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Relation between odds ratio and relative risk

  1. Aug 12, 2004 #1
    i am required to show that the odds ratio, "OR", and relative risk, "RR", are related by:
    [tex] OR = \frac{RR}{(1-p_{0})} \frac{1}{(1-p_{0} RR)}[/tex]

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

    from the notes i have that
    [tex] RR = \frac{p_{1}}{p_{0}}[/tex]
    [tex] OR = \frac{p_{1} (1-p_{0})}{p_{0} (1-p_{1})} [/tex]
    so when i put these into the mixing pot out pops
    [tex] OR = \frac{RR (1-p_{0})}{1-p_{1}} [/tex]
    but there is a troublesome [tex] p_{1}[/tex] 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 [tex] p_{1}[/tex]
    perhaps i am going the wrong way about it after doing a bit of backward engineering, but these are all the formulas i know

  2. jcsd
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