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How is this equation derived? thanks

RR=OR/((1−Pref)+(Pref∗OR))

RR = risk ratio; OR = odds ratio; Pref = Prevalence of the outcome in the reference group

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Relative Risk

RR = p1/p0

Odds Ratio

OR = (p1/(1-p1)) * ((1-p0)/p0)

OR * (p0/(1-p0)) = p1/(1-p1) 

(1-p0)/(OR*p0) = (1-p1)/p1

(1-p0)/(OR*p0) = 1/p1 - 1

1 + (1-p0)/(OR*p0) = 1/p1

(OR*p0+(1-p0))/(OR*p0) = 1/p1

(OR*p0)/(OR*p0+(1-p0)) = p1

p1 = (OR*p0)/(OR*p0+(1-p0))

Since RR = p1/p0

p1 = (OR*p0)/(OR*p0+(1-p0))

p1/p0 = (OR*p0)/((OR*p0+(1-p0))*p0)

p1/p0 = OR / OR*p0+(1-p0) 

which means:

RR = OR / ((1-p0)+(OR*p0)) 

RR = risk ratio; OR = odds ratio; p1 = the outcome in the experiment/exposed group; p0 = the outcome in the reference group

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