This tab displays the uploaded data. Review your data here to ensure it has been correctly loaded and formatted.
Forest Plot: Displays effect sizes and confidence intervals for each study, with the pooled random-effects estimate shown as a diamond. Square sizes are proportional to study weights. If the diamond does not cross the line of no effect (1 for OR/RR, 0 for SMD), the pooled result is statistically significant.
Subgroup Configuration
Subgroup analysis using the random effects model will compare effect sizes between different subgroups and test for subgroup differences.
Upload data with categorical variables to perform subgroup analysis.
Random Effects Subgroup Analysis: Forest plot showing studies grouped by the selected variable, with random effects pooled estimates for each subgroup.
Subgroup Test Results
Ready for Random Effects Subgroup Analysis
Select a subgroup variable and click 'Run Subgroup Analysis' to begin.
Normality Assessment
These plots assess whether the random effects model assumptions are met:
Deleted Residuals Comparison
Deleted Residuals Q-Q: Compares fixed effects (left) vs random effects (right) deleted residuals against N(0,1). Red dashed line = identity; gray region = 95% simulation envelope. If RE residuals align better than FE residuals, this provides informal evidence that heterogeneity is present and the RE model may be more appropriate.
Best Linear Unbiased Predictors (BLUPs)
BLUPs Q-Q: An informal diagnostic for whether study-specific effects follow a normal distribution. Red dashed line = identity; gray region = 95% envelope. S-shaped curves or points outside the envelope may suggest departures from normality, potential outliers, or unmodeled subgroups.
Formal Statistical Tests
Additional Diagnostics
Outlier Detection: Displays standardized residuals for each study with reference lines at ±1.96. Studies outside these bounds may be outliers that warrant investigation.
Funnel Plot: Plots effect sizes against precision (1/SE). In the absence of bias, studies should scatter symmetrically around the pooled effect. Asymmetry may suggest publication bias or other small-study effects, though it can also arise from genuine heterogeneity.
Trim & Fill: Estimates and imputes potentially missing studies (shown as open circles) to restore funnel symmetry. The adjusted pooled estimate shows how results might change if suspected missing studies were included. Large differences between original and adjusted estimates suggest sensitivity to potential publication bias.
Leave-One-Out: Recalculates the pooled effect by sequentially removing each study. If removing a study substantially changes the overall estimate or its significance, the results may be sensitive to that study, which warrants further investigation.
Baujat Plot: Plots each study's contribution to the overall heterogeneity (Q statistic) against its influence on the pooled effect. Studies in the top-right quadrant contribute most to both heterogeneity and the overall result, and may warrant closer examination.
Fixed Effects Forest Plot: Displays effect sizes under the fixed-effect model, which assumes all studies share a single true effect. The diamond represents the pooled estimate. This model may be appropriate when heterogeneity is low (non-significant Q-test, low I²) and study confidence intervals largely overlap.
Subgroup Configuration
Subgroup analysis using the fixed effects model assumes a common effect within each subgroup and tests for differences between subgroups.
Upload data with categorical variables to perform subgroup analysis.
Fixed Effects Subgroup Analysis: Forest plot showing studies grouped by the selected variable, with fixed effects pooled estimates for each subgroup.
Subgroup Test Results
Ready for Fixed Effects Subgroup Analysis
Select a subgroup variable and click 'Run Subgroup Analysis' to begin.
Normality Assessment
This plot assesses whether the fixed effects model assumptions are met:
Standardized Residuals Q-Q: An informal diagnostic for whether residuals follow a standard normal distribution. Red dashed line = identity; gray region = 95% envelope. Systematic deviations from the diagonal may suggest non-normality or the presence of heterogeneity not captured by the fixed-effect model.
Formal Statistical Test
Outlier Detection
Outlier Detection: Identifies potential outliers based on standardized residuals. Studies with large residuals may be outliers or may not follow the fixed-effect assumption.
Funnel Plot: Plots effect sizes against precision. For a fixed-effect model, the plot should be symmetrical around the pooled estimate. Asymmetry, particularly gaps in the bottom corners, may suggest publication bias or small-study effects.
Trim & Fill: Imputes potentially missing studies (open circles) to restore funnel symmetry. The adjusted estimate shows how results might change if publication bias were present. Large differences between original and adjusted estimates suggest sensitivity to potential bias.
Leave-One-Out: Shows how the fixed-effect estimate changes when each study is sequentially removed. If removing a study substantially changes the overall estimate or significance, the results are sensitive to that study.
Baujat Plot: Plots each study's contribution to the Q statistic (heterogeneity) against its influence on the pooled effect. Since the fixed-effect model assumes no heterogeneity, studies contributing significantly to Q may be potential outliers or violate model assumptions.
Forest Plot: Displays individual study effect sizes and the pooled estimate (diamond). The pooled estimate is derived from Maximum Likelihood Estimation, which jointly estimates μ and τ.
Joint Confidence Region: Shows the joint confidence region for the overall effect (μ) and heterogeneity (τ) at multiple confidence levels (50%, 90%, 95%, 99%). The cross marks the MLE. A wider region indicates greater uncertainty. Unlike traditional methods that treat τ as fixed, this visualizes how uncertainty in μ and τ are interrelated.
Note (binary outcomes): For OR/RR, the model estimates μ on the log scale, but for convenience we display the x-axis on the original OR/RR scale (i.e., exp(μ)) using a log-scaled axis.
Efficacy-Harm Plot: Shows the probability that a new study's true effect exceeds (or falls below) clinical thresholds, with confidence bands derived from the joint (μ, τ) uncertainty. The steepness of the curve indicates certainty. This translates statistical uncertainty into clinically interpretable probabilities.
Probability Table for Key Clinical Thresholds
What it shows: This table mirrors the Efficacy/Harm plot. For each threshold value T, it reports whichever probability you selected above (either P(θ ≥ T) or P(θ ≤ T)), along with 95% confidence intervals.
How to use: Toggle the probability direction to switch between "benefit" and "harm" perspectives and use custom thresholds to pull precise numbers from the curve.
Subgroup Configuration
Subgroup analysis using the JCR method performs separate JCR meta-analyses for each subgroup, providing joint MLE estimation of effect and heterogeneity parameters.
Upload data with categorical variables to perform subgroup analysis.
Subgroup Analysis: Forest plot showing studies grouped by the selected variable, with pooled estimates for each subgroup derived from joint MLE.
Subgroup Comparison
Ready for JCR Subgroup Analysis
Select a subgroup variable and click 'Run Subgroup Analysis' to begin.
Normality Assessment
These plots assess whether the JCR meta-analysis model assumptions are met using joint MLE estimation:
Deleted Residuals Comparison
Deleted Residuals Q-Q: Compares fixed effects (left) vs MLE (right) deleted residuals against N(0,1). Red dashed line = identity; gray region = 95% simulation envelope. Comparing the two panels may reveal differences in how well each model captures the data structure.
Best Linear Unbiased Predictors (BLUPs)
BLUPs Q-Q: An informal diagnostic for whether study-specific effects follow a normal distribution. Red dashed line = identity; gray region = 95% envelope. Deviations may suggest departures from the assumed normal distribution.
Formal Statistical Tests
Funnel Plot: Plots study-specific effect sizes against their standard errors. The plot should be symmetrical in the absence of publication bias. Asymmetry may suggest that small studies with non-significant results are missing.
Confidence Region Shift: Shows how the joint confidence region for (μ, τ) shifts when each study is removed. The black contour is from the full dataset; colored contours show leave-one-out results. Large shifts indicate that results may be sensitive to that particular study.
Note (binary outcomes): For OR/RR, the x-axis is shown on the original OR/RR scale (exp(μ)) using a log-scaled axis.
Baujat Plot: Plots each study's contribution to heterogeneity (Q statistic) against its influence on the pooled effect. Studies in the top-right quadrant contribute most to both and may warrant closer examination.
Meta-Regression Configuration
Configure meta-regression analysis with continuous or categorical moderators.
Meta-regression investigates how study characteristics (moderators) relate to effect sizes. This helps explain heterogeneity and identify factors that influence treatment effectiveness.
To perform meta-regression, upload data that includes additional columns with continuous or categorical variables (e.g., 'moderator1', 'moderator2', etc.).
What it is: A scatter plot showing the relationship between the moderator variable (x-axis) and effect sizes (y-axis). The regression line shows the predicted relationship.
How to interpret: The slope indicates how effect size changes per unit increase in the moderator. A significant slope suggests the moderator explains heterogeneity between studies.
Model Interpretation
What it is: A bubble plot where bubble size represents study precision (inverse variance). Studies with larger bubbles have more influence on the regression.
How to interpret: This helps identify whether the relationship is driven by a few large studies or is consistent across studies of different sizes.
What it is: A plot of residuals (observed - predicted effect sizes) against fitted values. This helps assess model assumptions.
How to interpret: Random scatter suggests good model fit. Patterns may indicate violations of assumptions or need for additional moderators.
What it is: Influence diagnostics identify studies that disproportionately affect the meta-regression results. Cook's distance and hat values are plotted.
How to interpret: Points to the right/top indicate influential studies. Investigate them for data quality or study-level differences.
Influence Summary
Ready for Meta-Regression
Select a moderator variable and click 'Run Meta-Regression' to begin.
Meta-regression helps identify study characteristics that may explain differences in effect sizes across studies.