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Medical University of South Carolina

Odds Ratio vs. Relative Risk


In a prospective study, either a Randomized Clinical Trial or a Cohort study, use Relative Risk.

 

The Outcome

 

 +

 -

 The Exposure

 +

a

 b

a / (a+b)
Risk Rate of Developing Outcome in Exposed

Relative Risk
(Risk Ratio)
=(a / (a+b))
-----------
(c / (c+d))

Relative Risk Reduction =
(a/(a+b))-(c/(c+d))
---------------------
(c/(c+d))

 -

c

d

c / (c+d)
Risk Rate of Developing Outcome in NON-Exposed

In a case-control, retrospective study, use Odds Ratio.

 

The Outcome

 +

 -

 The Exposure

 +

a

 b

 -

c

d

 

 a/c
Odds of Being
Exposed in Cases

 b/d
Odds of Being
Exposed in Controls

 Odds Ratio =
a/c
----
b/d

A fine point:

In a rare condition, a and c are very small compared to b and d. So, if one were able to do a prospective study, and generate the Relative Risk (or Risk Ratio)...

Relative Risk (or Risk Ratio) = (a / (a+b)) / (c / (c+d))

In a rare condition, b would not add much to a. So, a+b = a; and, similarly, c+d = d.

So, the Relative Risk would = (a / b) / (c / d) OR (a * d) / (b * c)

This formula is identical to the Odds Ratio.

So, given a rare condition, the Odds Ratio approximates the Relative Risk (or Risk Ratio).

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Last Modified November 25, 2000