In a meta-analysis of clinical trials with binary outcomes (for example, remission versus no remission, adverse event versus no adverse event), the forest plot shows us the relative effect sizes (odds ratios, relative risks, or risk differences) and their combination. However, a limitation of the forest plot is that it conceals information about the absolute event rates in each group. The L'Abbe plot, proposed by Kristen L'Abbe and colleagues in 1987, addresses precisely this limitation by graphically representing the event rates in both groups for each study included in the meta-analysis.
Construction of the plot
The L'Abbe plot is conceptually straightforward. It is a scatter diagram in which each study is represented as a circle whose position is determined by two coordinates. The horizontal axis shows the event rate in the control group of the study, that is, the proportion of control group participants who experienced the event of interest. The vertical axis shows the event rate in the experimental or treatment group. Both axes range from 0 to 1, representing proportions.
The size of each circle is proportional to the study's sample size (or, in some implementations, to the weight the study receives in the meta-analysis). This allows visual identification of which studies are the largest and, therefore, most influential in the combined estimate.
The diagonal line and its interpretation
The key element for interpreting the L'Abbe plot is the diagonal line that runs from the lower-left corner (0,0) to the upper-right corner (1,1). This line represents equality between the two groups: any study whose point falls exactly on the diagonal has an identical event rate in both the control and treatment groups, meaning there is no treatment effect.
The interpretation of points that deviate from the diagonal depends on the nature of the event being measured. If the event is a negative outcome (death, relapse, adverse effect), points that fall below the diagonal indicate that the treatment is beneficial, because the event rate is lower in the treatment group than in the control group. Points above the diagonal would indicate that the treatment is harmful. If, conversely, the event is a positive outcome (remission, clinical improvement), the interpretation is reversed.
Advantages over the forest plot
The main advantage of the L'Abbe plot over the forest plot is that it shows the absolute event rates in both groups, not just the relative effect. This distinction is fundamental in clinical decision-making. A relative risk of 0.50 sounds very impressive, but its clinical significance depends entirely on the baseline event rate. If the rate in the control group is 2%, a 50% relative reduction means going from 2% to 1%, an absolute difference of merely 1 percentage point. If the baseline rate is 40%, the same relative reduction implies going from 40% to 20%, an absolute difference of 20 percentage points with much more relevant clinical implications.
The L'Abbe plot allows us to visualize exactly this information. Studies with high baseline rates will appear on the right side of the plot, while studies with low baseline rates will be on the left. The vertical distance between each point and the diagonal line represents the absolute risk difference in that study.
Detecting heterogeneity
The L'Abbe plot is also useful for assessing heterogeneity, although in a different way than the forest plot or the Galbraith plot. If all studies show a similar treatment effect, the points on the plot will form a coherent pattern: they will be grouped on the same side of the diagonal and at a relatively constant distance from it. If the points are scattered, with some above and others below the diagonal, or with highly variable distances, this suggests heterogeneity.
A particular source of heterogeneity that the L'Abbe plot can reveal is the interaction between the baseline event rate and the magnitude of the treatment effect. In some meta-analyses, the treatment works better in populations with high baseline rates than in populations with low baseline rates (or vice versa). This type of pattern is difficult to detect with a conventional forest plot but can be visually evident in a L'Abbe plot: points on the right (high baseline rates) will be further from the diagonal than those on the left.
Limitations and scope of application
It is important to note that the L'Abbe plot is designed exclusively for meta-analyses with binary outcomes. It cannot be applied to meta-analyses of continuous outcomes, because the concept of event rates does not exist in that context. For continuous outcomes, tools such as the forest plot, the Galbraith plot, or funnel plots remain the appropriate options.
Furthermore, the L'Abbe plot does not provide a formal statistical test of heterogeneity or a quantitative estimate of the combined effect. It should always be used as a complement to quantitative analyses, not as a substitute. Its value lies in its ability to reveal patterns that numbers alone do not show with the same clarity.
Implementation in R
In R, the L'Abbe plot can be easily generated with the meta package. Once we have performed our meta-analysis with the metabin() function (for binary data), we simply call the labbe() function:
library(meta)
result <- metabin(event.e, n.e, event.c, n.c,
data = dataset, studlab = study)
labbe(result)The function accepts arguments for customization, such as col for point color, bg for fill color, and cex for controlling the relative size of the circles. It is also possible to specify whether the diagonal line should represent a particular relative risk or odds ratio, rather than simply equality. In practice, the plot with the equality line is the most commonly used and intuitive approach for a first visual exploration of the data.