Test the robustness of your meta-analysis pooled estimate. Remove each study one at a time to see how the overall effect shifts. Identify influential studies and assess whether your conclusion depends on any single study.
| Study | Effect | CI Lower | CI Upper | |
|---|---|---|---|---|
Add each study with its name, effect size, and 95% confidence interval. Use the example button to load sample data and see the expected format.
Select fixed-effect (inverse-variance) or random-effects (DerSimonian-Laird) model. The same model is applied to each leave-one-out iteration.
The tool re-runs the meta-analysis removing each study one at a time. Compare each result to the overall pooled estimate to identify influential studies.
Download the influence plot as SVG or PNG. Copy the results table for your manuscript's sensitivity analysis section.
If the pooled estimate and its significance remain stable when any single study is removed, the meta-analysis conclusion is robust. Document this stability explicitly in your results section — reviewers and editors look for this.
A study that substantially shifts the pooled estimate when removed may simply be the largest or most precise study. Influence is not the same as bias. Investigate why a study is influential (sample size, population, methodology) rather than automatically excluding it.
Cochrane and PRISMA guidelines recommend pre-specifying which sensitivity analyses will be performed. Common pre-specified analyses include: removing high-risk-of-bias studies, comparing fixed vs. random effects, and leave-one-out analysis.
When reporting leave-one-out results, describe both the direction and magnitude of change in the pooled estimate. State whether any individual study removal changed the statistical significance or clinical interpretation of the result.
Sensitivity analysis is a core component of rigorous meta-analysis, required by both PRISMA 2020 reporting guidelines (Page et al., 2021) and the Cochrane Handbook for Systematic Reviews of Interventions (Higgins et al., 2023, Chapter 10). A sensitivity analysis meta-analysis examines whether analytical decisions — such as which studies to include, which statistical model to use, or how to handle missing data — materially change the pooled result. When the conclusion remains stable across all tested scenarios, the evidence is considered robust.
The leave one out analysis tool implements the most common form of sensitivity analysis: sequential omission. Each study is removed one at a time, and the meta-analysis is re-computed with the remaining k−1 studies. The resulting series of pooled estimates reveals which individual studies exert disproportionate influence on the overall result. A study is considered influential when its removal causes the pooled effect to cross the null line (changing statistical significance), shifts the point estimate by more than 10–20%, or substantially alters the I² heterogeneity statistic. The Baujat plot provides a complementary influence diagnostic by plotting each study's contribution to the overall Q heterogeneity statistic against its influence on the pooled result, and the Galbraith (radial) plot offers an alternative visualization where outlier studies appear as points falling outside the confidence band around the regression line.
This meta-analysis robustness check complements other sensitivity approaches described in the Cochrane Handbook. GOSH (Graphical Overview of Study Heterogeneity) analysis extends the leave-one-out logic by computing the pooled estimate for every possible subset of studies, producing a scatter plot that reveals distinct clusters corresponding to different underlying subpopulations. Cook's distance, adapted from regression diagnostics to the meta-analytic context, quantifies each study's overall influence on the pooled estimate and its variance in a single summary measure. Pre-specifying these sensitivity analyses in your PROSPERO protocol before data extraction begins strengthens credibility by preventing post-hoc analytic decisions. Fixed-effect versus random-effects model comparison tests whether the variance structure assumption changes the conclusion. Excluding studies at high risk of bias (assessed using RoB 2 for randomized trials or ROBINS-I for non-randomized studies) determines whether methodological quality drives the result. Restricting to studies with directly measured outcomes versus proxy outcomes tests indirectness.
When reporting leave-one-out results, present the influence plot alongside a table showing the pooled estimate, 95% confidence interval, and I² for each iteration. Identify any studies whose removal changes the clinical or statistical interpretation. If the overall estimate depends critically on a single study, discuss whether that study has unique characteristics (largest sample size, different population, atypical methodology) that explain its influence.
The sensitivity analysis workflow connects directly to other meta-analytic assessments. Visualize the full set of study results using our forest plot generator to identify potential outliers before running leave-one-out analysis. Assess whether missing studies may bias the pooled estimate using our funnel plot and publication bias tool with Egger's regression test. If high heterogeneity persists across leave-one-out iterations, explore moderator variables using our meta-regression data formatter. Rate the overall certainty of your evidence — incorporating sensitivity analysis findings — with the GRADE certainty of evidence assessment tool.
Leave-one-out sensitivity analysis is a method for assessing the influence of individual studies on the pooled meta-analysis result. Each study is removed one at a time, and the meta-analysis is re-run with the remaining studies. If the pooled estimate changes substantially when a particular study is removed, that study is considered influential. This technique helps identify studies that disproportionately drive the overall result and informs decisions about the robustness of the meta-analytic conclusion.
Sensitivity analysis should be performed routinely in every meta-analysis, as recommended by Cochrane and PRISMA guidelines. It is especially important when: (1) studies differ in quality or risk of bias, (2) there is substantial heterogeneity (high I²), (3) one or more studies are outliers, (4) studies differ in design (e.g., RCTs mixed with observational studies), or (5) there are concerns about the influence of a single large study. Pre-specifying sensitivity analyses in your protocol strengthens the credibility of the review.
Compare each 'study-removed' pooled estimate to the overall pooled estimate. If removing a single study causes the pooled effect to cross the null line (e.g., the confidence interval shifts from significant to non-significant or vice versa), or if the point estimate changes by more than 10-20%, that study is influential. A robust pooled estimate should remain relatively stable regardless of which study is removed. Identify and discuss influential studies in your results section.
Sensitivity analysis tests the robustness of the overall result by varying analytical decisions (e.g., removing studies, changing the model, excluding high-risk-of-bias studies). Subgroup analysis tests whether the effect differs across predefined groups (e.g., by age, intervention dose, or study design). Sensitivity analyses answer 'Is the result robust?' while subgroup analyses answer 'Does the effect vary by group?' Both are important but serve different purposes.
Leave-one-out sensitivity analysis is not designed to detect publication bias directly. However, it can reveal if the pooled estimate is driven primarily by one or two small studies with extreme effects — a pattern that could overlap with publication bias. For formal publication bias assessment, use funnel plots with Egger's test or trim-and-fill analysis. Sensitivity analysis complements, but does not replace, dedicated publication bias methods.
The Cochrane Handbook recommends pre-specifying sensitivity analyses in your protocol. Common scenarios include: restricting to low risk-of-bias studies, excluding outliers, comparing fixed-effect versus random-effects models, testing different effect size metrics (OR vs. RR), and varying inclusion criteria. Sensitivity analyses should be planned a priori to avoid data-driven decisions.
Sensitivity analysis tests whether methodological or analytical decisions change the overall result (e.g., removing high-bias studies). Subgroup analysis explores whether the effect differs across pre-specified clinical or demographic categories (e.g., adults vs. children). Both address heterogeneity, but sensitivity analysis focuses on robustness while subgroup analysis focuses on effect modification.
Visualize your full meta-analysis results with our forest plot generator with weighted squares and diamond summary . Assess publication bias using our funnel plot and publication bias tool with Egger's test and trim-and-fill. Calculate individual study effect sizes with our effect size calculator for SMD, OR, and RR. Assess the certainty of your evidence with our GRADE certainty of evidence assessment tool.
Our biostatisticians can conduct complete meta-analyses with rigorous sensitivity and subgroup analyses, produce publication-ready plots, and write the statistical methods and results sections for your systematic review.