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A conundrum about confidence intervals

Published online by Cambridge University Press:  02 January 2018

Zekria Ibrahimi*
Affiliation:
Psychiatric patient, Coombs Library, West London Mental Health Trust, Southall UB1 3EU, UK. Email: ibrahimizekria@googlemail.com
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Abstract

Type
Correspondence
Copyright
Copyright © The Royal College of Psychiatrists 2011 

The article by Reference Hodgson, Cookson and TaylorHodgson et al(2011) unfortunately glosses over a problem with confidence intervals and numbers needed to treat. The problem is that, when the result is not significant, the confidence interval will include infinity (Reference AltmanAltman 1998) (since the absolute risk difference at zero implies a number needed to treat of 1 divided by zero, which is infinity). This is a mathematical conundrum that detracts from any medical interpretation and can confuse forest plots.

Some statisticians are suspicious of the number needed to treat, although it is preferred by many clinicians. The consensus seems to be that the number needed to treat is less easy to understand without an emphasis on the underlying absolute risk difference. The number needed to treat is not as efficient an indicator of effect size as are the odds ratio or relative risk in meta-analyses.

Clinicians have to navigate with much difficulty through the statistical fog of evidence-based medicine. There is a lack of articles such as that by Hodgson et al and one can often feel shipwrecked on the mathematical complexities of concepts such as the number needed to treat.

References

Altman, DG (1998) Confidence intervals for the number needed to treat. BMJ 317: 1309–12.CrossRefGoogle ScholarPubMed
Hodgson, R, Cookson, J, Taylor, M (2011) Numbers-needed-to-treat analysis: an explanation using antipsychotic trials in schizophrenia. Advances in Psychiatric Treatment 17: 6371.Google Scholar
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