# Simple question on odds ratios interpretation

I am trying to interpret the Odds Ratios (ORs) from a multiple logistic regression model that compares the performance of various clinics in terms of preterm birth rate (measured as "Yes/No preterm birth").

Here are some simplified results for purpose of discussion:

• Clinic 1 is used as a reference clinic

• OR for Clinic 2 = 0.5

• OR for Clinic 3 = 2.0

One conclusion is: "the odds to have preterm birth in Clinic 3 are 4 times higher than in Clinic 2 (2.0 / 0.5)."

Can I make a similar statement in terms of the probability of having preterm birth in Clinic 3 compared to Clinic 2? Something like: "the probability of having preterm birth in Clinic 3 is X times that in Clinic 2"

Would appreciate any input here.

Most of the times no.

The ratio of probability you mentioned is called relative risk (RR). OR estimates the ratio of odds, and it can also be used to approximate RR when the actual numbers of people in the denominators cannot be ascertained. For instance, in case-control studies in which people are sampled by outcome status, we don't know the exact case incidence rate and population at risk. At those times, we will resort to OR. OR and RR are close if the outcome is rare and both cases and controls are representative of the general population. Otherwise, they are not interchangeable.

Back to your case. If your study is a longitudinal study and you know the total number of patients in each of the clinics, then you can build a 2x3 (preterm by clinic) table and compute the relative risk manually. (You may also use Poisson regression, but in this case it may be easier to tabulate unless you need to adjust for other variables.)

If your study is to interview a fixed amount of preterm babies' mother and interview the same amount of full-term babies' mother in order to figure out if their clinic visit histories differ, then you have to stick with odds ratio.

For in-depth information, try search "Relative risk odds ratio difference" and you should find plenty of other discussions and resources.

• "OR and RR are close if the outcome is rare , and both cases and controls are representative of the general population." A point which is notoriously difficult to achieve with case-control study designs. – Alexis Mar 24 '15 at 16:20
• @Alexis, thanks. I agree and have added your comment into the answer. – Penguin_Knight Mar 24 '15 at 16:54
• I would not say that an OR is meant as an approximate RR. I would say that an OR is means to measure the Ratio of Odds, nothing more and nothing less. If you want an RR you should have used a log link function and lived with the consequences. Thinking in terms of one approximating the other just leads to way too many misinterpretations. – Maarten Buis Mar 24 '15 at 19:49
• @MaartenBuis, thanks for the input! I guess it's due to different ways of seeing it in different fields. For instance, Woodward wrote in Epidemiology: Study Design and Data Analysis that "the odds ratio is often a good approximation to the relative risk, and in some cases the odds ratio is all that we can estimated..." (p94, 3rd edition) While I fully agree with your concern about the murky application, I'd just have to chalk it up to we epidemiologists' funny ways of naming things. I softened the wording in my answer somewhat. Hope that'd help. – Penguin_Knight Mar 24 '15 at 21:50
• To follow up on Penguin_Knight's point: "Back to your case. If your study is a longitudinal study and you know the total number of patients in each of the clinics, then you can build a 2x3 (preterm by clinic) table and compute the relative risk manually." The reason why I am using logistic regression here is to control for various risk factors of preterm birth at the different clinics (e.g. ethnicity, age, etc), i.e. the odds ratios should adjust for confounding factors. (continued in next comment).. – dav Mar 25 '15 at 0:44