A Meta-Analysis Package for R https://metafor-project.org/ 2026-04-16T04:54:21+00:00 https://metafor-project.org/ https://metafor-project.org/lib/exe/fetch.php/wiki:logo.png text/html 2023-10-22T13:43:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:baujat_plot?rev=1697982227 Baujat Plot Description Baujat et al. (2002) proposed a diagnostic plot to detect sources of heterogeneity in meta-analytic data. The plot shows the contribution of each study to the overall Q-test statistic for heterogeneity on the horizontal axis versus the influence of each study (defined as the standardized squared difference between the overall estimate based on an equal-effects model with and without the $i$ text/html 2024-09-18T15:47:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:caterpillar_plot?rev=1726674426 Caterpillar Plot Description A caterpillar plot is in essence nothing different than what is often called a forest plot in the meta-analytic literature, except that the estimates are ordered by their magnitude. Also, the term tends to be used under circumstances where the number of estimates is rather large, so focus is on showing the general pattern of the results and not making individual estimates fully discernible. The code below shows how such a plot can be created with the text/html 2024-04-16T12:26:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:contour_enhanced_funnel_plot_2?rev=1713270374 Contour-Enhanced Funnel Plot 2 Description Here is another example of a contour-enhanced funnel plot (Peters et al., 2008) (see here for a brief discussion of the idea behind such plots). This one is a very close re-creation of Figure 2(b) from Peters et al. (2008). Note that the values for text/html 2024-04-16T12:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:contour_enhanced_funnel_plot?rev=1713270037 Contour-Enhanced Funnel Plot Description Below is an example of what is sometimes called a contour-enhanced funnel plot (Peters et al., 2008). Note that the funnel is centered not at the model estimate (as is usually done when drawing funnel plots), but at 0 (i.e., at the value under the null hypothesis of no effect). Various levels of statistical significance of the points/studies are indicated by the shaded regions. In particular, the unshaded (i.e., white) region in the middle corresponds t… text/html 2023-08-19T13:38:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:cumulative_forest_plot?rev=1692452317 Cumulative Forest Plot Description A cumulative meta-analysis describes the accumulation of evidence (e.g., about the effectiveness of a particular treatment or intervention) as the available estimates are added to the analysis in (typically) chronological order (Chalmers & Lau, 1993; Lau et al., 1995). After fitting a model, for example with the text/html 2025-09-16T11:16:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_bmj?rev=1758021376 Forest Plot in BMJ Style Description Journals have different requirements as to how a forest plot should be drawn and the various pieces of information that should be included in the figure. For example, the figure below was extracted from the article by text/html 2024-09-18T16:02:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_revman?rev=1726675363 Forest Plot in RevMan Style Description Different software for meta-analysis draws forest plots in different styles and includes various pieces of information in the figure. For example, the figure below was created using RevMan, the software provided by the text/html 2024-09-18T20:15:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_with_multiple_cis?rev=1726690516 Forest Plot with Multiple CIs Description The question has come up how one can draw a forest plot where multiple confidence intervals with different confidence levels are shown for the same set of studies. To accomplish this, we can use a trick where we draw the same forest plot twice on top of each other (using text/html 2024-10-24T09:03:51+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_with_subgroups?rev=1729760631 Forest Plot with Subgroups Description Below is an example of a forest plot with three subgroups. The results of the individual studies are shown grouped together according to their subgroup. Below each subgroup, a summary polygon shows the results when fitting a random-effects model just to the studies within that group. The summary polygon at the bottom of the plot shows the results from a random-effects model when analyzing all 13 studies. text/html 2024-10-24T09:06:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_with_superscripts?rev=1729760772 Forest Plot with Superscripts Description Some journals require reference numbers to be shown in forest plots (in addition to the study authors and publication years). Typically, the reference numbers are supposed to be shown as superscripts. How to accomplish this with R and the metafor package has occasionally been asked. Text involving superscripts can be added to plots using 'expressions', which are more generally used to add mathematical equations to plots. See text/html 2024-10-24T09:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot_with_textpos?rev=1729760915 Forest Plot with Adjusted Text Position Description By default, the forest() function places the annotations (giving the study-specific estimates and corresponding confidence interval bounds) to the right of the actual forest plot. See here for an example. Sometimes, we might prefer to show those annotations in a different position. This can be done with the text/html 2024-10-24T08:58:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:forest_plot?rev=1729760323 Forest Plot Description A forest plot is a commonly used visualization technique in meta-analyses, showing the results of the individual studies (i.e., the estimated effects or observed outcomes) together with their (usually 95%) confidence intervals. A four-sided polygon, sometimes called a summary 'diamond', is added to the bottom of the plot, showing the summary estimate based on the model (with the center of the polygon corresponding to the estimate and the left/right edges indicating the … text/html 2021-11-08T15:50:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:funnel_plot_variations?rev=1636386606 Funnel Plot Variations Description A funnel plot shows the observed effect sizes or outcomes on the x-axis against some measure of precision of the observed effect sizes or outcomes on the y-axis. Based on Sterne and Egger (2001), the recommended choice for the y-axis is the standard error (in decreasing order) and this is also the default for the $\hat{\theta} \pm 1.96 SE$$\hat{\theta}$$SE$ text/html 2022-04-22T11:40:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:funnel_plot_with_limit_estimate?rev=1650627648 Funnel Plot with Limit Estimate Description Based on the regression test for funnel plot asymmetry, one can obtain a 'limit estimate' of the (average) true effect. The underlying idea is quite simple: When the standard error, sampling variance, or inverse (square root) sample size is used as the predictor for the regression test, the intercept of the model underlying the regression test in essence reflects the estimate under infinite precision. This is sometimes (cautiously) interpreted as an … text/html 2023-08-29T19:24:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:funnel_plot_with_trim_and_fill?rev=1693337054 Funnel Plot with Trim and Fill Description The trim and fill method is a nonparametric (rank-based) data augmentation technique proposed by Duval and Tweedie (2000a, 2000b; see also Duval, 2005). The method can be used to estimate the number of studies missing from a meta-analysis due to the suppression of the most extreme results on one side of the funnel plot. The method then augments the observed data so that the funnel plot is more symmetric. The method should not be regarded as a way of y… text/html 2021-11-08T15:40:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:gosh_plot?rev=1636386042 GOSH Plot Description Olkin, Dahabreh, and Trikalinos (2012) proposed the GOSH (graphical display of study heterogeneity) plot, which is based on examining the results of an equal-effects model in all possible subsets of size $1, \ldots, k$ of the $k$ studies included in a meta-analysis. In a homogeneous set of studies, the model estimates obtained this way should form a roughly symmetric, contiguous, and unimodal distribution. On the other hand, when the distribution is multimodal, then this … text/html 2024-04-18T14:17:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:labbe_plot?rev=1713449866 L'Abbé Plot Description In a L'Abbé plot (based on L'Abbé, Detsky, & O'Rourke, 1987), the arm-level outcomes for two groups (e.g., treatment and control groups) are plotted against each other. The example below is based on a meta-analysis examining the effectiveness of a particular treatment (topical plus systemic antibiotics) for preventing respiratory tract infections. Since the meta-analysis is conducted with log odds ratios, the points in the first plot show by default the log odds of a re… text/html 2022-03-26T16:15:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:meta_analytic_scatterplot?rev=1648311335 Meta-Analytic Scatter Plot (Bubble Plot) Description Below is an example of a scatter plot (also known as a bubble plot), showing the observed outcomes (i.e., risk ratios) of the individual studies plotted against a quantitative predictor (i.e., the absolute latitude of the study locations). The size of the points is drawn proportional to the weight that the studies received in the analysis (with larger points for studies that received more weight). Based on the mixed-effects meta-regression m… text/html 2022-08-03T11:29:03+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:normal_qq_plots?rev=1659526143 Normal QQ Plots Description A normal quantile-quantile (QQ) plot can be useful in meta-analyses to check various aspects and assumptions of the data. Ideally, the points in the plot should fall on a diagonal line with slope of 1, going through the (0,0) point. Deviations from this may indicate that (a) the (residual) heterogeneity in the true effects is non-normally distributed, (b) there are subgroups in the data (that are not adequately modeled by any moderators already included in the model… text/html 2022-04-22T11:42:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:plot_of_cumulative_results?rev=1650627752 Plot of Cumulative Results Description Instead of using a cumulative forest plot, another way to illustrate the results from a cumulative meta-analysis is to plot the estimate of the average effect against the estimated amount of heterogeneity as each study is added to the analysis in turn. An object returned by the text/html 2024-11-06T15:26:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:plot_of_influence_diagnostics?rev=1730906761 Plot of Influence Diagnostics Description A variety of outlier and influential case diagnostics can be computed when conducting a meta-analysis (Viechtbauer & Cheung, 2010). The figure below shows a plot of the (1) externally standardized residuals, (2) DFFITS values, (3) Cook's distances, (4) covariance ratios, (5) leave-one-out estimates of the amount of heterogeneity, (6) leave-one-out values of the test statistics for heterogeneity, (7) hat values, and (8) weights. Three studies have rathe… text/html 2021-11-08T13:22:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://metafor-project.org/doku.php/plots:radial_plot?rev=1636377720 Radial (Galbraith) Plot Description The radial plot (also called Galbraith plot) was introduced by Rex Galbraith (1988a, 1988b, 1994) and can be useful in the meta-analytic context to examine the data for heterogeneity. For an equal-effects model, the plot shows the inverse of the standard errors on the horizontal axis against the observed effect sizes or outcomes standardized by their corresponding standard errors on the vertical axis. On the right hand side of the plot, an arc is drawn corre…