Forest Plot

Each horizontal line represents a single study's point estimate (the observed effect size) and its confidence interval (typically 95%). The length of the line indicates the precision of the study; shorter lines denote higher precision and narrower confidence intervals. The central square or dot is often sized proportionally to the weight assigned to that study in the meta-analysis, usually based on the inverse of its variance.

The pooled summary effect is represented by a diamond at the bottom of the plot. The center of the diamond marks the combined point estimate. The lateral tips of the diamond represent the confidence interval for this summary measure. If the diamond does not cross the line of no effect (e.g., 1.0 for odds ratios, 0 for mean differences), the overall result is statistically significant.

A vertical line traversing the plot that represents the null hypothesis value. For ratio measures like odds ratios or hazard ratios, this line is drawn at 1.0. For continuous measures like mean differences, it is drawn at 0. If an individual study's confidence interval or the summary diamond crosses this line, the result is not statistically significant at the chosen alpha level.

Key metrics quantifying the variability in effect sizes across studies are typically displayed in a corner of the plot. The I-squared (I²) statistic describes the percentage of total variation attributable to heterogeneity rather than chance. Cochran's Q test provides a p-value for the presence of heterogeneity. High I² values (e.g., >75%) suggest substantial inconsistency, often warranting a random-effects model over a fixed-effect model.

Forest plots are often flanked by columns of raw data for transparency and verification. Common columns include:

• Study ID: Author and year of publication.
• Effect Size: The calculated metric (e.g., log odds ratio).
• Lower/Upper CI: The bounds of the 95% confidence interval.
• Weight: The relative contribution of the study to the pooled estimate, often expressed as a percentage.

In complex forest plots, studies are grouped into distinct subgroups (e.g., by drug dosage or patient demographics). A separate summary diamond is calculated for each subgroup, and an overall diamond for the total pooled effect is shown. This allows the reader to visually compare treatment effects across different clinical contexts and assess if the effect modification is significant.

A forest plot graphically displays the point estimate and confidence interval from each participating institution's local analysis. This allows a biostatistician to immediately identify outlier sites where the treatment effect deviates from the federated consensus, triggering a privacy-preserving audit of local inclusion criteria or data quality without exposing patient-level records.

The summary effect is represented by a diamond at the bottom of the plot, where the diamond's width corresponds to the 95% confidence interval of the federated aggregate. This visual cue is generated by a Secure Aggregation Protocol that combines local hazard ratios or odds ratios using inverse variance weighting, giving more influence to sites with larger sample sizes or more precise estimates.

The plot's line of no effect (typically at 1.0 for ratio measures) provides an immediate visual test:

• If a study's confidence interval crosses this line, the result is not statistically significant at that site.
• Federated systems can overlay a clinical significance zone to distinguish statistically detectable effects from those large enough to warrant a change in medical practice.

The size of the square representing each site's estimate is proportional to the weight assigned in the meta-analysis. In a federated context, this weight is often derived from the inverse of the variance of the local estimate. This visual encoding immediately reveals if the global model is being dominated by a single large health system, prompting a review of population stratification and site-specific biases.

Federated forest plots can be stratified by computable phenotypes or demographic variables. A researcher can request separate forest plots for male vs. female patients or for different age brackets. Each site executes the stratified Cox Proportional Hazards Model locally and returns only the subgroup-specific hazard ratios, which are then rendered as distinct rows in the plot to reveal effect modification.

The I-squared statistic quantifies the percentage of total variation across sites due to heterogeneity rather than chance. In a federated dashboard, the forest plot is dynamically linked to this metric. If I-squared exceeds a pre-registered threshold (e.g., 50%), the system can automatically flag the analysis, suggesting a switch from a fixed-effect to a random-effects model to account for between-site variance.