摘要：Objectives. We sought to address denominator neglect (i.e. the focus on the number of treated and nontreated patients who died, without sufficiently considering the overall numbers of patients) in estimates of treatment risk reduction, and analyzed whether icon arrays aid comprehension. Methods. We performed a survey of probabilistic, national samples in the United States and Germany in July and August of 2008. Participants received scenarios involving equally effective treatments but differing in the overall number of treated and nontreated patients. In some conditions, the number who received a treatment equaled the number who did not; in others the number was smaller or larger. Some participants received icon arrays. Results. Participants—particularly those with low numeracy skills—showed denominator neglect in treatment risk reduction perceptions. Icon arrays were an effective method for eliminating denominator neglect. We found cross-cultural differences that are important in light of the countries' different medical systems. Conclusions. Problems understanding numerical information often reside not in the mind but in the problem's representation. These findings suggest suitable ways to communicate quantitative medical data. Recent research on numeracy in health decision making has shown that many patients have difficulties grasping a host of numerical concepts that are necessary for them to understand health-relevant risk communications. 1 – 3 These communications often take the form of baseline risk estimates and risk reduction with 1 or more treatments. 4 , 5 Health numeracy is the individual-level skill needed to understand and use quantitative health information 6 and has a significant impact on risk perception. 7 – 10 Individuals with low numerical ability, for instance, are especially vulnerable to having difficulty following a complicated dosing regimen, 11 have higher history of hospitalization, 12 and are more susceptible to being influenced by the way the health information is framed in problems involving probabilities. 3 Ratio concepts—of which risks and probabilities are examples—are particularly challenging both in medical and nonmedical contexts. 13 – 15 For instance, people often pay too much attention to the number of times a target event has happened and insufficient attention to the overall number of opportunities for it to happen. 16 , 17 This denominator-neglect effect—described by Reyna 18 —has been extensively studied. 15 In an experiment by Yamagishi, 19 participants were presented with estimates of the number of deaths in the population attributable to 11 causes of deaths (e.g., cancer) and had to assess the risk of dying of such causes. Participants rated the likelihood of a cancer killing 1286 out of 10 000 people as higher than 24.14 out of 100 people. The degree of riskiness, therefore, varied according to the number of deaths presented, irrespective of the total possible number of deaths. Denominator neglect could have important consequences when one estimates treatment risk reduction. In medical practice, for example, the overall number of patients who receive a certain treatment is often smaller than the number of those who do not. 20 – 22 Similarly, patients might be able to think of more people who did not go to a certain screening or take a novel drug than they are able to think of those who did. If patients—and their physicians—disregard the overall number of treated and nontreated people (e.g., 100 and 800, respectively), they might perceive the treatment to be more effective than it actually is. Thus, they might underestimate the number of patients who died after receiving the treatment (e.g., n = 5), while overestimating the number of people who died and did not receive the treatment (e.g., n = 80). To the best of our knowledge, however, most of the studies of people's perceptions of risk reductions provided samples of treated and nontreated patients of the same size, 7 , 23 and even experts in the field recommend doing so. 24 – 26 The only exception is a study conducted by Garcia-Retamero et al. 27 which showed that participants overestimated risk reduction when the overall number of treated patients was lower than the number of those who did not receive the treatment. Yet no empirical data exist on whether people with low numeracy skills show more denominator neglect than those with high numeracy skills. As so many individuals have poor numeracy skills, 2 it is important to understand how numeracy impacts understanding of treatment risk reduction in tasks that reproduce the situations we often encounter when making health-related choices. As Fagerlin et al. 7 pointed out, low-numeracy patients might have more need for consistent denominators than would high-numeracy patients because their lack of facility with numbers puts them at a disadvantage. To our knowledge, however, this suggestion has not been investigated experimentally. More importantly, there is a dearth of published research on whether people with low numeracy skills can be aided when making decisions about their health by using displays designed to enhance comprehension. 4 , 25 As Reyna and Brainerd 15 pointed out, visual displays can help people represent superordinate classes such as the overall number of patients who did and did not receive a treatment, thus reducing denominator neglect. 28 Icon arrays are graphical representations consisting of a number of circles or other icons symbolizing individuals who are affected by some risk, 25 , 26 , 29 and they have been shown to be a promising method for communicating medical risk reduction. 23 , 30 – 32 Icon arrays might then help draw people's attention to the overall number of unaffected patients and, thus, reduce denominator neglect—especially in those with low numeracy skills. Finally, all of the studies on denominator neglect conducted so far (see Reyna and Brainerd 15 for a review) have used relatively limited laboratory samples of participants. Although these studies provide valuable information about the accuracy of understanding of these participants, because of nonprobabilistic sampling methods, the results cannot be generalized to any wider population. We conducted studies on probabilistic, representative samples in 2 countries with very different medical systems—the United States and Germany—to test the generalizability of denominator neglect and the effect of icon arrays on a wider population. In summary, we sought to determine (1) whether participants show denominator neglect in their estimates of risk reduction, and whether participants with low numeracy show more denominator neglect than those with high numeracy; (2) whether icon arrays help reduce denominator neglect, and whether they are especially helpful for participants with low numeracy; and (3) whether US participants show more denominator neglect than German participants, and whether icon arrays improve accuracy of risk understanding in participants from both countries.
