What's the Denominator? A Lesson on Risk

[ILLUSTRATION OMITTED] If you had acne, would you use a medication that can cause depression, stomach pain, blurred vision, diarrhea, and rectal bleeding? Perhaps you would answer, "Depends on how bad the acne is." What about a medication that caused scores of infants to be born with severe birth defects, including malformations of the face, skull, heart, and central nervous system? Still interested? All these side effects can be caused by isotretinoin (trade name Accutane). In the late 1980s and early 1990s, there was great concern over the side effects of this widely used and effective therapy for the treatment of disfiguring nodular acne. If those dangers seem alarming, you might be asking, "How could the Food and Drug Administration have allowed Accutane to remain on the market?" An accurate answer to that question requires more information than given. In fact, it is impossible to evaluate the safety of new drugs-or household products or toys or anything else-until you have a great deal of information. Most often the missing information is the population size from which the mortality and morbidity data are being drawn or the baseline incidence of complications in the absence of the potential treatment. Without those numbers-the denominators against which meaningful comparisons can be made-the data are not helpful in rational risk analysis. Mathematics is at the heart of all science and is central to the interpretation of research findings in settings ranging from the clinical application of new medications to personal decisions about acceptable levels of risk. The National Science Education Standards (NRC, 1996) include the following statement as part of "understandings about scientific inquiry:" Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations and communicating results. Unfortunately, many Americans, including most of our students, have a poor grasp of mathematics, and rational risk analysis is one casualty. People who lack the skill of relating one number to another may overreact to relatively minor risks, perceiving certain situations or activities as dangerous when, in fact, they are not. Conversely, these people may disregard real risks. The tear of flying by someone who never wears a seat belt in his car is one example. Consider that, on average for the U.S. population, airline accidents will subtract four days off a person's life whereas auto accidents subtract an average of 182 days (Morgan, 1993). A variety of psychosocial factors affect how one perceives risk. For example, genetic counselors have discovered that the "perceived burden" of a genetic illness is more significant to parents than the empirical risk of being affected, which can influence pregnancy decisions (Ekwo, 1987; Meryash, 1989, 1992). For example, parents might be more reluctant to take the relatively low risk recurrence (e.g., 3%-5%) for a neural tube defect, which can be a very burdensonre disorder, than to take the 25% recurrence risk of phenylketonuria, which is perceived as less burdensome. Likewise, most people view the risk of acute but unlikely illness (e.g., mercury poisoning) as more disturbing than the risk of chronic and common illness (e.g., heart disease or diabetes). This is consistent with our tendency to evaluate a risk, in part, according to our perception of "dread" (Morgan, 1993). But this is not the whole story. Ignorance about how to analyze the numbers used to describe risk is yet another reason for faulty risk assessment. Many people have never been challenged to answer and internalize the question: What is the risk being compared to? This is a question that teachers can address with their students, and this brief activity may help students begin to evaluate risk more thoughtfully. * Background Expressions of risk fall into two categories: absolute and relative. …