The Patient Was…

This is an article about statistics, but if it were so titled would you be interested enough to read it?

Statistics is a mandated course in medical school; but in my day, at least, it was dreaded by almost all of us. Our professor recognized this from bitter experience with prior classes, so he enticed us to attend in two ways: First, he promised lectures on concepts called “skirt volume and tail area,” which to a mostly male class had a certain salacious appeal; second, he promised a passing grade to everybody and no final exam if we all attended the lectures. We never missed a class.

Statistics can be defined as the collection, analysis, interpretation and presentation of numerical or quantitative data. What I want to discuss in this piece is actually important because it has a profound influence on how we receive and respond to statistical information. Although statistics are used in a variety of disciplines, my focus here is mainly on medical data and medical information. The two concepts of most importance in this context are “absolute” and “relative.”

An absolute value is a fixed, specific number or measurement that does not change regardless of context or circumstances. It is set and precise. A relative value or measurement, on the other hand, is one that is dependent on or compared to another number or value. 

Why does this matter in looking at medical data and information?

Well, let us suppose that there is a rare medical condition, so rare that it occurs in only two out of a million people. Now suppose I had a drug that would cut that risk in half. In other words, the disease would occur in only one in a million people if you took that drug. I could tell you that the reduction in risk with the drug was one in a million, an absolute value. Would you be very impressed? Probably not.

But now suppose I told you that the drug reduced the risk by fifty percent? That is, in fact, the relative reduction in risk, going from two in a million to one in a million. Fifty percent decrease. Wow!

Same data, same information, but a different way of presenting it.

It is notable that much of the medical data available to physicians is presented in relative terms, because the numbers are usually much more impressive and impactful. (For the same reason, much information presented to the public is done in the same fashion.) Medical journals, in my view, should always give equal or greater emphasis to absolute values compared to relative values when they report results of clinical trials. This, however, is not usually the case.

If the example of two in a million and one in a million sounds a little far-fetched, let me give you two real examples from the medical literature. Some years ago, a clinical trial of a drug that reduced levels of cholesterol in the blood showed that heart attacks and deaths from coronary heart disease were also reduced. This was crucial information, because all the interest in lowering cholesterol might be of little value if there were not a real-life benefit from doing so. The data were presented focusing on the relative reduction in risk: Heart attacks and coronary deaths over a four year period were lowered by a relative 80 percent in patients who took a medicine to lower cholesterol compared to those who did not take the medicine. This was dramatic.

When the absolute figures were reported, however, the results did not seem so striking. Patients who did not take medicine for lowering cholesterol had a 5 percent chance of having a fatal or non-fatal heart attack over a four-year period, while those who took medicine had a 1 percent chance during the same period. This meant that over that period of time, the real or absolute difference was only 4 percent, not 80 percent. And if you averaged it out by year, the actual difference was 1 percent per year over the four years. Important, but not so overwhelming.

In another medical study, controversial for a number of reasons unrelated to the reporting of results, a group of elderly women was given a medication designed to strengthen bones and prevent hip fractures. This was a very important study, because hip fractures are a serious problem, especially in the elderly. They can lead to long-term morbidity and disability and can even be responsible for death. They also are very costly to the health system in economic terms.

The results as reported showed a 50 percent reduction in hip fractures among the women who were given the medication, compared to the women who were not given the medicine. A 50 percent reduction in a serious condition is a dramatic outcome, and it generateded a lot of interest. But 50 percent was the relative risk reduction in the women on the medication.

It turns out that the actual rate of hip fractures among the women not taking the medication during the time period of the study was only 2 percent. Over the same time period, the rate of hip fractures among women taking the medicine was 1 percent. So, the actual or absolute risk reduction in hip fractures was only 1 percent, a far cry from the reported 50 percent. In addition, some women who took the medicine experienced adverse side effects from the drug, making it even less appealing.

It is well known, and even a subject of study, that manipulation of numbers plays a prominent role in many aspects of life. Shoppers should recognize how often prices are listed ending in .99 rather than the next higher whole number. A $4.99 item, for example, will sell much more frequently than one priced at $5.00 even though the difference is merely one penny. Even larger items, like houses, will sell more easily at $299,000 than at $300,000, although the difference is small at those large values.

In restaurants, especially costlier ones, one or two items on the menu may be priced exceedingly high, making other items seem reasonable even though they, too, may be priced exorbitantly. Restaurant wine lists are often similarly designed, with one or two bottles listed at very high prices, making other selections seem reasonable even though they also are considerably marked up in price.

Two rather well-known phrases more or less sum up the message I’m trying to convey: “Figures don’t lie, but liars figure,” and “Lies, damn lies, and statistics.”

Each of these is meant to suggest that while numbers are actual and factual, the way they are presented and interpreted can be misleading or deceptive. Figures can be manipulated in ways to promote or support particular ideas or goals, and to influence opinions and behaviors of others. In medicine, the emphasis on relative rather than absolute values tends to distort some realities, and to make some things seem more effective and valuable than, perhaps, is warranted.