# The forest plot

This is a section from Martin Bland’s text book An Introduction to Medical Statistics, Fourth Edition. I hope that the topic will be useful in its own right, as well as giving a flavour of the book. Section references are to the book.

## 17.2 The forest plot

Figure 17.1 shows an example of a forest plot, a graphical representation of the results of a meta-analysis, in this case of the association between migraine and ischaemic stroke.

Figure 17.1 Meta-analysis of the association between migraine and ischaemic stroke (data from Etminan et al. 2005). (Log relative risks for case–control studies are in fact log odds ratios, Section 13.7.)

A forest plot shows the estimate and associated confidence interval for each of the studies. In Figure 17.1, the grey circles represent the logarithms of the relative risks for the individual studies and the vertical lines their confidence intervals. It is called a forest plot because the vertical lines are thought to resemble trees in a forest. There are three pooled or meta-analysis estimates: one for all the studies combined, at the extreme right of the picture, and one each for the case–control and the cohort studies, shown as black circles. The pooled estimates have much narrower confidence intervals than any of the individual studies and are therefore much more precise estimates than any one study can give. In this case the study difference is shown as the log of the relative risk. The value for no difference in stroke incidence between migraine sufferers and non-sufferers is therefore zero, which is well outside the confidence interval for the pooled estimates, showing good evidence that migraine is a risk factor for stroke.

Figure 17.1 is a rather old-fashioned forest plot. The studies are arranged horizontally, with the outcome variable on the vertical axis in the conventional way for statistical graphs. This makes it difficult to put in the study labels, which are too big to go in the usual way and have been slanted to make them legible. The imprecise studies with wide confidence intervals are much more visible than those with narrow intervals and look the most important, which is quite wrong. The three meta-analysis estimates look quite unimportant by comparison. These are distinguished by colour in the original, shaded in my version, but otherwise look like the other studies. Figure 17.2 shows the results of a meta-analysis of elastic multilayer high compression bandaging versus inelastic multilayer compression for venous leg ulcers (Fletcher et al. 1997).

Figure 17.2 Meta-analysis of the effect of elastic multilayer high compression bandaging versus inelastic multilayer compression for venous leg ulcers (complete healing, after varying lengths of treatment) (data from Fletcher et al. 1997).

The outcome variable is complete healing, after lengths of treatment which varied between the three trials. This is based on a graph which was actually published several years before the study shown in Figure 17.1, but is a more developed version of the forest plot. This forest plot has been rotated so that the outcome variable is shown along the horizontal axis and the studies are arranged vertically. The squares represent the odds ratios for the three individual studies and the horizontal lines their confidence intervals. This orientation makes it much easier to label the studies and also to include other information, here the numbers healed and treated in each group. The size of the squares can represent the amount of information which the study contributes. If they are not all the same size, their area should be proportional to the weight given to them, their contribution to the overall estimate. This depends at least partly on the standard error of the estimates and hence on the study sample sizes. This means that larger studies appear more important than smaller studies, as they are. A different point symbol is shown for the pooled estimate, a diamond rather than a square, making it easy to distinguish.

The horizontal scale in Figure 17.2 is logarithmic, labelling the scale with the numerical odds ratio rather than showing the logarithm itself. A vertical line is shown at 1.0, the odds ratio for no effect, making it easy to see whether this is included in any of the confidence intervals.

Figure 17.3 shows a more evolved forest plot, showing the meta-analysis of three studies of metoclopramide for the treatment of migraine.

Figure 17.3 Graphical representation of a meta-analysis of metoclopramide compared with placebo in reducing pain from acute migraine (data from Colman et al. 2004).

On the right-hand side of Figure 17.3 are the individual trial estimates and the combined meta-analysis estimate in numerical form. On the left-hand side are the raw data from the three studies. The pooled estimate is now represented by a diamond or lozenge shape, making it much easier to distinguish from the individual study estimates than in Figure 17.1. The deepest point marks the position of the point estimate and the width of the diamond is the confidence interval. The choice of the diamond is now widely accepted, but other point symbols may yet be used for the individual study estimates. The vertical caps at the ends of the confidence interval lines have been dropped. I think this was a good idea; graphs like Figure 17.2 remind me of the view in Luke Skywalker’s rear-view mirror.

### References

Colman, I., Brown, M.D., Innes, G.D., Grafstein, E., Roberts, T.E., and Rowe, B.H. (2004). Parenteral metoclopramide for acute migraine: meta-analysis of randomised controlled trials. British Medical Journal, 329, 1369.

Etminan, M., Takkouche, B., Isorna, F.C., and Samii, A. (2005). Risk of ischaemic stroke in people with migraine: systematic review and meta-analysis of observational studies. British Medical Journal, 330, 63.

Fletcher, A., Cullum, N., and Sheldon, T.A. (1997). A systematic review of compression treatment for venous leg ulcers. British Medical Journal, 315, 576–80.

Adapted from pages 265–267 of An Introduction to Medical Statistics by Martin Bland, 2015, reproduced by permission of Oxford University Press.