# Odds ratio

## Description

In a retrospective study the subjects with positive and negative outcome are known and are subsequently grouped according to a specific characteristic. Use the Odds ratio calculator to calculate the ratio of the odds of the outcome in two groups.

## Required input

- The number of subjects in the 1st and 2nd group that have a positive or negative outcome.

## Results

The program calculates:

- the odds ratio, this is the ratio of the odds of the outcome in the two groups
- 95% confidence interval for the odds ratio
- z-statistic and associated P-value

If P is less than 0.05 it can be concluded that the odds ratio is significantly different from 1 and that there is an increased relative risk in one group compared to the other.

## Computational notes

The odds ratio (OR), its standard error and 95% confidence interval are calculated according to Altman, 1991.

The odds ratio is given by

with the standard error of the log odds ratio being

and 95% confidence interval

Where zeros cause problems with computation of the odds ratio or its standard error, 0.5 is added to all cells (a, b, c, d) (Pagano & Gauvreau, 2000; Deeks & Higgins, 2010).

Test of significance: the P-value is calculated according to Sheskin, 2004 (p. 542). A standard normal deviate (*z*-value) is calculated as ln(OR)/SE{ln(OR)}, and the P-value is the area of the normal distribution that falls outside ±*z* (see Values of the Normal distribution table).

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Altman DG, Deeks JJ, Sackett DL. Odds ratios should be avoided when events are common [letter]. BMJ 1998;317:1318.
- Deeks JJ, Higgins JPT (2010) Statistical algorithms in Review Manager 5. Retrieved from https://training.cochrane.org/
- Pagano M, Gauvreau K (2000) Principles of biostatistics. 2nd ed. Belmont, CA: Brooks/Cole.
- Parshall MB (2013) Unpacking the 2 x 2 table. Heart & Lung 42:221-226.
- Sheskin DJ (2004) Handbook of parametric and nonparametric statistical procedures. 3
^{rd}ed. Boca Raton: Chapman & Hall /CRC.

## Link

Go to Odds ratio.