Odds Ratio

Odds Ratio

 
An odds ratio (OR) is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. OR is most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

1. Confidence Interval of OR

Consider two binomial random variables. There is X times success with N trials.

There is a joint function of log odds ratio ln(OR):

Standard error of log odds and log odds ratio:

(1-α)100% CI of lnOR is

(1-α)100% CI of OR is

2. Calculate OR by a 2x2 table

We will calculate odds ratios (OR) using a two-by-two frequency table.

		Outcome status
		+	-
Exposure status	+	a	b
	-	c	d

Where

   a = Number of exposed cases

   b = Number of exposed non-cases

   c = Number of unexposed cases

   d = Number of unexposed non-cases

So there is odds and odds ratio (OR):

High OR usually indicates high associations between exposure and outcome. However, presence of a positive OR for an outcome given an exposure status does not necessarily indicate that this association is statistically significant. One must consider the confidence intervals and p value (where provided) to determine significance.