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Odds ratio calculator

Subjects with positive (bad) outcome

a
c

Subjects with negative (good) outcome

b
d

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

Odds ratio formula

with the standard error of the log odds ratio being

Odds ratio standard error formula

and 95% confidence interval

Odds ratio confidence interval formula

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. Buy from Amazon
  • 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/handbook/statistical-methods-revman5
  • Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2nd ed. Oxford: Blackwell Science. Buy from Amazon
  • Pagano M, Gauvreau K (2000) Principles of biostatistics. 2nd ed. Belmont, CA: Brooks/Cole. Buy from Amazon
  • Parshall MB (2013) Unpacking the 2 x 2 table. Heart & Lung 42:221-226. PubMed
  • Sheskin DJ (2004) Handbook of parametric and nonparametric statistical procedures. 3rd ed. Boca Raton: Chapman & Hall /CRC. Buy from Amazon

How to cite this page

  • MedCalc Software Ltd. Odds ratio calculator. https://www.medcalc.org/calc/odds_ratio.php (Version 20.014; accessed October 23, 2021)

See also

Recommended book

Principles of Biostatistics
M Pagano, K Gauvreau

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Principles of Biostatistics is aimed at students in the biological and health sciences who wish to learn modern research methods.

The book is divided into three parts. The first five chapters deal with collections of numbers and ways in which to summarize, explore, and explain them. The next two chapters focus on probability and introduce the tools needed for the subsequent investigation of uncertainty. It is only in the eighth chapter and thereafter that the authors distinguish between populations and samples and begin to investigate the inherent variability introduced by sampling, thus progressing to inference. Postponing the slightly more difficult concepts until a solid foundation has been established makes it easier for the reader to comprehend them.