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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

See also

Recommended book

Essentials of Medical Statistics
Betty Kirkwood, Jonathan Sterne

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

Essential Medical Statistics is a classic amongst medical statisticians. An introductory textbook, it presents statistics with a clarity and logic that demystifies the subject, while providing a comprehensive coverage of advanced as well as basic methods.

The second edition of Essential Medical Statistics has been comprehensively revised and updated to include modern statistical methods and modern approaches to statistical analysis, while retaining the approachable and non-mathematical style of the first edition. The book now includes full coverage of the most commonly used regression models, multiple linear regression, logistic regression, Poisson regression and Cox regression, as well as a chapter on general issues in regression modelling. In addition, new chapters introduce more advanced topics such as meta-analysis, likelihood, bootstrapping and robust standard errors, and analysis of clustered data.