# Relation between odds ratio and relative risk

1. Aug 12, 2004

i am required to show that the odds ratio, "OR", and relative risk, "RR", are related by:
$$OR = \frac{RR}{(1-p_{0})} \frac{1}{(1-p_{0} RR)}$$

where $$p_{0}$$ is the probability of disease for a non-exposed person and $$p_{1}$$ is the probability of disease for an exposed person.

from the notes i have that
$$RR = \frac{p_{1}}{p_{0}}$$
and
$$OR = \frac{p_{1} (1-p_{0})}{p_{0} (1-p_{1})}$$
so when i put these into the mixing pot out pops
$$OR = \frac{RR (1-p_{0})}{1-p_{1}}$$
but there is a troublesome $$p_{1}$$ in there which i cant seem to easily get rid of. i have tried using bayes formula but it just gets messy

could someone pls show me how to get rid of the $$p_{1}$$
perhaps i am going the wrong way about it after doing a bit of backward engineering, but these are all the formulas i know

thnx,