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).