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Computational notes

The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991.

The relative risk or risk ratio is given by

Relative risk

with the standard error of the log relative risk being

Relative risk - standard error

and 95% confidence interval

Relative risk - confidence interval

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

Number Needed to Treat (NNT)

The number needed to treat (NNT) is the estimated number of patients who need to be treated with the new treatment rather than the standard treatment (or no treatment) for one additional patient to benefit (Altman 1998).

A negative number for the number needed to treat has been called the number needed to harm.

MedCalc uses the terminology suggested by Altman (1998) with NNT(Benefit) and NNT(Harm) being the number of patients needed to be treated for one additional patient to benefit or to be harmed respectively.

The 95% confidence interval is calculated according to Daly (1998) and is reported as suggested by Altman (1998).

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


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall. Buy from Amazon
  • Altman DG (1998) Confidence intervals for the number needed to treat. British Medical Journal 317: 1309-1312. PubMed
  • Daly LE (1998) Confidence limits made easy: interval estimation using a substitution method. American Journal of Epidemiology 147: 783-790. PubMed
  • Deeks JJ, Higgins JPT (2010) Statistical algorithms in Review Manager 5. Retrieved from
  • 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

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.