when they make their decisions. The problem is that we know from experimental studies that people don't behave this way.
There is a nice story that illustrates the whole conflict: A famous decision theorist who once taught at Columbia got an offer from a rival university and was struggling with the question of whether to stay where he was or accept the new post. His friend, a philosopher, took him aside and said, "What's the problem? Just do what you write about and what you teach your students. Maximize your expected utility." The decision theorist, exasperated, responded, "Come on, get serious!"