Forest plot: not seeing the wood for the logs
According to Wikipedia (1), a forest plot may have a natural
logarithmic scale on the x- axis so that confidence intervals can appear
symmetrical about the means, and ratios (relative risk being a ratio) seem
equivalent both above one and below one. A log scale will give the same
length in a confidence interval for a ratio of ten, whether this is ten to
one or one to one tenth.
'One' at the bottom of the y- axis is the null hypothesis of no
effect. The forest plot provides a display of the null hypothesis as the y
- axis. If the confidence interval intrudes on this y- axis, then there is
no statistical significance.
But ... the forest plot on a logarithmic scale still may be capable
of the lie factor (2)- that is, graphical misrepresentation.
Natural logaritms are to base e, that is, 2.718 ... Confidence
intervals are worked out to base e in the BMJ book, Statistics with
However, most forest plots are to base 10, not base e. Traipsing
unsteadily through the Internet, I also happened upon a forest plot of
base 2 on the x- axis(4). There are linear forest plots too.
Different log bases would manipulate the visual lay- out, perhaps to
I am not a mathematician, and my own previous rapid responses to this
article, and indeed the transcription error in the article, indicate the
confusion possible over forest plots and their x- axis.
The difficulty with the x- axis in forest plots emerges most when the
effect size is numbers needed to treat- then the null hypothesis is set at
The term, forest plot, only emerged during the 1990's. The unhappy
suggestion has to be that it remains an immature statistical device. It is
not yet thoroughly confident and sound in root and branch.
As far as forest plots are concerned, one is not seeing the wood for
(1) Forest Plot. Wikipedia.
(2) The Cambridge Dictionary of Statistics in the Medical Sciences.
B. S. Everitt. CUP. 1995. Pg. 142.
(3) Statistics with Confidence- Confidence intervals and statistical
guidelines. Martin J Gardner and Douglas G Altman. BMJ. 1990. Pgs. 51-52.
(4) Statins and cancer Risk: A Literature- Based Meta- Analysis and
Meta- Regression Analysis of 35 Randomized Controlled trials. Journal of
Clinical Oncology. Vol. 24. No. 30. Pgs. 4808-4817. (October 20). 2006. S.
Bonovas et al.
(5) Confidence intervals for the number needed to treat. Douglas G
Altman. BMJ 1998;317:1309-12.
Competing interests: No competing interests