# odds ratio

In case control studies the relative risk cannot be calculated because the incidence is not determined by the study. Thus the useful manipulation of the data is into odds ratios, thus:

• suspected cause present: number of cases = a; number of controls = b
• suspected cause absent: number of cases = c; number of controls = d

Here the odds ratio is given by:

• Odds ratio (OR) = ad/cb

This equation is a result of manipulation of the relative risk equation where the assumption is made that since a and c are in fact relatively very small, the a+b and c+d parts of the equation tend to b and d respectively. It is then a matter of simplification of resulting equation.

If:

the OR =1, or the confidence interval (CI) includes 1, then there is no significant difference between the treatment and control groups

the OR>1 and the CI does not include 1, events are significantly more likely in the treatment group than the control group

the OR<1 and CI does not include 1, events are significantly less likely in the treatment group than the control group

Last reviewed 08/2020