# relative risk/ odds ratio

Peter Thomson PeterT at agric.usyd.edu.au
Sun Feb 8 18:21:02 EST 1998

```In relation to odds rations and relative risks:

Firstly, the risk of an event is the probability of that event occurring,
say p.  The odds of an event occurring is p/(1-p), and so if the event
being studied is rare, then the risk is approximately the odds.

Now say we are compring two groups, a reference group (group "0" say) and a
treatment group, (group "1" say).  The the relative risk (RR) is
RR = risk(1)/risk(0) = p1 / p0
whereas the odds ratio (OR) is
OR = odds(1) / odds(0) = [p1/(1-p1)] / [p0/(1-p0)].
Again, if the event is rare, then the OR and RR are very similar, and tend
to interpreted similarly.

Staistically, they tend to occur from two different modelling strategies.
First, with modelling proportions (y "successes" in n "trials"), they are
the natural output from logistic regression.  Alternatively, with modelling
counts (from a Poisson distribution), they are the ourtput from Poisson
regression and log-linear models.

Good descriptions of all of these can be found in:
Kleinbaum, D.G., Kupper, L.L., and Morgenstern, H. (1982).  Epidemiologic
Research: Principles and Quantitative Methods.  Belmont, California:

Peter Thomson
University of Sydney

erdmann <jea at ukrv.de> wrote in article <34DC2F02.7ABC at ukrv.de>...
> I have a problem to understand the difference between odds ratio and
> relative risk, is there someone who can explainit to me.