The Risk of Risk: Explaining Difficult Concepts to Patients

MDNG Primary CareMarch 2009
Volume 11
Issue 3

A key component of health literacy is the ability to understand statistics and concepts like "probability" and "risk."

Much has been made of the American public's general lack of health literacy and the effect it has on patients’ abilities to make informed health decisions. A key component of health literacy is the ability to understand statistics and concepts like “probability” and “risk.” Thus, it is important that physicians be able to explain these concepts in a way that enables patients to incorporate the information into their decision-making process.

Life is uncertain, and, as stated by Kathryn Montgomery in her treatise How Doctors Think, “few experiences feel as uncertain as illness.” Furthermore, what is true for patients is equally true for their physicians. Uncertainty has been rightly described as “a fundamental feature of medicine… the physician’s constant companion.” Much of medicine is, in fact, about making effective decisions in the face of uncertainty.

Sound medical decisions depend on an informed physician and an informed patient. Physicians must know or be able to find relevant data to support assessments of the risks and benefits of studies and treatments. They must understand the limitations of such data along with basic statistical concepts of uncertainty. Furthermore, physicians must be able to communicate this information in such a way that a patient can comprehend it within his or her unique cultural and educational background and values. Clearly, guiding patients to sound, informed medical decisions in the face of inherent uncertainty is no small feat.

Evaluating and expressing risk

Much of the medical decision-making process involves evaluating risk. Risk is defined as uncertainty about the state of the world that can be quantified as a probability. Assessment of risk therefore depends on the availability of reliable empirical data. Unfortunately, in spite of the advances made by evidence-based medicine, such data often remains illusory or incomplete, introducing uncertainty even into the things we “know.”

Risk is classically expressed using several methods. The absolute risk reduction (ARR) (or, in the case of harm, absolute risk increase) is the most straightforward measure of risk. The ARR is defined as the absolute difference in the proportion of treated and untreated patients who experience an outcome. Another commonly used measure is the relative risk ratio (RRR). RRR is the difference in the proportions of untreated and treated patients who experience a particular outcome relative to the proportion of untreated patients who would experience the outcome. The major problem with RRR is that relative risk measures tend to exaggerate small differences in effect (it is for this reason that relative risk measures might be preferentially reported when the purpose is to support sales of a product or to create sensationalism).

Another risk descriptor preferred by many is number needed to treat. The number needed to treat is the reciprocal of the absolute risk reduction and represents the total number of patients who must be treated to produce the target outcome in one patient. Number needed to treat has the advantage of facilitating comparisons of risks and benefits between several options. The smaller the number needed to treat, the better the treatment. Conversely, the larger the number needed to harm, the less the risk.

The relative merits and disadvantages of using each of these measures to communicate risk can be illustrated by the following example. Suppose 100,000 subjects are given a drug thought to prevent death from heart disease and 100,000 subjects are given placebo. If two subjects in the control group die while only one in the drug group dies, the absolute risk reduction is 1/100,000 (2 out of 100,000 minus 1 out of 100,000). If a similarly designed study of 100,000 subjects using another drug found that 20,000 control subjects and 10,000 drug subjects died, the absolute risk reduction would be 10,000/100,000 (20,000/100,000 minus 10,000/100,000). The number needed to treat in the first study would be 100,000, whereas it would be just 10 for the second. In essence, the second drug is 1000 times more effective. This benefit is completely obscured, however, if expressed as relative risk reduction (a 50% reduction in each study). Clearly, RRR is not the best way to convey risk information.

Do doctors and patients understand risk?

It turns out that a large proportion of people, including otherwise well-educated adults, simply do not know how to think and understand using numbers. This problem has been termed innumeracy by the mathematician John Allen Paulos. Kurz-Milcke and colleagues describe one well-publicized example that reported findings in terms of a relative risk:

“In the mid-1990s, the British press reported the results of a study that women who took [a particular] contraceptive pill increased their risk of thromboembolism by 100%... Hearing the bad news, thousands of British women panicked and stopped taking the pill, which led to a wave of unwanted pregnancies. But what did the study in fact show? Out of every 14,000 who took it, this number increased from one to two. That is, the absolute risk increase is 1 in 14,000, but the relative increase is 100%. Most of these women, like the majority of people, had never learned the difference between absolute and relative risks and thus could easily be frightened by the 100% figure.”

Similarly, Schwartz and Bergus summarized the results of a study by Hux and Naylor that found that 88% of subjects indicated they would take a hypothetical lipid-lowering drug that would result in a 34% reduction in heart attacks (relative risk reduction), but only 42% would take the drug when told it would result in 1.4% fewer patients having heart attacks (the equivalent absolute rate reduction). When informed that 71 subjects would have to be treated for five years to prevent one heart attack (the equivalent NNT), only 31% would do so. Yet, another study found that death rates expressed as “1,286 out of 10,000” were rated by subjects as more risky than rates of “24.14 out of 100.”

Unfortunately, statistical innumeracy is not limited to the lay public. Hoffrage and Gigerenzer studied 48 physicians with an average of 14 years of professional experience. Each physician was asked to estimate the chances of breast cancer in a woman age 40-50 years given a positive routine screening. Physicians who were given the relevant information in probabilities (eg, 0.8%) estimated the likelihood to be between 1% and 90% with surprisingly little consensus (the correct answer was 9%). Physicians did better when they were given the same information in natural frequencies (for example, “8 out of every 1,000”) instead of probabilities. Presented this way, the majority were able to respond with the correct answer or close to it. Other researchers have found similar results. Since patients also find percentages difficult to comprehend, it is suggested that risks always be considered and described in terms of natural frequencies.

Some patients prefer to avoid any reference to numerical descriptions. For example, Woloshin and colleagues found that nearly 30% of subjects preferred that risk information be conveyed using words only. However, avoiding numerical risk information did not remove the potential for misunderstanding. Only 80.3% of their subjects agreed that “certain” meant 100 of 100 people, and only 67.8% agreed that “never” meant zero of 100 people. As would be expected, words describing less polarized alternatives were even more ambiguously interpreted.

Is a picture worth a thousand words?

Newer approaches to communicating risk involve visual representations designed to convey information more intuitively. One simple approach uses a diagram containing 100 icons designed to represent patients and possible outcomes. For example, an absolute risk reduction of 7% might be visually represented by shading seven of the 100 icons differently to indicate that this number of patients would be expected to benefit from a therapy relative to the total population of 100. Such a diagram incorporates the advantages of absolute risk reductions represented as a natural frequency. Rifkin and Bouwer have modified this concept to create the “risk characterization theater,” a simple graphic illustration of a typical theater seating chart with 1000 seats. In this easily understandable example of a population sample, seats are colored differently to indicate the number of individuals in a hypothetical theater audience who would be expected to experience a given outcome.

Dr. Chris Cates has further extended visual risk representation in an innovative and entertaining method that represents numbers needed to treat and/or numbers needed to harm in a single diagram (Figure 1). In my opinion, this clever plot provides a significant and practical advance in risk communication. Furthermore, Dr. Cates has created the program Visual Rx, which allows anyone to generate such a plot by entering data available from the medical literature for the condition and treatment of interest.

What’s a person to do?

Given the difficulty that both patients and physicians have in innately understanding numerical concepts of risk and the lack of consensus about the meaning of even commonly used words to describe uncertainty, how can we communicate risk to patients? Are there available guidelines?

First, clinicians must be sure that they understand the merits and drawbacks of the commonly used measures of risk, as reviewed above. Risks should be communicated using absolute measures, such as number needed to treat (or harm) and absolute risk reduction (or increase). Given their inherent potential for misinterpretation, relative risk measures should generally be avoided in discussions with patients. Probabilities should be described as natural frequencies instead of percentages, and commonplace words such as “likely” and “uncommon,” if used, should be defined as explicitly as possible. Visual aids, such as the Risk Characterization Theater and Cates Plots, may be particularly helpful in conveying quantitative concepts more intuitively.

Apart from the content, attention should also be given to the context in which risk information is given. For example, patients have been shown to be sensitive to the ways in which risk information might be framed. Framing the benefit of a screening test in terms of what the patient might lose by not having it has been shown to be more persuasive than framing involving potential gains. Likewise, framing risk information in positive terms (for example, chance of survival) is more likely to persuade patients to accept risky options than information presented in negative terms (chance of death).

Risk communication is multidimensional and must be primarily patient-centered. To remind physicians of this, Crowson, et al, suggest approaching risk communication using the mnemonic RISK: R — Relate relevant evidence; I – Individualize the message, using a flexible approach; S – Seek the patient’s perspectives and share the decision-making; and K-checK the patient’s understanding, monitor, and review decisions. In regard to the last point, I have found that asking a patient to teach back to me what I have just explained is one of the simplest ways to find out whether or not they truly comprehend the message.

We cannot attain certainty in life (with the exception of death and taxes, according to Benjamin Franklin). At best, we can try to offer clear information to our patients by attempting to quantify and communicate anticipated risks. Ultimately, the success of that communication will not be gauged by how we convey risk information, but by whether or not it is understood by patients who make important decisions based on the information we provide. Certainly, we owe this to them.


Dr. Nace is an editorial board member, and assistant professor of clinical medicine and associate program director in the Department of Medicine at the University of Illinois College of Medicine, Peoria, IL.

Figure 1

The Cates Plot shown above is an example of the output from a Cochrane Review of the use of antibiotics in Acute Otitis Media (middle ear infection) in children. The data is taken from the Cochrane Library 1999 issue 4.

The picture represents 100 children who are all given antibiotics for ear infections. The 86 green faces are children who would have been free from pain at 2 to 7 days even if they had not received an antibiotic. The 9 red faces are children who are still in pain even with antibiotics. The 5 yellow faces are the only children who show a benefit; they would have been in pain without the antibiotic but are not when they receive one.

Since it is not possible to identify which children will benefit all 100 need to be given the antibiotic for 5 to benefit. This represents the number needed to treat (NNT) of 20 for a single child to benefit.

Source: Reproduced with permission of Dr. Chris Cates.

Additional Resources:


  • Cancer Risk: Understanding the Puzzle
  • Understanding Risks


  • Communicating Risk: The Main Work of Doctors
  • Communicating Risks
  • Demystifying Risk: Understanding and Communicating Medical Risks
  • Fuzzy Math: Some Medical Stats Confuse Patients
  • Helping Doctors and Patients Make Sense of Health Statistics
  • How Can Doctors Communicate Information about Risk More Effectively?
  • Making Sense of Risk Information on the Web
  • Patients’ Understanding of Risk
  • Risk Communication in Practice: The Contribution of Decision Aids
  • Risk Communication: Problems of Presentation and Understanding
  • The Risk Communication Institute
  • The Role of Risk Communication in Shared Decision Making
  • Simple Tools for Understanding Risks: From Innumeracy to Insight
  • Strategies to Help patients Understand Risks
  • Teaching Medical Students and Doctors How to Communicate Risk
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