Simpson's paradox and calculation of number needed to treat from meta-analysis

BMC Med Res Methodol. 2002;2:1. doi: 10.1186/1471-2288-2-1. Epub 2002 Jan 25.


Background: Calculation of numbers needed to treat (NNT) is more complex from meta-analysis than from single trials. Treating the data as if it all came from one trial may lead to misleading results when the trial arms are imbalanced.

Discussion: An example is shown from a published Cochrane review in which the benefit of nursing intervention for smoking cessation is shown by formal meta-analysis of the individual trial results. However if these patients were added together as if they all came from one trial the direction of the effect appears to be reversed (due to Simpson's paradox). Whilst NNT from meta-analysis can be calculated from pooled Risk Differences, this is unlikely to be a stable method unless the event rates in the control groups are very similar. Since in practice event rates vary considerably, the use a relative measure, such as Odds Ratio or Relative Risk is advocated. These can be applied to different levels of baseline risk to generate a risk specific NNT for the treatment.

Summary: The method used to calculate NNT from meta-analysis should be clearly stated, and adding the patients from separate trials as if they all came from one trial should be avoided.

MeSH terms

  • Bias
  • Clinical Trials as Topic / nursing
  • Clinical Trials as Topic / statistics & numerical data
  • Data Interpretation, Statistical
  • Humans
  • Meta-Analysis as Topic*
  • Odds Ratio
  • Reproducibility of Results
  • Sample Size
  • Smoking Cessation / statistics & numerical data
  • Statistics as Topic / methods*
  • Statistics as Topic / standards*