. in this world there is nothing certain but death and taxes.
During a routine medical visit at a Virginia hospital in the mid-1990s, Susan, a 26-year-old single mother, was screened for HIV. She used illicit drugs, but not intravenously, and she did not consider herself at risk of having the virus. But a few weeks later the test came back positive—which at the time amounted to a terminal diagnosis. The news left Susan shocked and distraught: Word of her diagnosis spread, her colleagues refused to touch her phone for fear of contagion, and Susan eventually lost her job. Finally, she moved into a halfway house for HIV-infected patients. While there, she had unprotected sex with another resident, thinking, `Why take precautions if the virus is already inside of you?` Out of concern for her 7-year-old son's health, Susan decided to stop kissing him and began to worry about handling his food. The physical distance she kept from him, intended to be protective, caused her intense emotional suffering. Months later, she developed bronchitis, and the physician who treated her for it asked her to have her blood retested for HIV. `What's the point?` she thought.
The test came back negative. Susan's original blood sample was then retested and also showed a negative result. What had happened? At the time the data were entered into a computer in the Virginia hospital, Susan's original blood test result seems to have been inadvertently exchanged with those of a patient who was HIV positive. The error not only gave Susan false despair, but it gave the other patient false hope.
The fact that an HIV test could give a false positive result was news to Susan. At no point did a health care provider inform her that laboratories, which run two tests for HIV (the ELISA and Western blot) on each blood sample, occasionally make mistakes. Instead, she was told repeatedly that HIV test results are absolutely conclusive—or rather, that although one test might give false positives, if her other, `confirmatory` test on her initial blood sample also came out positive, the diagnosis was absolutely certain.
By the end of her ordeal, Susan had lived for 9 months in the grip of a terminal diagnosis for no reason except that her medical counselors believed wrongly that HIV tests are infallible. She eventually filed suit against her doctors for making her suffer from the illusion of certainty. The result was a generous settlement, with which she bought a house. She also stopped taking drugs and experienced a religious conversion. The nightmare had changed her life.
Prozac's Side Effects
A psychiatrist friend of mine prescribes Prozac to his depressive patients. Like many drugs, Prozac has side effects. My friend used to inform each patient that he or she had a 30 to 50 percent chance of developing a sexual problem, such as impotence or loss of sexual interest, from taking the medication. Hearing this, many of his patients became concerned and anxious. But they did not ask further questions, which had always surprised him. After learning about the ideas presented in this book, he changed his method of communicating risks. He now tells patients that out of every ten people to whom he prescribes Prozac, three to five experience a sexual problem. Mathematically, these numbers are the same as the percentages he used before. Psychologically, however, they made a difference. Patients who were informed about the risk of side effects in terms of frequencies rather than percentages were less anxious about taking Prozac—and they asked questions such as what to do if they were among the three to five people. Only then did the psychiatrist realize that he had never checked how his patients understood what `a 30 to 50 percent chance of developing a sexual problem` meant. It turned out that many of them had thought that something would go awry in 30 to 50 percent of their sexual encounters. For years, my friend had simply not noticed that what he intended to say was not what his patients heard.
The First Mammogram
When women turn 40, their gynecologists typically remind them that it is time to undergo biennial mammography screening. Think of a family friend of yours who has no symptoms or family history of breast cancer. On her physician's advice, she has her first mammogram. It is positive. You are now talking to your friend, who is in tears and wondering what a positive result means. Is it absolutely certain that she has breast cancer, or is the chance 99 percent, 95 percent, 90 percent, 50 percent, or something else? I will give you the information relevant to answering this question, and I will do it in two different ways. First I will present the information in probabilities, as is usual in medical texts.1 Don't worry if you're confused; many, if not most, people are. That's the point of the demonstration. Then I will give you the same information in a form that turns your confusion into insight. Ready?
The probability that a woman of age 40 has breast cancer is about 1 percent. If she has breast cancer, the probability that she tests positive on a screening mammogram is 90 percent. If she does not have breast cancer, the probability that she nevertheless tests positive is 9 percent. What are the chances that a woman who tests positive actually has breast cancer?
Most likely, the way to an answer seems foggy to you. Just let the fog sit there for a moment and feel the confusion. Many people in your situation think that the probability of your friend's having breast cancer, given that she has a positive mammogram, is about 90 percent. But they are not sure; they don't really understand what to do with the percentages. Now I will give you the same information again, this time not in probabilities but in what I call natural frequencies:
Think of 100 women. One has breast cancer, and she will probably test positive. Of the 99 who do not have breast cancer, 9 will also test positive. Thus, a total of 10 women will test positive. How many of those who test positive actually have breast cancer?
Now it is easy to see that only 1 woman out of 10 who test positive actually has breast cancer. This is a chance of 10 percent, not 90 percent. The fog in your mind should have lifted by now. A positive mammogram is not good news. But given the relevant information in natural frequencies, one can see that the majority of women who test positive in screening do not really have breast cancer.
Imagine you have been accused of committing a murder and are standing before the court. There is only one piece of evidence against you, but it is a potentially damning one: Your DNA matches a trace found on the victim. What does this match imply? The court calls an expert witness who gives this testimony:
`The probability that this match has occurred by chance is 1 in 100,000.`
You can already see yourself behind bars. However, imagine that the expert had phrased the same information differently:
`Out of every 100,000 people, 1 will show a match.`
Now this makes us ask, how many people are there who could have committed this murder? If you live in a city with 1 million adult inhabitants, then there should be 10 inhabitants whose DNA would match the sample on the victim. On its own, this fact seems very unlikely to land you behind bars.
Technology Needs Psychology
Susan's ordeal illustrates the illusion of certainty; the Prozac and DNA stories are about risk communication; and the mammogram scenario is about drawing conclusions from numbers. This book presents tools to help people to deal with these kinds of situations, that is, to understand and communicate uncertainties.
One simple tool is what I call `Franklin's law`: Nothing is certain but death and taxes? If Susan (or her doctors) had learned this law in school, she might have asked immediately for a second HIV test on a different blood sample, which most likely would have spared her the nightmare of living with a diagnosis of HIV. However, this is not to say that the results of a second test would have been absolutely certain either. Because the error was due to the accidental confusion of two test results, a second test would most likely have revealed it, as later happened. If the error, instead, had been due to antibodies that mimic HIV antibodies in her blood, then the second test might have confirmed the first one. But whatever the risk of error, it was her doctor's responsibility to inform her that the test results were uncertain. Sadly, Susan's case is not an exception. In this book, we will meet medical experts, legal experts, and other professionals who continue to tell the lay public that DNA fingerprinting, HIV tests, and other modern technologies are foolproof—period.
Franklin's law helps us to overcome the illusion of certainty by making us aware that we live in a twilight of uncertainty, but it does not tell us how to go one step further and deal with risk. Such a step is illustrated, however, in the Prozac story, where a mind tool is suggested that can help people understand risks: When thinking and talking about risks, use frequencies rather than probabilities. Frequencies can facilitate risk communication for several reasons, as we will see. The psychiatrist's statement `You have a 30 to 50 percent chance of developing a sexual problem` left the reference class unclear: Does the percentage refer to a class of people such as patients who take Prozac, to a class of events such as a given person's sexual encounters, or to some other class? To the psychiatrist it was clear that the statement referred to his patients who take Prozac, whereas his patients thought that the statement referred to their own sexual encounters. Each person chose a reference class based on his or her own perspective. Frequencies, such as `3 out of 10 patients,` in contrast, make the reference class clear, reducing the possibility of miscommunication.
My agenda is to present mind tools that can help my fellow human beings to improve their understanding of the myriad uncertainties in our modern technological world. The best technology is of little value if people do not comprehend it.