The Laws of Medicine (3 page)

A strong intuition is much more powerful than a weak test.

I
discovered the first law of medicine by chance—which is exactly as it should be since it largely concerns chance. In the spring of 2001, toward the end of my internship year, I was asked to see a man with unexplained weight loss and fatigue. He was fifty-six years old, and a resident of Beacon Hill, the tony neighborhood with brick town houses and tree-lined, cobblestone streets that abuts Massachusetts General Hospital.

Mr. Carlton—as I'll call him—was the Hill distilled to its essence. With his starched blue shirt, a jacket with elbow patches, and a silk necktie fraying just so, he suggested money, but old money, the kind that can be stuffed under blankets. There was something in his manner—a quicksilver volatility, an irritability—that I could not quite pin down. When he stood up, I noticed that the leather belt around his waist had been cinched tightly. More ominously, the muscles on the side of his forehead had begun to shrivel—a phenomenon called temporal wasting—which clearly suggested the weight loss had been recent and quite severe. He stood up to be weighed and told me that he had lost nearly twenty-six pounds over the last four months. Even the journey from the chair to the scale was like crossing an ocean. He had to sit down again afterward to catch his breath.

The most obvious culprit was cancer—some occult, hidden malignancy that was driving this severe cachexia. He had no obvious risk factors: he was not a smoker and had no suggestive family history. I ran some preliminary labs on him, but they were largely normal, save for a mild drop in his white-cell count that could be attributed to virtually anything.

Over the next four weeks, we scoured his body for signs of cancer. CAT scans were negative. A colonoscopy, looking for an occult colon cancer, revealed nothing except for an occasional polyp. He saw a rheumatologist—for the fleeting arthritic pains in his fingers—but again, nothing was diagnosed. I sent out another volley of lab tests. The technician in the blood lab complained that Mr. Carlton's veins were so pinched that she could hardly draw any blood.

For a while nothing happened. It felt like a diagnostic stalemate. More tests came back negative. Mr. Carlton was frustrated; his weight kept dropping, threatening to go all the way down to zero. Then, one evening, returning home from the hospital, I witnessed an event that changed my entire perspective on the case.

Boston is a small town—and the geography of illness tracks the geography of its neighborhoods (I'll risk admonishment here, but this is how medical interns think). To the northeast lie the Italian neighborhoods of the North End and the rough-and-tumble shipyards of Charlestown and Dorchester, with high densities of smokers and asbestos-exposed ship workers (think lung cancer, emphysema, asbestosis). To the south are desperately poor neighborhoods overrun by heroin and cocaine. Beacon Hill and Brookline, sitting somewhere in the middle, are firmly middle-class bastions, with the spectra of chronic illnesses that generally affect the middle class.

What happened that evening amounted to this: around six o'clock as I left the hospital after rounds, I saw Mr. Carlton in the lobby, by the Coffee Exchange, conversing with a man whom I
had admitted months ago with a severe skin infection related to a heroin needle inserted incorrectly into a vein. The conversation could not have lasted for more than a few minutes. It may have involved something as innocuous as change for a twenty-dollar bill, or directions to the nearest ATM. But on my way home on the train, the image kept haunting me:
the Beacon Hill scion chatting with the Mission Hill addict.
There was a dissonant familiarity in their body language that I could not shake off—a violation of geography, of accent, of ancestry, of dress code, of class. By the time I reached my station, I knew the answer. Boston is a small town. It should have been obvious all along: Mr. Carlton was a heroin user. Perhaps the man at the Coffee Exchange was his sometime dealer, or an acquaintance of an acquaintance. In retrospect, I should also have listened to the blood-lab worker who had had such a hard time drawing Mr. Carlton's blood: his veins were likely scarred from habitual use.

The next week, I matter-of-factly offered Mr. Carlton an HIV test. I told him nothing of the meeting that I had witnessed. Nor did I ever confirm that he knew the man from Mission Hill. The test was strikingly positive. By the time the requisite viral-load and the CD4 counts had been completed, we had clinched the diagnosis: Mr. Carlton had AIDS.

....

I'm describing this case in such detail because it contains a crucial insight. Every diagnostic challenge in medicine can be imagined as a probability game. This is how you play the game: you assign a probability that a patient's symptoms can be explained by some pathological dysfunction—heart failure, say, or rheumatoid arthritis—and then you summon evidence to increase or decrease the probability. Every scrap of evidence—a patient's medical history, a doctor's instincts, findings from a physical examination, past experiences, rumors, hunches, behaviors, gossip—raises or lowers the probability. Once the probability tips over a certain point, you order a confirmatory test—and then you read the test in the context of the prior probability. My encounter with Mr. Carlton in the lobby of the hospital can be now reconceived as such a probability game. From my perceptual biases, I had assigned Mr. Carlton an infinitesimally low chance of HIV infection. By the end of that fateful evening, though, my corner-of-the-eye encounter had shifted that probability dramatically. The shift was enough to tip the scales, trigger the test, and reveal the ultimate diagnosis.

But this, you might object, is a strange way to diagnose an illness. What sense does it make to assess the probability of a positive test
before
a test? Why not go to the test directly? A more thoughtful internist, you might argue, would have screened a patient for HIV right away and converged swiftly on the diagnosis without fumbling along, as I had, for months.

It is here that an insight enters our discussion—and it might sound peculiar at first:
a test can only be interpreted sanely in
the context of prior probabilities.
It seems like a rule taken from a Groucho Marx handbook: you need to have a glimpse of an answer before you have the glimpse of the answer (nor, for that matter, should you seek to become a member of a club that will accept you as a member).

To understand the logic behind this paradox, we need to understand that every test in medicine—any test in any field, for that matter—has a false-positive and false-negative rate. In a false positive, a test is positive even when the patient does not have the disease or abnormality (the HIV test reads positive, but you don't have the virus). In a false negative, a patient tests negative, but actually has the abnormality being screened for (you are infected, but the test is negative).

The point is this: if patients are screened without any
prior
knowledge about their risks, then the false-positive or false-negative rates can confound any attempt at diagnosis. Consider the following scenario. Suppose the HIV test has a false-positive rate of 1 in 1,000—i.e., one of out every thousand patients tests positive, even though the patient carries no infection (the actual false-positive rate has decreased since my time as an intern, but remains in this range). And suppose, further, we deploy this test in a population of patients where the prevalence of HIV infection is also 1 in 1,000. To a close approximation, for every infected patient who tests positive, there will also be one uninfected person who will also test positive. For every test that comes back positive, in short, there is only a 50 percent chance that the patient is actually positive. Such a test, we'd all agree, is not particularly useful: it only works half the time. The “more
thoughtful internist” in our original scenario gains very little by ordering an HIV test on a man with no risk factors: if the
test
comes back positive, it is more likely that the test is false, rather than the infection is real. If the false-positive rate rises to 1 percent and the prevalence falls to 0.05 percent—both realistic numbers—then the chance of a positive test's being real falls to an abysmal 5 percent. The test is now wrong
95 percent
of the time.

In contrast, watch what happens if the same population is
preselected
, based on risk behaviors or exposures. Suppose our preselection strategy is so accurate that we can stratify patients as “high risk”
before
the test. Now, the up-front prevalence of infection climbs to 19 in 100, and the situation changes dramatically. For every twenty positive tests, only one is a false positive, and nineteen are true positives—an accuracy rate of 95 percent. It seems like a trick pulled out of a magician's hat: by merely changing the structure of the tested population, the same test is transformed from perfectly useless to perfectly useful. You need a strong piece of “prior knowledge”—I've loosely called it an intuition—to overcome the weakness of a test.

The “prior knowledge” that I am describing is the kind of thing that old-school doctors do very well, and that new technologies in medicine often neglect. “Prior knowledge” is what is at stake when your doctor—rather than ordering yet another echocardiogram or a stress test—asks you about whether your feet have been swelling or takes your pulse for no apparent reason. I once saw a masterful oncologist examining a patient
with lung cancer. The exam proceeded quite predictably. He listened to her heart and lungs. He checked her skin for rashes. He made her walk across the room. And then, as the exam came to a close, he began to ask her a volley of bizarre questions. He fussed about his office, writing his notes, then blurted out a wrong date. She corrected him, laughing. When was the last time she had gone out with her friends? he asked. Had her handwriting changed? Was she wearing an extra pair of socks with her open-toed shoes?

Once he had finished and she had left the office, I asked him about the questions. The answer was surprisingly simple: he was screening her for depression, anxiety, sleeplessness, sexual dysfunction, neuropathy, and a host of other sequelae of her illness or its treatment. He had refined the process over so many iterations that his questions, seemingly oblique, had been sharpened into needlelike probes. A woman doesn't know what to say if you ask her if she has “neuropathy,” he told me, but no one can forget putting on an extra pair of socks. It's easier to summon a date that you are specifically asked for. Picking out a blurted-out date that's wrong requires a more subtle combination of attention, memory, and cognition. None of his questions was anywhere near diagnostic or definitive; if there were positive or negative signs, he would certainly need to order confirmatory tests. But he was doing the thing that the most incisive doctors do: he was weighing evidence and making inferences. He was playing with probability.

This line of reasoning, it's worthwhile noting, is not a unique feature of any particular test. It applies not only to medicine
but to any other discipline that is predicated on predictions: economics or banking, gambling or astrology. The core logic holds true whether you are trying to forecast tomorrow's weather or seeking to predict rises and falls in the stock market. It is a universal feature of
all
tests.

....

The man responsible for this strange and illuminating idea was neither a doctor nor a scientist by trade. Born in Hertfordshire in 1702, Thomas Bayes was a clergyman and philosopher who served as the minister at the chapel in Tunbridge Wells, near London. He published only two significant papers in his lifetime—the first, a defense of God, and the second, a defense of Newton's theory of calculus (it was a sign of the times that in 1732, a clergyman found no cognitive dissonance between these two efforts). His best-known work—on probability theory—was not published during his lifetime and was only rediscovered decades after his death.

The statistical problem that concerned Bayes requires a sophisticated piece of mathematical reasoning. Most of Bayes's mathematical compatriots were concerned with problems of pure statistics: If you have a box of twenty-five white balls and seventy-five black balls, say, what is the chance of drawing two black balls in a row? Bayes, instead, was concerned with a converse conundrum—the problem of knowledge acquisition from observed realities. If you draw two black balls in a row from a box containing a mix of balls, he asked, what can you say about the composition of white versus black balls in the box? What if you draw two white and one black ball in a row? How does your assessment of the contents of the box change?

Perhaps the most striking illustration of Bayes's theorem comes from a riddle that a mathematics teacher that I knew would pose to his students on the first day of their class. Suppose, he would ask, you go to a roadside fair and meet a man tossing coins. The first toss lands “heads.” So does the second.
And the third, fourth . . . and so forth, for twelve straight tosses. What are the chances that the next toss will land “heads” ? Most of the students in the class, trained in standard statistics and probability, would nod knowingly and say: 50 percent. But even a child knows the real answer:
it's the coin that is rigged
. Pure statistical reasoning cannot tell you the answer to the question—but common sense does. The fact that the coin has landed “heads” twelve times tells you more about its future chances of landing “heads” than any abstract formula. If you fail to use prior information, you will inevitably make foolish judgments about the future.
This is the way we intuit the world
, Bayes argued. There is no absolute knowledge; there is only conditional knowledge. History repeats itself—and so do statistical patterns. The past is the best guide to the future.