L'Abbé Plot

Meta-Analysis

To understand what the L'Abbé plot is, it is necessary to have a discussion about meta-analysis. Briefly, meta-analysis is a statistical method to provide a summary estimate by combining the results of many similar studies. A hypothesized meta-analysis of 10 clinical trials is used here to illustrate the use of the L'Abbé plot. The most commonly used graph in meta-analysis is the forest plot (as shown in Figure 1) to display data from individual trials and the summary estimate (including point estimates and 95% confidence intervals). The precision or statistical power of the summary estimate will be much improved by combining the results of many small studies. In this hypothesized meta-analysis, the pooled estimate of relative risk is 0.72 (95% confidence interval: 0.53–0.97), which suggests that the risk of lack of clinical improvement in the treatment group is statistically significantly lower than that in the control group. However, the results from the 10 trials vary considerably (Figure 1), and it is important to investigate why similar trials of the same intervention might yield different results.

Figure 2 is the L'Abbé plot for the hypothesized meta-analysis. The vertical axis shows the event rate (or risk) of a lack of clinical improvement in the treatment group, and the horizontal axis shows the event rate of a lack of clinical improvement in the control group. Each point represents the result of a trial, according to the corresponding event rates in the treatment and the control group. The size of the points is proportionate to the trial size or the precision of the result. The larger the sample size, the larger the point in Figure 2. However, it should be mentioned that smaller points might represent larger trials in a L'Abbé plot produced by some meta-analysis software.

The diagonal line (line A) in Figure 2 is called the equal line, indicating the same event rate between the two arms within a trial. That is, a trial point will lie on the equal line when the event rate in the treatment group equals that in the control group. Points below the equal line indicate that the risk in the treatment group is lower than that [Page 682]in the control group, and vice versa for points above the equal line. In the hypothesized meta-analysis, the central points of two trials (T01 and T04) are above the equal line, indicating that the event rate in the treatment group is higher than that in the control group. The points of the remaining eight trials locate below the equal line, showing that the risk in the treatment group is reduced in these trials.

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