For example: the IARC recently released a statement along the lines of “eating processed meat increases your risk of cancer by 18%.” Now, that sounds pretty bad, doesn’t it? I mean, 18% is close to a fifth, which is a lot, right? Well…….not so fast!
Bayes Theorem always begins with a prior plausibility, or, what do we already know about the incidence of cancer (and specifically colorectal cancer, NOT all cancers) before that 18% increase is applied? Turns out that the base rate of colorectal cancer in the population is only 6%, which isn’t very high at all. So if there is an 18% increase, that means an 18% increase of 6%! So what is 18% of 6%? Well, it’s just a little over 1%. ONE PERCENT! So basically, eating 50mg of processed meat every day makes your risk of colorectal cancer increase from 6% to a whopping 7%! At this point, you’re probably thinking, “Damn, that means I can eat that bacon I was avoiding, after all!” And yup, go right ahead.
So any time someone tells you that “X increases the risk of Y by Z%,” ALWAYS remember to ask, “Well, what’s the base rate?”
Because if you don’t know the base rate, you really don’t know anything except that there was a relative increase in risk. And there’s a HUGE difference in understanding between saying that the “relative risk increases by 18%” and saying “absolute risk only increases by 1% since we started at just 6%.”
http://theness.com/neurologicablog/index.php/what-is-bayes-theorem/