# Forest Plot

## Definition

### Health Economics

• This is a diagram used in meta-analysis to show the effects estimated in a variety of trials together with their means and confidence intervals. It provides a diagrammatic representation of the amount of variation between the results of the trials and an estimate of the overall result of the studies as a whole. The results of the included studies are usually shown as squares in a column centred on the point estimate of each study's result. The length of a horizontal line through the square indicates its confidence interval. The overall estimate and its confidence interval are shown as a diamond whose centre is the pooled point estimate and whose horizontal tips indicate its confidence interval. It is so-called on account of the 'forest' of lines a typical graph may contain.

This is constructed as follows. The horizontal axis in the figure below measures the treatment effect - for example, the probability of death, so that to the left of the vertical axis death is less likely and to its right it is more likely. Where the vertical axis meets the horizontal corresponds to a probability of 1 (better outcomes are usually but not always to the left). The line ab shows the result of a single research study. The square dot in the middle of the line is the point estimate of the mean effect in this study. This is a measure of the effect of the treatment compared with a control group and is most often represented as an odds ratio. The square is small or large depending on the weight this study is to be given in the combined analysis. The length of the line around the point estimate is the confidence interval for the result. When a study has only a few patients the line will be long and the size of the square in its middle will be small.

Suppose there are two other studies, shown by the lines cd and ef. The study represented by cd shows the opposite effect to that in the previous study (in this study, the experimental arm does better than the control) and the confidence interval is narrower and the weight this study receives will be larger. There is a third study also, which has relatively low statistical significance and a small weight. Taking all three together, the summary is represented by the diamond, whose height locates the best estimate of effect and whose width indicates its confidence interval. Its position relative to the vertical axis shows what the conclusion is, on balance, taking the whole literature (in this case a forest plot of three items) into account. If the diamond crosses the vertical line, the conclusion is that the literature as a whole does not yield a clear answer about the relative effectiveness of the procedure in question (conventionally at the 95 per cent confidence level). The technique originated in the field of education research.

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