That’s not what that means: Relative risk factors

I spend about 18-23 hours a day on facebook, correcting all of the wrong things my friends say.  It’s a tough job, but somebody’s got to do it.

Yesterday, I noticed this show up in my feed:

The accompanying text read:  One can of diet soda each day can increase Leukemia risk in men and women by 42%, increase multiple myeloma risk in men by 102%, and increase the risk of non-Hodgkin lymphoma by 31% in men.

Dun dun DUN.

Zonks, Batman! Those numbers sure sound scary!

As I pointed out to this friend who had somewhat mindlessly clicked “share,” these numbers don’t represent “increased risk” so much as they reflect the relative risk of these two populations (those that drink fewer than 1 can per day, and those that drink more 1 can per day).

A relative risk is just that: it’s your risk relative to another group. It’s not the same as your risk relative to if you, specifically, had not done this particular thing, because whether you drink more diet soda than another cohort may be indexed to a third causal variable.  Correlation is not causation.

It’s also not your absolute risk (you don’t have a 102% chance of developing Lymphoma if you drink a can of soda a day).  Yet I see this shit all the time by people with an agenda and a poor understanding of epidemiology (my understanding is solidly lower-mediocre, so I’m qualified to sneer).

What does it mean to have a relative risk of 102%? It just means that in the two cohorts, about twice as many people developed Lymphoma in one group versus another.  It doesn’t tell us anything about the base rate of Lymphoma.  If you have a population of a hundred thousand people, and the base rate is ten cases, that means that if all 100,000 people drank a can of diet soda a day for many years, twenty people would develop multiple myeloma.  If the base rate of Leukemia in the same population was 10, you’d end up with 14 cases in the diet soda group.  If the base rate of lymphoma was 10, you’d end up with 13 cases. Et cetera.

When put that way, it’s easy to see why these relative risks aren’t exactly impressive.  And again, they are correlations, not causations.  With a big enough sample, you can find relative risks with pretty much any and every random variable you happen to look at.

You see this a lot with weight, where every analysis looks at the relative risk of being overweight or obese.  Where obesity represents a positive risk factor – you’re more likely to get disease X if you are obese – obesity gets the blame.  Mysteriously, it is less well known that obesity is correlated with a lower relative risk for many things, including death, relative to thin counterparts past a certain age.

For comparison, the relative risk of lung cancer from smoking cigarettes is represented by this graph below, taken from here.  The Y axis numbers represent X-fold risk factors.  (102% =~ two-fold risk).

As the site explains:

The link between lung cancer and cigarette smoking was first established in 1950, with a study showing a 26-fold increased risk of lung cancer among smokers of 15-24 cigarettes a day, compared with non-smokers.

A 26-fold increase, put another way, is a relative risk of 2600%.  Since that correlation was first established, science has pinned down the causal relationship between smoking cigarettes and the development of lung cancers.  Compared to a relative risk of 31%, or 1.3-fold, it’s hard for me to be too frightened of diet soda.  What irritates me is that the people creating these images either know full well they’re being deceptive, or they don’t understand the science they’re quoting well enough to be handing out nutritional scare advice.

Either way, I’m glad I’m a skeptic, though for the record, diet soda still tastes like ass, which is reason enough to avoid it.