The inclusion of the estimated inter-study variation into forest plots for random-effects meta-analyses - a suggestion for a graphical representation

Article type
Authors
Skipka G
Abstract
Background: Meta-analyses are widely used to combine the results of clinical studies by calculating statistics for overall treatment effects. Basically, two different models exist for meta-analyses. The fixed-effect model (FEM) assumes each study is measuring the same treatment effect. Different estimations for the treatment effecct are expected to arise from sampling error only. By contrast, the random-effects model (REM) incorporates an inter-study variation [symbol] taking heterogeneous results into account. Usually, it is assumed that the true treatment effects are normally distributed with expectation [symbol] and variance [symbol]2. Although these two approaches estimate different parameters (true effect vs expectation of the distribution of true effects) the results are represented in the same way in practice. Commonly, the point and interval estimation of [symbol] is drawn in a forest plot as a diamond. But the estimation for the inter-study variation [symbol]2 is ignored in the representation of the results of REMs.

Objectives: To suggest a graphical possibility for including the estimated inter-study variation into forest plots when representing the results of random-effects meta-analyses.

Results: We include two rows for the summary statistics in the forest plot in case of REMs: The row 'total expectation (95% CI)' represents the point and interval estimation for [symbol]. The row 'total heterogeneity (95% CI)' represents the interval [a-1.96xb; a+1.96xb], where a and b indicate estimators for [symbol] and [symbol], respectively. This 'heterogeneity interval' delivers an approximated interval, where 95% of the true effects are to be expected.

Conclusions: This proposed extension of the forest plot may be helpful to distinguish accurately the results of meta-analyses from FEMs and REMs and to illustrate the amount of heterogeneity graphically.