- #1
vladimir69
- 130
- 0
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]
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 can't 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
[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 can't 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