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Journal of Public Health 26(1) © Faculty of Public Health 2004; all rights reserved.

The number needed to treat needs an associated odds estimation



Hiroshi Aino, Professor of Health Sciences

Shinichiro Yanagisawa, Research Associate

Isao Kamae, Consultant in Public Health Medicine
Division of Health Informatics and Sciences, Research Center for Urban Safety and Security, and Graduate School of Medicine, Kobe University, 7-5-1 Kusunoki-cho, Chuou-ku, Kobe, Japan 650-0017

Address correspondence to Professor Isao Kamae. E-mail: ikamae{at}med.kobe-u.ac.jp

Background The number needed to treat (NNT) is a practically useful indicator that represents how many patients must be treated to prevent one adverse event when provided with a new intervention instead of the standard one. The NNT associates the net-benefit of an experimental treatment with the number of patients, or the size of trials, expecting one outcome of success. The NNT, however, also suggests that we assume an implicit execution of independent Bernouilli trials – as it were, the hypothetical NNT trials – independently repeated the same number of times as the value of NNT and with the same occurrence-probability of success as the value of absolute risk reduction. These independent Bernouilli trials, of course, have some probabilities of failure. Most decision-makers in practice would be more interested in how much the hypothetical NNT trials can achieve ‘success/failure’ with ‘how many’ patients, or the ‘odds’ of success versus failure, rather than ‘one’ outcome of success as the mean value.

Methods We investigated the properties of hypothetical NNT trials. A binomial distribution was employed to develop formulae for estimating the odds of success versus failure to gain net-benefit in the NNT-associated trials.

Results Most of the estimates of odds expected by the new intervention are between three and 1.72, converging to e – 1 as the NNT increases.

Conclusion When basing decisions on an NNT, clinicians and public health specialists should take account of the odds of achieving the theoretical NNT.

Keywords: number needed to treat, risk–benefit of therapy, binomial distribution, heuristic error


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