9.4.25 Forest Plots, Chi-Square Test and Galbraith Plot
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Recognise Statistical Heterogeneity: Visual Inspection of Forest Plots, Chi-Square Test and Galbraith Plot
Statistical heterogeneity refers to the variability in effect estimates observed across studies in a meta-analysis beyond what could be attributed to chance. It can arise from differences in study design, population characteristics, interventions, and outcomes, among other factors. It is important to identify and quantify statistical heterogeneity in a meta-analysis to determine the appropriateness of pooling the study results.
Forest plots:
Visual inspection of forest plots is a common approach to detecting statistical heterogeneity. Forest plots are graphs that display the effect estimates and confidence intervals from each study included in a meta-analysis, with the summary estimate at the bottom. If the forest plot displays considerable dispersion of the effect estimates around the summary estimate, this may suggest heterogeneity.
| Element | Description |
| Study ID | Identifier for each study included in the meta-analysis (usually the first author’s name and year of publication) |
| Effect estimate | The estimate of the effect size for each study (e.g., odds ratio, risk ratio, mean difference, etc.) |
| Confidence interval | A range within which the true effect size is likely to fall, usually expressed as a 95% confidence interval (CI) |
| Weight | The proportion of the total combined effect estimate contributed by each study, usually based on the inverse of the variance (precision) of the study’s effect estimate |
| Horizontal line | Represents the confidence interval of the effect estimate for each study; the length of the line indicates the precision of the estimate (shorter lines indicate higher precision) |
| Square or dot | Represents the point estimate of the effect size for each study; the size of the square or dot may be proportional to the study’s weight in the meta-analysis |
| Vertical line at 1 (or 0) | Represents the line of no effect (e.g., odds ratio or risk ratio of 1, or mean difference of 0); effect estimates on the right side of the line indicate a positive effect, while those on the left side indicate a negative effect |
| Diamond | Represents the combined effect estimate from the meta-analysis, with the lateral points of the diamond representing the confidence interval of the combined effect estimate |
Chi-square test:
The chi-square test for heterogeneity is another method for detecting statistical heterogeneity. The test calculates a chi-square statistic that measures the amount of heterogeneity between studies. A significant chi-square test result (p<0.05) indicates that the observed heterogeneity is beyond what could be expected by chance.
Galbraith plot:
The Galbraith plot is a graphical tool that can help identify studies that contribute disproportionately to heterogeneity. The plot displays the effect estimate from each study against its precision (e.g., inverse variance or sample size) and includes a line that represents the summary estimate. Studies that lie far away from the line may be potential sources of heterogeneity.
To recognize statistical heterogeneity using the Galbraith plot, follow these steps:
- Plot the studies: Each study included in the meta-analysis is plotted on the Galbraith plot with its effect estimate (e.g., odds ratio, risk ratio, or mean difference) on the x-axis and the precision of the estimate (e.g., the inverse of the standard error) on the y-axis.
- Draw the regression line: A regression line is fitted to the data points representing the studies. This line represents the overall effect estimate, accounting for the precision of individual study estimates.
- Inspect the distribution of the studies around the regression line: If the studies are evenly distributed around the regression line without any clear pattern or clustering, this suggests that there is little or no statistical heterogeneity. However, if the studies are scattered and form clusters or display a distinct pattern, this may indicate the presence of statistical heterogeneity.
- Identify potential sources of heterogeneity: By examining the position of individual studies on the Galbraith plot, you may identify studies that contribute disproportionately to the heterogeneity. These studies can be further investigated to determine potential sources of heterogeneity, such as differences in population, intervention, or study design.
In summary, the Galbraith plot can be used to visually inspect statistical heterogeneity in a meta-analysis. By examining the distribution of studies around the regression line and identifying potential sources of heterogeneity, you can make more informed decisions about the appropriate model for the meta-analysis and interpret the results accurately.
It is important to note that the presence of statistical heterogeneity does not necessarily mean that the meta-analysis is invalid or that the summary estimate is not meaningful. However, it does indicate that caution should be taken when interpreting the results, and further exploration of potential sources of heterogeneity may be warranted.
References:
- Higgins, J. P. T., & Green, S. (Eds.). (2011). Cochrane handbook for systematic reviews of interventions. Wiley-Blackwell.