title: Meta-analysis, Simpson's paradox, and the number needed to treat.
abstract: BACKGROUND
  There is debate concerning methods for calculating numbers needed to treat (NNT) from results of systematic reviews.
  
  
  METHODS
  We investigate the susceptibility to bias for alternative methods for calculating NNTs through illustrative examples and mathematical theory.
  
  
  RESULTS
  Two competing methods have been recommended: one method involves calculating the NNT from meta-analytical estimates, the other by treating the data as if it all arose from a single trial. The 'treat-as-one-trial' method was found to be susceptible to bias when there were imbalances between groups within one or more trials in the meta-analysis (Simpson's paradox). Calculation of NNTs from meta-analytical estimates is not prone to the same bias. The method of calculating the NNT from a meta-analysis depends on the treatment effect used. When relative measures of treatment effect are used the estimates of NNTs can be tailored to the level of baseline risk.
  
  
  CONCLUSIONS
  The treat-as-one-trial method of calculating numbers needed to treat should not be used as it is prone to bias. Analysts should always report the method they use to compute estimates to enable readers to judge whether it is appropriate.
authors.affiliation: Centre for Statistics in Medicine, Institute of Health Sciences, Old Road, Headington, Oxford, UK. doug.altman@cancer.org.uk
authors.forename: Douglas G
authors.initials: DG
authors.lastname: Altman
authors.forename: Jonathan J
authors.initials: JJ
authors.lastname: Deeks
mesh_terms: D015982:Bias; D002986:Clinical Trials as Topic / Q000451:nursing / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D015201:Meta-Analysis as Topic; D016017:Odds Ratio; D015203:Reproducibility of Results; D012306:Risk; D018401:Sample Size; D016540:Smoking Cessation / Q000706:statistics & numerical data; D013223:Statistics as Topic / Q000379:methods* / Q000592:standards*