Man must learn to simplify, but not to the point of falsification. Aldous Huxley

Assessment of new therapies through clinical trials is well established, and results should obviously be expressed clearly and correctly. For results to be useful, data must be appropriately collected and analysed. The subsequent choice of presentation of results can be made separately from the method of analysis.

Results of clinical trials that compare the rates or proportions achieving an outcome, such as thromboembolism or bleeding, can be analysed and presented in several ways. Common methods of comparing rates or proportions are the relative risk (RR), the difference in proportions, which is also known as the absolute risk reduction (ARR), the odds ratio (OR), and the log odds ratio (log OR). A measure called the ‘number needed to treat’ (NNT), the inverse of the difference in probabilities, has been advocated in medical journals, first in the context of randomised controlled trials (RCTs) (Laupacis *et al*, 1988; Cook & Sackett, 1995; Sackett *et al*, 1996). As treatments can have detrimental effects, the expression ‘number needed to harm’ (NNH), was introduced (Altman, 1998).

We let *p*_{1} be the baseline or placebo response rate, and *p*_{2} the response rate for the intervention group in a clinical trial. The ARR is the difference between the rates: ARR = *p*_{1} − *p*_{2}. The use of the inverse of the difference between the rates: NNT = 1/(*p*_{1} − *p*_{2}), was suggested as an alternative presentation of such results (Laupacis *et al*, 1988). The correct interpretation of this statistic is quite subtle, and expressing it correctly requires considerable care. If *p*_{1} > *p*_{2}, and if NNT patients similar to those in the study were treated with treatment 1, on average one more patient would have a positive response within the time interval considered in the trial than if the NNT patients were treated with treatment 2. The NNT is the average number of typical patients ‘needed to be treated’ under treatment 1 to achieve one additional positive response over treatment 2. A negative NNT corresponds to a negative ARR, i.e. a poorer outcome on the drug, and should be interpreted as ‘the number needed to treat to harm’ (NNTH); a positive NNT is then to be interpreted as ‘the number needed to treat to benefit’ (NNTB) (Altman, 1998).

For example, a meta-analysis reported several measures: ‘Extended-duration prophylaxis for 30–42 d significantly reduced the frequency of symptomatic venous thromboembolism [1·3% vs. 3·3%, OR 0·38; 95% confidence interval (CI) 0·24–0·61, numbers needed to treat (NNT) = 50],’ without specific interpretation of NNT (Eikelboom *et al*, 2001). Another meta-analysis was more explicit: ‘For treatment effects that were statistically significant, the authors determined the absolute risk reduction and the number needed to treat for benefit [NNT (B)] to prevent an outcome. During anticoagulant prophylaxis, patients had significant reductions in any PE [relative risk, 0·43 (CI, 0·26–0·71); absolute risk reduction, 0·29%; NNT (B), 345]’ (Dentali *et al*, 1977).

For estimating the effects of treatment on a success or failure outcome, statisticians generally prefer to use the log OR, for theoretical reasons: essentially, this scale provides the most accurate and reliable comparison of treatments. Medical journals have generally accepted the importance of indicating the precision or accuracy of the main outcome measures, and estimates reported, as recommend in the Consolidated Standards of Reporting Trials (CONSORT) statement (CONSORT, 1994). These considerations – correct analysis and reporting the precision of outcome measures – are important in assessing the claims made in the articles which introduce and advocate NNT.