# What is the difference between an odds ratio and a risk ratio?

#### Rose

##### New Member
Hi - struggling to understand what the difference is between an odds ratio and a risk ratio?
Can anyone help?
Thanks!

#### d21e7x11

##### New Member
Hi Rose,

I'll write the definitions in terms of probabilities of disease and exposure.

Odds Ratio = odds of disease given exposure / odds of disease given non-exposure,

where

odds of disease given exposure = P(D+|E+) / P(D-|E+) = P(D+|E+) / (1 - P(D+|E+)),
and
odds of disease given non-exposure = P(D+|E-) / P(D-|E-) = P(D+|E-) / (1 - P(D+|E-)).

Risk Ratio = risk of disease given exposure / risk of disease given non-exposure,

where

risk of disease given exposure = P(D+|E+),
and
risk of disease given non-exposure = P(D+|E-).

#### noetsi

##### Fortran must die
A practical difference is that odds ratios are expressed in terms of the odds of something taking on the level of the dependent variable maximised by your statistic (which varies with the software, for SPSS it is normally the odds of it taking on the value of 1 if it is bivariate data, for SAS it is 0). So if you get an odds ratio of 11 it means as you go up from 1 to 2 on the independent variable it is 11 times more likely that the dependent variable will take on the value of 1 (for SPSS with bivariate dependent variable data).

Relative risk shows percentage (not odds) change and for most is far easier to understand.