Mathematical problems are medical problems
This is a late apology to Professor Altman about how I was so
misleading in my trek through log scales and meta-analyses. I have been
confused and confusing.
Customarily, a forest plot will have a relative risk (or odds ratio)
on a logarithmic x- axis. A log axis is resorted to because the standard
error of relative risk is logarithmic (1). A linear framework would
possess skewed, irregular confidence intervals, which are based on the
One is unhappily reminded of Alice's uncomfortable variations in
dimensions through that vertiginous looking glass.
With numbers needed to treat, another difficulty pops up- that the
null hypothesis of no effect is at infinity. Various weird things then
happen to the confidence intervals! (2) A forest plot becomes most
problematic. Curiouser and curiouser...
What one might fear is that forest plots are not always 'particularly
elegant and intuitively comprehensible' (3). They suffer from mathematical
complexities, revolving round the confidence intervals. There are relative
axes that are linear, that are to log 2 or log 10, that could thus be
manipulated to make them appear what they are not in the cliche of
evidence biased medicine.
Professor Altman claims: 'the NNT should never be used as the basis
for a meta- analysis' (4).
But the actual article on Irritable Bowel Syndrome (IBS) is a meta-
analysis that does resort to numbers needed to treat (5). NNT is quoted in
the conclusion ('What This Study Adds'). NNT is a mathematical draw- back
only when the confidence interval is not statistically significant. NNT
is, as Professor Altman nervously implies, only partially applicable in a
Anti- spasmodics are said to be first- line treatment by NICE and the
British Society of Gastroenterology, but have an inferior NNT to the
apparently natural remedy of peppermint oil. Peppermint oil is not
recommended at all in the official prescribing guidelines. Without this
article, and its homely reliance on NNT, we would be less aware of the
peppermint oil factor in IBS.
Graphs more than any other part of statistical presentation can be
prone to deformation and distortion. Against all the brave efforts of
people such as Professor Altman, not enough down to earth explanations of
statistical methods exist. Medicine is even more bewildered than Alice as
it confronts the Chesire cats and Jabberwockys of mathematics.
Mathematical problems can be medical problems.
Again I am sorry to Professor Altman and the BMJ for having been such
an idiot over these dreadfully complex issues. Any layman must feel
bewildered by the not always well fitting nexus between medicine and
(1) Statistics with Confidence. M.J.Gardner and D.G.Altman. BMJ.
(2) Confidence Intervals and the number needed to treat. D.G.Altman.
(3) How to read and understand and use systematic reviews and meta-
analyses. S.Leucht et al. Acta Psychiatr Scand 2009:119:pg. 447.
(4) Re: Forest Plot: not seeing the wood for the logs. BMJ Rapid
response. D.G.Altman. 18 May 2009.
(5) Effect of fibre, antispasmodics and peppermint oil in the
treatment of irritable bowel syndrome: systematic review and meta-
analysis. Alexander c. Ford et al. BMJ 2008;337:a2313.
Competing interests: No competing interests