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.