This blog posting is taken largely from the chapter, “Breast Cancer Screening,” which comes from the book, *Calculated Risks: How to Know When Numbers Deceive You *by Gerd Gigerenzer. I highly recommend this book. It provides important insights into risks and how they can be misinterpreted. This blog posting takes no position on screening. Its objective is to provide an accurate understanding of risks. The four ways of presenting risk reduction are not specific to breast cancer and are applicable to risk reduction in general.

*Relative Risk Reduction. *This is the most common means of presenting risk reduction, but the question is relative to what. The question is relative to what. Most people do not ask this question and misinterpret the statistic. Many believe that of 100 people participating in the screening that the lives of 25 will be saved. Here is the correct interpretation. Consider two groups of people, 1,000 who participated in screening and 1,000 who did not. Say within ten years (and this time period needs to be specified) 4 people in the first group and 3 in the second group died. This decrease from 4 to 3 is a relative risk reduction of 25%.

*Absolute Risk Reduction.* Consider the same numbers as in the preceding paragraph. The absolute risk reduction if 4 minus 3, that is 1 out of 1.000, or 01.%. In other words, if 1,000 participate in screening for 10 years, one life will be saved.

*Number Needed to Treat. *Again, we are considering the same data, but reporting it in a different manner. This statistic is the number needed to treat, or screen in this case, in order to save a life. The smaller the number needed, the more effective the treatment or screening. In this case the number is 1,000 because 1,000 women need to be screened to save a life.

*Increase in Life Expectancy.* This is the true bottom line statistic. This is the benefit expressed as an increase in life expectancy. For example, women who participate in screening from the age of 50 to 69 increase their life expectancy by an average of 12 days. Rarely, does one find benefits expressed in this manner. When news arrive that treatment x is beneficial or that lifestyle change b is beneficial, the conclusion is based on tests of statistical significance. The actual benefits can be small (in addition to future studies either failing to replicate or contradicting the study). The risk reduction statistics here are much more beneficial. Unfortunately the most popular of these, relative risk reduction, is usually presented without sufficient information for its accurate interpretation with the resulting interpretation being overly optimistic. For myself, give me the increase in life expectancy. Before I take screening test x, or engage in behavioral change b, I want to have an estimate of how many days it buys me.

Tags: Data Presentation, Risk Reduction

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