# Prerequisite for conversion from odds ratio to relative risk to be valid

as question, since we can do the conversion from odds ratio (p1/q1)/(p2/q2) to relative risk (p1/(p1+q1))/(p2/(p2+q2)) fairly easily, I wonder if there is anything that I need to pay attention before doing this?

It is obvious that if I am doing a case-control study, I shouldn't do a conversion, because I never know the relative risk from this kind of study, but anything other things that I need to consider?

Thanks.

• Odds ratio versus relative risk offers a good summary of those two measures. Another caveat that is frequently seen is people that apply a logistic regression model, but interpret the results with RR instead of OR. – chl Jan 28 '11 at 9:05

## 2 Answers

In a sense, odds ratios are more universal than risk ratios so we spend too much time on risk ratios. Risk ratios are incapable of being constant over a wide range of risks, whereas an odds ratio is capable of being constant. For example, if a risk ratio is 3, the starting risk level cannot exceed 1/3. Because of this, models stated in terms of odds ratios often contain fewer interaction terms than models for relative risk (or for risk difference).

Answering, even though this question is quite old.

The biggest caveat is that you cannot use a measurement of RR in a case-control study, because it cannot be calculated. If you have the data to compare between them, then there's no reason not to - differences between the two measures can often yield some insight.

Note however that in circumstances of highly prevalent diseases (~>10%), the OR won't well approximate the RR. Since what most studies are looking for is an RR or something that approximates it under special circumstances (OR, IDR, etc.), if the OR can't be expected to closely approximate the RR, it would be better to go with something that will.

Generally speaking, the OR is a convenience measurement to allow for the case-control study design, and because binomial regression models often have convergence issues.