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.
 A: 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.
