# When are odds ratios worse/better than risk ratios as measures of the effect size of associations between categorical variables?

Wikipedia gives some information on this. However, I seek more detailed information on when odds ratios/risk ratios are better, and why one is better than the other in certain circumstances.

It depends on what you mean by "better", but for most reasons I can think of, the "Risk Ratio" is the superior measure in terms of better reflecting what most people are looking for, having a slightly easier interpretation, etc.

But there are some study types that prevent the calculation of a risk ratio (case-control studies) and logistic regression, which is used to calculate odds ratios, is somewhat easier to do - less likely to end up with weird values or convergence problems. But for most of those cases, people are using the odds ratio as a reasonable approximation of the risk ratio they'd actually like in an ideal world.

To expand on gung's question a little bit, to explain this reasoning: In an ideal world, an observational epidemiologist would run nothing but cohort studies. As a field, the "desirable" estimate is a risk - there's a back and forth about whether or not the comparison between groups should be a relative risk or a risk difference, but the core is risk, not odds, and right now the de facto effect estimate is relative risk.

But cohorts are super-expensive, especially for rare diseases, so case-control studies exist to make the study of those diseases feasible. You can't estimate a relative risk for those however, but it's a decent approximation for rare diseases, so we accept odds ratios as "close enough".

• +1, but I'd love to hear more detail about this. To me it seems like odds ratios would always be better, but I also don't deal w/ that sort of thing in the matter that / as much as epidemiologists do. – gung - Reinstate Monica Apr 5 '14 at 4:07
• @gung Some expansion of my answer - I don't know the exact history of the evolution of the field, but the big debate is over risk ratios or risk differences, but it's always been trying to look at differences between rates. Odds are...an acceptable compromise in some circumstances. That may not generalize to other fields, but I've never heard it advanced that odds may be directly preferable beyond logistic regression having less convergence issues than binomial regression. I'd be interested in your thoughts. – Fomite Apr 5 '14 at 6:30

There are many advantages of measures that have unrestricted ranges and that can be interpreted out of context. A risk ratio of 2 cannot apply to a risk exceeding $\frac{1}{2}$ whereas an odds ratio has an unrestricted range and can apply to any base risk. Also, odds are tied to fair bets in gambling. Odds ratios tend to be more constant over strata than risk ratios (and certainly more constant than risk differences).