Percentages and the pastrami panic…

the hot dog horror, and the salami scare. This story in the NYT quotes a source:

 “We see a 4 percent increase in the risk of cancer even at 15 grams a day, which is a single slice of ham on a sandwich,” said Dr. Nigel Brockton, director of research for the American Institute for Cancer Research.  
Eating a more typical serving of 50 grams of processed meat a day would increase the risk of colorectal cancer by 18 percent, a 
2011 review of studies found.

What does this really mean? Lifetime risk of colorectal cancer is about 1 in 23, or a little over 4%.  Now, does that slice of ham double your risk (4% to 8%), or merely increase it from 4.3% to (1.04*.043 = .045), 4.5%? Do a full fifth (18 + 4 = 22) of the 50-gram noshers get these specific cancers? Of course not. The quote, and the story, are completely ambiguous, but if you follow the link, you find that the data are relative risk values, which is the second interpretation. 50 grams a day entails about a 1% extra risk, and that’s not even counting all the people already in the 4.3% who eat deli meat and get cancer. If you do, and you stop, your risk of these cancers goes down from about 4% to…a little more than 3%. Perhaps Zabar’s should sue the Times over this alarmism.

Eating a reasonable amount of these exceptionally yummy foods seems to me a good deal, at the price of being 1% more likely to get this type of cancer before I get one of the other kinds or a heart attack. YMMV, of course. Everyone dies of something, so a much more useful statistic would be the average number of [quality adjusted ?] life years I’m putting at risk from a ham habit, and from an occasional indulgence.

The lesson here is that any statistics involving percentages have to be stated carefully to make it clear whether an increase adds to an existing rate or multiplies it, and “X% added risk” simply doesn’t cut it. Dr. Brockton and the reporter are equally at fault here, along with the Times copy editor. Students and colleagues: don’t make this mistake, especially when you’re explaining science to the public. What Dr. Brockton meant to say is that “the 15g pigout habit raises your lifetime risk from 4 to 5%”. There’s no escaping the additional words. Or reporting base rates: something that “quadruples your risk of contracting the gleeps” is not a big deal if the incidence of gleeps is a fraction of a percent.

Author: Michael O'Hare

Professor of Public Policy at the Goldman School of Public Policy, University of California, Berkeley, Michael O'Hare was raised in New York City and trained at Harvard as an architect and structural engineer. Diverted from an honest career designing buildings by the offer of a job in which he could think about anything he wanted to and spend his time with very smart and curious young people, he fell among economists and such like, and continues to benefit from their generosity with on-the-job social science training. He has followed the process and principles of design into "nonphysical environments" such as production processes in organizations, regulation, and information management and published a variety of research in environmental policy, government policy towards the arts, and management, with special interests in energy, facility siting, information and perceptions in public choice and work environments, and policy design. His current research is focused on transportation biofuels and their effects on global land use, food security, and international trade; regulatory policy in the face of scientific uncertainty; and, after a three-decade hiatus, on NIMBY conflicts afflicting high speed rail right-of-way and nuclear waste disposal sites. He is also a regular writer on pedagogy, especially teaching in professional education, and co-edited the "Curriculum and Case Notes" section of the Journal of Policy Analysis and Management. Between faculty appointments at the MIT Department of Urban Studies and Planning and the John F. Kennedy School of Government at Harvard, he was director of policy analysis at the Massachusetts Executive Office of Environmental Affairs. He has had visiting appointments at Università Bocconi in Milan and the National University of Singapore and teaches regularly in the Goldman School's executive (mid-career) programs. At GSPP, O'Hare has taught a studio course in Program and Policy Design, Arts and Cultural Policy, Public Management, the pedagogy course for graduate student instructors, Quantitative Methods, Environmental Policy, and the introduction to public policy for its undergraduate minor, which he supervises. Generally, he considers himself the school's resident expert in any subject in which there is no such thing as real expertise (a recent project concerned the governance and design of California county fairs), but is secure in the distinction of being the only faculty member with a metal lathe in his basement and a 4×5 Ebony view camera. At the moment, he would rather be making something with his hands than writing this blurb.

4 thoughts on “Percentages and the pastrami panic…”

  1. “Fifty percent chance of rain.” Fifty percent of what? Of the time, of the area, and for how long? Dynamic radar maps make this statistic all but obsolete, except for deciding whether to grab an umbrella.

  2. new cars allow you to turn on one windshield wiper for this forecast. You could always go out wearing one wellie.

  3. The point is made even more important by the recent ability to crunch enormous numbers of data points. One recent epidemiological study on the risk of Alzheimer’s etc from air pollution took the entire population of Medicare enrollees on the US east coast, 9.8 million. When your sample size is in the millions, practically any correlation will be statistically significant – even when the effect size is far too small to bother about in your own life. NB this does not apply to the study cited: the “hazard ratio” (another baffling trade term) for Alzheimer’s from higher exposure to fine particles is given as 1.15, and with a natural frequency around 10% of all over-65s, that’s not to be shrugged off.

    Relative risks should benchmarked against the stated natural frequency, as the standard form of presenting results to the public. Ben Goldacre is good on this (link).

  4. I think it should be required standard practice for articles such as this to calculate the probable impact on life expectancy, and/or disability or other life-affecting consequence — and show there work. I believe that in many cases the result would be no determinable effects at all, or vanishingly small ones. Authors in those cases would still be free to follow up with an argument that, even though the demonstrable effects on life or health are zero or negligible, the results are still important for other reasons. In really life, most scientists prefer a vaguely ominous work salad.

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