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odds ratio

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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

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