Junkfood Science: Study Sidebar: Odds Ratios

## December 08, 2006

### Study Sidebar: Odds Ratios

Reporting statistical findings are rife with problems. Did you know that in the medical literature, you’ll find researchers taking the same data and coming up with exactly the opposite of the findings reported by another researcher? This demonstrates the problems with different mathematical models and calculation errors...

Health studies rarely give us the actual numbers and how a factor might change our real risks for a disease. While that would be more accurate in giving us a true picture of our probability or risks for a disease (or cure), those numbers almost never sound impressive enough to sell us on the importance of the research.

Most often, we’re given relative risks, which are ratios comparing two groups and their probabilities of a disease. They are fractions, so a relative risk of 1 (1/1) means there is no difference between the groups. If one group has one case of a disease and the second group has two cases, that’s a relative risk of 2.00 for the second group. It’s also an impressive-sounding “100% increase in relative risks!” — but in real life reflects only one additional case.

So a 50% reduction in our relative risks of dying from heart disease sounds awesome. Until you learn that your actual chances are, for example, 0.5%. So a women might lower her actual (absolute) risk from 0.5% to 0.25% — not nearly as impressive. The real (absolute) numbers are important to know.

Still, relative risks are what most of us think of when we’re looking at our chances for getting a disease. But a new way to report risks is becoming increasingly common and is much harder for most of us to interpret: odds ratios. An odds ratio compares odds, rather than actual incidences. As professor John Brignell, author of The Epidemiologists: Have they got scares for you!, has noted, it’s a popular tactic found in junk science because it can exaggerate an apparent effect when there’s really nothing significant. Here’s an example:

If the proportion of boys to girls is even, then out of 100 children there are 50 boys and 50 girls and the ratio (expressed as relative risk) is 50/50 which is 1. If we have one extra boy per hundred, however, we have to have one less girl to make up the total, so the ratio (expressed as odds ratio) now becomes 51/49 or 1.04, a 4% increase. Thus the proportion has changed by 1%, while the ratio has changed by 4%."

When event rates are high (commonly the case in trials and systematic reviews) the odds reduction can be many times larger than the relative risk reduction. These discrepancies in magnitude are large enough to mislead, according to medical statistician, Jon Deeks of the Centre for Statistics in Medicine, Institute of Health Services, Oxford. He explains it this way. Suppose there are two groups, one with a 25% chance of mortality and the other with a 75%. The change is a relative risk of three, but an odds ratio of nine. “A change from 10% to 90% mortality represents a relative risk of 9 but an odds ratio of 81.” Odds ratios may be the best estimates that can be obtained in certain types of statistical studies, such as case-controlled studies, but they still risk exaggerating perceived risks.

Making sense of odds ratios versus risks gets more complicated, but it’s probably more than most of us care to know. To make it easier, we can think of the numbers like relative risks, just keep in mind that their significance can appear greater than they really are. And when we’re reading about odds ratios, it is even more imperative to remember that risks less than 3 (or 200% difference) are untenable for any statistical finding. Now, back to the article.... 