i am required to show that the odds ratio, "OR", and relative risk, "RR", are related by:(adsbygoogle = window.adsbygoogle || []).push({});

[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]

and

[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

thnx,

vladimir

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# Relation between odds ratio and relative risk

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