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Woloshin S, Schwartz LM, Welch HG. Know Your Chances: Understanding Health Statistics. Berkeley (CA): University of California Press; 2008.

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Know Your Chances: Understanding Health Statistics.

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Chapter 4Judging the Benefit of a Health Intervention

So far, you’ve been learning about the risk of getting or dying from a disease. But most messages are about how you can reduce those risks; that is, most messages focus on benefit. The word benefit refers to how much a risk is reduced by taking an action. Whatever the action is—taking medicine, having surgery, or changing your lifestyle—the formula is the same. You start out with a specific chance of something happening (the outcome), you take the action, and then, you hope, you have a lower chance of experiencing that outcome.

The lessons you learned about risk in part one of this book also apply to messages about risk reduction (that is, benefit), although these messages add some new challenges. As an example of a risk reduction message, we’ll use a drug ad, simply because these ads have become so common. But what you learn will apply to any message about reducing risk.

In this section, we’ll review risk reduction using an advertisement for Zocor, a drug used to lower a person’s cholesterol level in order to reduce the chance of dying from a heart attack.

Before we go further, we’d like to make a few things clear. First, we chose this ad not because it is particularly egregious (in fact, it is probably better than the typical drug ad) but because it illustrates some common advertising tactics. Second, we did not choose this ad because we work for a drug company. We have no ties to any pharmaceutical company, and we use the trade name Zocor only to be consistent with the ad itself. Most important, we are not suggesting that you either use or avoid this drug. We just want to prepare you to make your own decisions.

Image ucalpkycf6.jpg

According to the ad, the man in the picture had a heart attack and has now found out that he has high cholesterol. He is worried about the future and wants to reduce his risk of another heart attack. The ad says that the medicine Zocor can help him. The white oval highlights the main message about how Zocor will change his risk. What does it mean?

As you know from the preceding chapters, the first two questions you should ask when you see a message about a risk are these:

Risk of what? (What is the outcome?)

How big is the risk? (What is the chance that you will experience the outcome, and over what time frame?)

You should ask similar questions when you see messages about risk reduction. The modified questions about risk reduction are the following:

Reduced risk of what?

How big is the risk reduction?

Look at the ad to try to answer these questions about Zocor:


Does the ad say that Zocor changes the chance of having a heart attack or the chance of dying from one?

  1. Having a heart attack
  2. Dying from a heart attack

How much does Zocor change the risk?

  1. From 1,000 in 1,000 to 580 in 1,000
  2. From 100 in 1,000 to 58 in 1,000
  3. From 10 in 1,000 to 5.8 in 1,000
  4. Can't tell

The correct answer to the first question is b. The ad is clear on this point: it concerns a change in the risk of dying from a heart attack. It doesn’t discuss how bad this risk is, but that’s okay—it’s obvious that dying from a heart attack is very bad. The ad, however, is not clear about the time frame. It turns out that the risk reduction reported (the benefit of taking Zocor) was calculated over a period of about 5 years.

The correct answer to the second question is d. Unfortunately, the main part of the ad doesn’t tell you the chance of a fatal heart attack if you don’t take Zocor compared to the chance if you do take Zocor (although the fine print contains some of this information). This is an important omission, and we’ll come back to it in a little while.

You should ask one other question as you read the ad. You encountered it in earlier chapters, but once again we’re modifying it to focus on risk reduction:

Does the risk reduction information reasonably apply to me? The ad does a relatively good job here. The message is about people with both high cholesterol and heart disease. If you have heart disease but normal cholesterol, or high cholesterol but no heart disease, this ad does not apply to you. What about age and sex? On these points, the ad is not clear. You have to go to the original article published in the medical journal to learn about who was actually in the study1 It turns out that the people who participated in the study were mostly men in their early 60s. Overall, however, the ages of the participants ranged from 35 to 70, so the information probably applies to people as young as 35 and as old as 70. Only 20 percent of the people in the study were women. So women should be less confident that the benefit information applies to them.

Overall, this ad, like many messages about how actions can reduce risk, is sketchy on important details. Because people’s minds have a tendency to fill in missing details, you might assume that the risk the drug addresses is big (why else would the drug be advertised?) and that it applies to all readers. The questions we’ve just reviewed point out the missing facts and are outlined in the quick summary in the Extra Help section of this book (pages 117—119). Whenever you’re faced with risk reduction messages, we encourage you to review the quick summary to help you see which facts are missing.

Now that we’ve established what risk is being reduced, let’s focus on how big the risk reduction might be for those who use Zocor. Here’s how the ad describes the benefit of Zocor: “A clinical study among people with high cholesterol and heart disease found 42 percent fewer deaths from heart attack among those taking Zocor.”

When someone tells you something like this—“42 percent fewer deaths”—the most important question to ask is “42 percent fewer than what?” Unless you know what number is being lowered by 42 percent, it’s impossible to judge how big the change is.

Thinking about risk reduction is like deciding when to use a coupon at a store. Imagine that you have a coupon for 50 percent off any one purchase. You go to the store to buy a pack of gum, which costs 50 cents, and a large Thanksgiving turkey, which costs $35.00. Will you use the coupon for the gum or for the turkey? Most people would use the coupon for the turkey. Here’s why:

ItemRegular Price“50% Off” Sale PriceSavings

In both cases, you save 50 percent. But with a cheap item, you save very little (25 cents); with an expensive item, you save a lot ($17.50). Obviously, to know what a discount means, you must know the regular price. The same is true in health care: “50 percent fewer deaths” is a different number in reference to a rare cause of death than it is in reference to a common cause. To understand how big a difference an action could make, you must find out the starting and modified risks—called absolute risks in the jargon of researchers. With the store coupon, the starting and modified risks are the regular price and the sales price. In a study about a medical treatment, the starting and modified risks are the chances of an outcome in the untreated and treated groups (that is, those who did not take the drug versus those who did).


Imagine that you are a typical 70-year-old woman who has never smoked. Consider two drugs. Both drugs lower the chance of dying from a disease by 50 percent, and they are equally safe. One works on cervical cancer, and the other works on heart attacks. Which drug is more likely to help keep you alive?

HINT: Refer to the risk charts in the Extra Help section to learn the risk of death for each disease.

  1. Drug for cervical cancer
  2. Drug for heart attack

The correct answer is b. For a typical 70-year-old woman, the chance of dying from cervical cancer in the next 10 years is 1 in 1,000. Her chance of dying from a heart attack is much larger: 46 in 1,000 (remember, she has never smoked, so when you consult the risk chart, you should be looking in the row for women who have never smoked). So she is much more likely to benefit from the drug that lowers the chance of heart attack death.

Let’s go back to the original Zocor ad and figure out what “42 percent fewer deaths from heart attack” really means. In (very) small print at the bottom of the ad, the following statement appears:

Image ucalpkycf7.jpg

This statement provides the data you need to answer the question “42 percent fewer than what?” It tells you the information needed to calculate the starting risk: the number of people in the untreated (placebo) group who had the outcome divided by the total number of people in the untreated group (189/2,223). This is to the manufacturer’s credit. It would have been nice if they had done the division for you, but at least the information is there. And, in fact, the ad also presents the information needed to calculate the modified risk: the number of people in the treated (Zocor) group who had the outcome divided by the total number of people in the treated group (111/2,221).

In any event, whenever you are given the data in this way (for example, 111/2,221 versus 189/2,223), we suggest that you do the division yourself. It involves two calculations, one for the group of people who were not treated with Zocor but instead took a placebo (a sugar pill that has no effect), and another for the group of people who took Zocor. Here’s how we did the math:

Starting risk=risk of heart attack death for people in the placebo group=189 heart attack deaths2,223 people who took a placebo=8.5%
Modified risk=risk of heart attack death for people in the Zocor group=111 heart attack deaths2,221 people who took Zocor=5.0%

So taking Zocor lowered the chance of dying from a heart attack in the next 5 years from 8.5 percent (the starting risk) to 5.0 percent (the modified risk). The following graph may help you to understand this difference better.

Image ucalpkycf8.jpg

Guess what 8.5 percent reduced by 42 percent is? It turns out to be 5.0 percent. The benefit of Zocor, “42 percent fewer deaths,” means that if you have heart disease and high cholesterol and you take Zocor, your chance of dying from a heart attack is 42 percent lower than it would be if you didn’t take Zocor. Another way to think about how Zocor changes your risk is to imagine a “42 percent off” sale in which the regular price is 8.5 percent, the sale price is 5.0 percent, and your savings equal 3.5 percent. (The Learn More box on page 45 shows how to do the calculations for each way of talking about risk reduction and provides the standard statistical language.)

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Learn More. So which is it? Does Zocor lower risk by 42 percent or 3.5 percent? Actually, both figures are correct. They are just two different ways of framing the answer. The 42 percent statistic is a relative risk reduction—in other words, it (more...)

These ways of describing a benefit can get confusing, for doctors and patients alike. We think that the best way to understand risk reduction information is to determine what your risk is if you do not take the medicine (or other treatment) and then compare it with your risk if you do—specifically, you need to look at your starting and modified risks, side by side. Here’s the message rewritten in this way:

“For men with heart disease and high cholesterol, Zocor reduces the 5-year chance of dying of a heart attack from 8.5 percent to 5.0 percent.”

Does this sound less impressive than the original “42 percent fewer deaths” version? Most people say yes. This is another example of framing (explained in chapter 1). The same information—the extent to which Zocor lowers the risk of dying from a heart attack—sounds very different depending on how it is expressed ("42 percent lower” or “8.5 percent versus 5.0 percent").2

To be sure you understand these different expressions, try this quiz:


Drug X is for people with high blood pressure. In a study, it reduced the chance of having a stroke over the next 10 years from 8% to 4%. Which of these statements is true?

  1. The starting risk = 8%
  2. The modified risk = 4%
  3. The drug lowers risk by 50%
  4. The drug lowers risk by 4 percentage points
  5. All of the above

The correct answer is e. All of the statements are true.

Now that you have good information about the starting and modified risks, you are faced with deciding whether this difference is big or small (or big enough to make it worth taking a pill). This is not an easy question, and the decision can be tricky. While it’s tempting to say that the difference between an 8.5 percent chance and a 5.0 percent chance of heart attack death over the next 5 years is pretty small, we’d say that it is actually pretty big. Why? Because, as you can see in the risk charts, heart attacks are a major cause of death for men and women, smokers and nonsmokers alike. And only a few drugs have been shown to reduce heart attack death at all.

So be careful about dismissing the importance of anything that can reduce a major cause of death (we’ll have more to say about that in the next chapter). Most people don’t have a good sense of how well drugs typically work. This is not surprising, since people rarely get to see the relevant information. We hope that this will change. Specifically, we hope that the U.S. Food and Drug Administration and others will help make drug benefit information more readily available to consumers (and that consumers will start demanding this information!) so that over time people will learn to better appreciate what constitutes a sizable benefit. In general, any treatment that reduces deaths from a major cause such as heart attack, even by a small amount (like 1 percentage point), is probably worth considering.

It’s no coincidence that drug ads—when they do provide some data about how well drugs work (which is not very often)—typically present risk reduction information in a format such as “42 percent fewer” or “42 percent lower.” Why? Because expressing benefit as a relative change makes even small risk reductions sound big. And it may contribute to an unrealistic sense about how effective various medications are. We think that failing to ask, “Fewer than what?” or “Lower than what?” is the single most important omission in trying to understand messages about risk reduction. If you hear only an expression of relative change, but not the starting and modified risks, you don’t have the data you really need to appreciate the magnitude of the benefit. When you’ve heard only a large number (like “42 percent lower”), you may tend to overestimate the size of the benefit.

A great way to highlight the information you need to understand how well a drug or other intervention works is to create a table like this one:

(Time frame: over ___ years)
Starting Risk
(Untreated group)
Modified Risk
(Treated group)

Our advice is to try filling in the table so that you can compare the starting and modified risks side by side. If you’re being advised to consider a major intervention, you should ask those offering the advice to complete the table for you. If they can’t—and if you can’t find a way to complete it your-self—you need to be very cautious about the intervention. If you’re unable to fill in the table, it means that you don’t know what the intervention really offers. Sometimes you do have to make important decisions in the face of great uncertainty. But that is very different from making decisions under the illusion that you know something when you don’t.

For practice, try reading the following “news story” about some hypothetical research findings concerning a (fictional) new drug:

Promising New Drug Hailed

Washington, D.C.—Researchers announced the results of a Long-awaited study of Argentex, a drug designed to prevent prostate cancer. In the study, 1,000 men ages 45 to 75 were randomly assigned to take either Argentex or a sugar pill called a placebo. The men were followed for 4 years. Men taking Argentex had a 40 percent lower risk of developing prostate cancer. Lead scientist Bernard Womba described the findings as “extremely promising” and predicted that the drug would be in wide use shortly.


What were the starting and modified risks in the study showing that Argentex reduced risk by 40%?

Starting Risk
(Placebo group)
Modified Risk
(Argentex group)

Sorry—this is another trick question. The answer is that you just can’t tell. All the answers listed in the quiz are possible, as are many other answers. But you can’t select the “right one” because key information—the actual starting risk—is missing. You may not have enjoyed this quiz: it’s annoying to be asked to do the impossible. But what’s really annoying is how often this scenario occurs in real life. As you begin to look for starting and modified risk numbers, you may discover that they can be very hard to find. Even articles in medical journals sometimes omit these basic statistics and provide only information about relative change, using expressions like “40 percent lower.”

For a little more practice, here’s a table for another fictional drug, this one called Pridclo. This drug is for people who already have heart disease (that is, they have already had a heart attack). After you read the table, try taking the quiz that follows.

(Time frame: over 2 years)
Starting Risk
(Placebo group)
Modified Risk
(Pridclo group)
Dying from a heart attack or stroke3%2%


For people with heart disease, who is Less Likely to die from a heart attack or stroke in the next 2 years: someone who takes Pridclo or someone who takes a placebo?

  1. Someone who takes Pridclo
  2. Someone who takes a placebo
  3. Can’t tell

Pridclo reduces the risk of dying from a heart attack or stroke by about 33 percent.

  1. True
  2. False
  3. Can’t tell

What is the difference between the starting risk and the modified risk with Pridclo?

  1. 3 percentage points
  2. 2 percentage points
  3. 1 percentage point

The correct answer to the first question is a. If you’ve read the table correctly, you’ll see that people with heart disease can reduce their chance of dying from a heart attack or stroke in the next 2 years from 3 percent to 2 percent by taking Pridclo. In other words, for every 100 people with heart disease who take Pridclo, there will be 1 less death in the next 2 years.

The correct answer to the second question is a. The statement is true. But since you know the starting and modified risks, you can appreciate that the 33 percent risk reduction corresponds to a change from 3 in 100 to 2 in 100:

starting risk − modified riskstarting risk=323=13=0.33=33%

The correct answer to the third question is c. Pridclo lowers risk of heart attack or stroke by 1 percentage point. Both the statements “33 percent lower” and “1 percentage point lower” correctly summarize the benefit of taking Pridclo. We think that the least ambiguous and most transparent way to describe the benefit is to show the starting and modified risks side by side, as we did in the table. Once you have those two statistics, you have the full picture (and in fact you can calculate the absolute risk reduction or the relative risk reduction, as shown in the Learn More box on page 45).

Why Starting Risk Matters

Starting risk determines how big the benefit of an action can be. People who start at a high risk usually stand to gain much more from taking action than people who start at a low risk.

Let’s take a closer look at the Zocor ad on page 38. This ad describes the benefit of taking the medicine for people with heart disease and high cholesterol. Do you think that the benefit might be different for people without heart disease?


Who has a greater chance of dying from a heart attack in the next 5 years?

  1. Men like Mr. Smith, a 55-year-old with very high cholesterol who has had two heart attacks already
  2. Men like Mr. Jones, a 55-year-old with mildly elevated cholesterol and no heart disease

The answer, of course, is a. So who is more likely to benefit from taking Zocor? The answer is a again. Men like Smith start out at higher risk than men like Jones. If Zocor lowers the risk of heart attack death by 42 percent for both groups, the benefit is greater for high-risk people. (Remember the earlier example: a coupon for 50 percent off the price is more valuable when you’re purchasing an expensive item like a turkey than it is when you’re buying something cheap like gum.) Let’s use a table to look at the numbers.

(Time frame: over 5 years)
Starting Risk
(Placebo group)
Modified Risk
(Zocor group)
Starting Risk Minus Modified Risk
(Change with Zocor)
Men with heart disease (like Smith) dying from a heart attack8.5%5.0%3.5 percentage points lower
Men without heart disease (like Jones) dying from a heart attack2.0%1.2%0.8 percentage point lower

Where you start matters! The higher your starting risk, the more you stand to benefit from treatments that reduce that risk. And the lower your starting risk, the less you stand to benefit even from the best intervention. This is true for heart disease and any other disease.

To understand why, think about the nature of an illness or health condition. In general, the sicker you are from a disease, the more likely you are to have a bad outcome related to that disease, such as a complication, hospitalization, or even death. Consequently, sicker people have a lot to gain from reducing their risk of a bad outcome: their starting risk is really high, so there’s much more risk to reduce.

Now consider people who are only mildly sick. They may still have a bad outcome, but it’s much less likely than it would be for very sick people. Since the starting risk of mildly sick people is low to begin with, even an effective intervention can help only a little, at best. There just isn’t that much risk to reduce.

As an example, the following table summarizes the chance that different groups of people will experience a bad outcome without treatment (look at the starting risk numbers) or with treatment (look at the modified risk numbers). For this example, we assert that the treatment lowers risk by 50 percent. This 50 percent reduction translates into benefits of varying size, depending on each group’s starting risk, as shown in the last column of the table.

How Sick?Starting RiskModified RiskRelative Change
(% lower risk)
Starting Risk Minus Modified Risk
Very sick50%25%50%25 percentage points lower
Moderately sick10%5%50%5 percentage points lower
Mildly sick5%2.5%50%2.5 percentage points lower
Not sick1%0.5%50%0.5 percentage points lower

The table illustrates a key point. The size of the benefit you might experience from a treatment depends on your starting risk. The same 50 percent reduction in risk translates to a much bigger benefit for people who are very sick compared to that for people who are well. As a general rule, sicker patients stand to gain more from treatments than do people who are less sick.

Thus, when a study indicates that a treatment has a good chance of working, you must be cautious about assuming that these results will apply to you. You need to be sure that the study involved people who are similar to you—not just in terms of age and sex but also in terms of their starting risk. Remember that if you aren’t at all like the people in the study, you can’t assume that you would experience the same benefit as the study participants. But the more you are like the people in the study, the more likely it is that you face the same starting risk and would experience the same benefit.

Starting Risks Can Be Hard to Find

Even though they are crucial to know, starting risks are often missing. We— and others—have documented this problem in several systematic studies of medical journals, medical journal press releases, news stories, and ads. Here’s what has been found:

Nearly 70 percent of articles published in major medical journals did not include starting risks in the abstract (the most widely read part of the article), and one-third did not include starting risks anywhere in the article.3

Forty-five percent of the press releases issued by major medical journals did not include starting risks, which may be one reason these statistics are often missing in news stories.4

News reports of medical research often do not contain starting risks.5

Direct-to-consumer prescription drug ads rarely provide starting risks— only 3 percent of the ads we studied contained them.6

If you start to pay close attention to drug ads and news stories, you’ll be amazed at how often you are told that a risk is “40 percent lower” without ever being told “lower than what?” (the starting risk).

Questions to Ask about Risk Reduction

As this chapter explained, there are three key questions you should ask when you hear a message about how some action can reduce your risk:

Reduced risk of what? Understand what outcome is being changed (getting a disease, dying from a disease, developing a symptom), and decide how much you care about it.

How big is the risk reduction? Find out your chance of experiencing the outcome if you don’t take an action (such as taking a medication or changing your lifestyle) and your chance if you do take the action. In other words, know your starting and modified risks. This is especially important if you hear a message like “drug X lowers your risk by 42 percent.” Always ask, “Lower than what?” Unless you know your starting risk (the “lower than what” part), the message really tells you nothing.

Does the risk information reasonably apply to me? Learn whether the message is based on studies of people like you (people of your age and sex, people whose health is like yours). The more you are like the participants in the studies, the more likely you are to face the same starting risk and experience the same benefit.

Copyright © 2008, The Regents of the University of California.

Know Your Chances: Understanding Health Statistics is hereby licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license, which permits copying, distribution, and transmission of the work, provided the original work is properly cited, not used for commercial purposes, nor is altered or transformed.

Bookshelf ID: NBK126170


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