Review

Visualizing Uncertainty About the Future

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Science  09 Sep 2011:
Vol. 333, Issue 6048, pp. 1393-1400
DOI: 10.1126/science.1191181

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  1. Fig. 1

    Florence Nightingale’s two rose-like graphs (4), each consisting of three overlaid polar area charts, representing deaths from sickness (blue), deaths from wounds (red), and deaths from other causes (black). Each sector corresponds to a month, and the area of a sector is proportional to the number of deaths per 1000 soldiers during that month. The drop in deaths from sickness followed the introduction of sanitary measures in early 1855.

  2. Fig. 2

    Image from the Isotype Institute illustrating the proportions of women employed in different countries in 1930 and their occupations. [From (63)]

  3. Fig. 3

    Visualizations of probabilities for discrete events. (A) Pie chart displaying possible results of a U.K. football match (64) between Leicester and Crystal Palace, with Leicester the home team. The size of each slice, determined by its angle at the center, represents the probability of a particular final goal score; for example, the probability of Leicester scoring 1, Crystal Palace 0, is 14%: this is assessed to be the most likely outcome and so the outer white band is colored. This probability is also represented by the radius of the inner strongly colored “wedge” in each slice, which may give a misleading impression because, for instance, the wedge representing 14% (2-0) is substantially larger than the wedge representing 10% (2-1). In contrast, Florence Nightingale used area rather than radius to represent her data in creating the rose diagram in Fig. 1. (The score in the actual football match was 1-1.) (B) The right vertical bar chart represents David Spiegelhalter’s risk of being diagnosed with prostate cancer, based on lifestyle information and the Harvard School of Public Health’s disease risk Web site, www.yourdiseaserisk.wustl.edu; the left vertical bar provides a qualitative scale (65). (C) A stacked horizontal bar chart from Adjuvant! Online (66) representing the benefits from adjuvant (labeled “additional”) chemotherapy for a fictitious woman with colon cancer. A text description of the expected outcomes for 100 women with and without chemotherapy is also supplied. [© 2008 American Society of Clinical Oncology (72)] (D) Icon plot provided by 23andMe (67) for David Spiegelhalter’s probability of developing type 2 diabetes between age 20 and age 79 based solely on specific genetic markers, relative to a standard population. In fact the subject has reached 58 without getting the disease. [Image © 2008–2011 23andMe, Inc. (72)]

  4. Fig. 4

    Visualizations of the predictive accuracy of a screening test. (A) Tree diagram showing the consequences for 1000 women attending mammography screening from a population with 1% prevalence of the disease, when the screening test correctly classifies 90% of women with cancer and 90% of women without cancer. Although nearly all the women with cancer are detected, they are greatly outnumbered by false-positive tests arising from those without cancer. (B) Icon array of the same information, which shows explicitly that out of 108 positive tests, only 9 (8%) would be expected to reveal breast cancer.

  5. Fig. 5

    Visualizations of probability distributions for continuous quantities. (A) “Roulette wheels” showing possible global temperature rises by 2100 under different policy scenarios (68). (B) 95% prediction intervals produced by the U.K. Meteorological Office for the maximum temperature expected for 5 days in Peterborough, U.K.; the central figure represents the most likely maximum temperature (69). (C) 95% uncertainty intervals obtained from the Cochrane Collaboration for the effect of adjuvant radiotherapy, after surgery for cancer of the cervix, on the incidence of hematological adverse events. There are two studies that together resulted in 7 of 188 adverse events in patients given radiation therapy, compared with 3 of 200 adverse events in control patients not given the treatment. The composite estimated risk ratio was 2.4, but with considerable uncertainty (56). The top right shows 95% uncertainty intervals represented by a horizontal line, with a square, whose size is proportional to the numbers of patients studied, drawing the eye to the more important central values of larger studies. In the row labeled Total, a diamond shape again deemphasizes the extremes values. Strictly speaking, this is not a visualization of future uncertainty. [Image © Cochrane Collaboration (72)] (D) “Cone of uncertainty” for hurricane path warnings in Florida. The central black line is the “most likely” path, and there is a two-thirds chance of the path being somewhere in the white region (70). (E) Fan chart for future economic growth in the U.K. as recorded in November 2007 by the Bank of England (43). The black line shows actual economic growth (according to current Office for National Statistics assessments) up to November 2007. Because these are provisional figures, there is still uncertainty as to the magnitude of past growth. (F) Probability distribution (top panel) and cumulative distribution (bottom panel) for change in maximum temperature between 2010 and 2020 under a medium-emission scenario for a 25-km2 area in the U.K. containing the University of Cambridge (71). The probability distribution expresses considerable uncertainty around a “most likely” estimate of around 1°C, while the cumulative distribution makes it easier to read off, for example, a central 90% interval. [© 2009 Crown Copyright (72)]

  6. Fig. 6

    Visualizations of potential benefits and harms of radiotherapy. (A) Expected outcomes for 100 women treated with adjuvant radiotherapy compared to 100 not treated. The three yellow dots indicate the evidence is of “moderate quality” using the GRADE scale. (B) Expected benefits and harms of treating 100 women with adjuvant radiotherapy; for example, we would expect 3 fewer deaths, 9 fewer women with disease progression, but extra adverse events. Whether the treatment is acceptable to a woman can depend on how she balances these benefits and harms. (C) Uncertainty about benefits and harms of treating 100 women, based on evidence from a Cochrane Collaboration review (56), using increased saturation of color to indicate greater certainty. The great uncertainty about the mortality benefit of adjuvant radiotherapy is clear.