Baujat Plots: Finding Which Studies Drive Heterogeneity in a Meta-Analysis

A Baujat plot is a diagnostic scatter plot used in meta-analysis to identify which included studies are driving observed heterogeneity in the pooled result. It plots each study’s contribution to the overall heterogeneity statistic on one axis against that same study’s influence on the pooled summary estimate on the other — making it possible to see, at a glance, which studies are worth a closer look or a formal sensitivity analysis.

The method comes from a single, specific source: Baujat B, Mahé C, Pignon JP, Hill C. “A graphical method for exploring heterogeneity in meta-analyses: application to a meta-analysis of 65 trials.” Statistics in Medicine. 2002;21(18):2641–2652. It is not a substitute for I² and τ² — it is a companion diagnostic that answers a different question: not “how much heterogeneity is there,” but “which specific studies are responsible for it, and does that same study also matter to the result.”

What a Baujat Plot Plots

Every point on a Baujat plot represents one included study. The two axes are:

• X-axis — contribution to heterogeneity. Each study’s individual contribution to the overall heterogeneity statistic (Cochran’s Q). A study that fits the pooled model poorly — its effect estimate sits far from the pooled estimate relative to its own precision — contributes more to Q and sits further right.
• Y-axis — influence on the pooled result. How much the overall pooled effect estimate would change if that one study were removed from the analysis. The standard formulation (following Baujat et al. and implemented this way in the metafor R package’s baujat() function) is the standardized squared difference between the pooled estimate calculated with the study included and the pooled estimate calculated with it excluded.

Under a random-effects model, the x-axis is typically computed from each study’s squared Pearson residual rather than its raw Q contribution — a technical adjustment for the fact that random-effects weighting already distributes some of the heterogeneity across the between-study variance component, but the interpretation of the plot is unchanged.

Reading the Four Quadrants

A Baujat plot divides naturally into four regions, and each carries a different message:

• Upper right — high contribution to heterogeneity AND high influence on the result. This is the quadrant that matters most. A study here is both an outlier relative to the other included studies and a study whose removal would meaningfully change the pooled effect estimate. These are the studies most worth scrutinizing: re-checking data extraction and eligibility, examining whether a real clinical, methodological, or population difference explains the divergent result, and running a formal sensitivity analysis that reports the pooled estimate with and without the study.
• Lower right — high contribution to heterogeneity, low influence. The study disagrees with the others but is small or imprecise enough that removing it barely moves the pooled estimate. Worth noting as a source of unexplained heterogeneity, but not a priority for a sensitivity re-run.
• Upper left — low contribution to heterogeneity, high influence. Typically a large, precise study that agrees reasonably well with the pooled model but, precisely because of its size, still pulls the pooled estimate toward its own result. This is normal, expected behavior for a well-conducted large trial — not evidence of a problem.
• Lower left — low contribution, low influence. The majority of well-behaved included studies land here: broadly consistent with the pooled model and individually unimportant to the final estimate.

There is no fixed numeric threshold separating “high” from “low” on either axis — unlike a p-value cutoff, the Baujat plot is read visually, relative to the spread of the other included studies in that specific meta-analysis. A study that stands out clearly from the rest of the cloud in the upper-right direction is the signal to follow up on, regardless of its exact coordinates.

Baujat Plots vs. I² and τ²: Complementary, Not Redundant

It is easy to assume that once a meta-analysis has already reported I² and τ², a Baujat plot adds nothing new. It does, because the two diagnostics answer genuinely different questions:

• I² and τ² are summary statistics describing the total amount of heterogeneity across all included studies, on average. They tell you heterogeneity exists and roughly how much, but nothing about which study or studies are responsible.
• A Baujat plot decomposes that same heterogeneity study by study, and cross-references it against each study’s actual influence on the number the meta-analysis reports.

A meta-analysis can report a high overall I² that turns out to be driven almost entirely by one or two studies in the upper-right quadrant — in which case a targeted sensitivity analysis excluding those studies, or investigating what makes them different, is the right next step. Equally, a meta-analysis can report a moderate I² that is spread fairly evenly across all included studies, with no single point standing out on a Baujat plot — in which case there is no obvious candidate to exclude, and the heterogeneity is better addressed through meta-regression against a plausible study-level covariate or accepted as part of a genuinely heterogeneous body of evidence reported with a prediction interval. The Cochrane Handbook’s guidance on interpreting I² itself cautions against a mechanical cutoff for exactly this reason: the same numeric I² value can mean different things depending on how the underlying heterogeneity is distributed across studies, which is precisely what a Baujat plot, and not I² alone, makes visible.

A Baujat plot also does a different job than a funnel plot. A funnel plot is a small-study-effects and publication-bias diagnostic, plotting each study’s effect estimate against its precision; it says nothing about whether a specific study is an outlier relative to the model, or how much that study moves the pooled result. The two are frequently produced side by side in a meta-analysis, but they are checking for different things and neither substitutes for the other.

Constructing and Using a Baujat Plot

In practice, a Baujat plot is generated after the pooled meta-analysis model has already been fit, using the same effect sizes and weights already computed for the forest plot and the overall heterogeneity statistics. The most common route is the baujat() function in R’s metafor package, which takes a fitted rma() model object directly and produces the plot with each study labeled by its study ID or a custom label — see CASRAI’s guide to running a meta-analysis in metafor for the underlying model-fitting step. Other meta-analysis software with influence-diagnostic modules, including recent versions of Stata’s meta suite and R’s dmetar/metasens packages, implement equivalent versions of the same plot.

A practical workflow:

1. Fit the pooled model (fixed-effect or random-effects, matching the choice already made for the primary analysis) and confirm the overall Q, I², and τ² statistics.
2. Generate the Baujat plot from that same fitted model and visually scan for any point that separates clearly from the main cluster toward the upper right.
3. For each flagged study, check the extraction against the original source: outcome definition, population, dose or duration, and risk-of-bias assessment. A genuinely different intervention, population, or measurement approach is a legitimate explanation for a divergent result; a data-entry or unit error is a correctable one.
4. Report a leave-one-out sensitivity analysis for each flagged study — the pooled estimate with and without it, and whether the conclusion changes — rather than silently excluding the study from the primary analysis. Pre-specifying this step in the protocol, where feasible, avoids the appearance of post-hoc cherry-picking.
5. If several studies land in the upper-right region rather than one clear outlier, that pattern itself is informative — it points toward genuine, structured heterogeneity worth exploring with meta-regression or a pre-planned subgroup split, rather than a single aberrant study to exclude.

Limitations

A Baujat plot has real limits worth stating plainly. It identifies statistical influence and disagreement with the pooled model, not the direction of causation — a study in the upper-right quadrant is not automatically wrong, biased, or lower quality; it is simply different from the others in a way that matters to the pooled number. Distinguishing a genuinely low-quality or biased study from one that is legitimately different (a different population, dose, or follow-up duration) still requires the reviewer’s own methodological judgment and, ideally, a risk-of-bias assessment run independently of the plot. The plot is also purely visual with no accompanying significance test or numeric threshold, and, like most influence diagnostics, is most useful and easiest to read with a moderate number of included studies; with very few studies (well under ten) the plot carries limited diagnostic value, and with a very large number of studies individual labels can become difficult to read without interactive tooling.

Frequently Asked Questions

Is a Baujat plot the same thing as a leave-one-out sensitivity analysis?

They are closely related but not identical. A leave-one-out analysis re-runs the pooled model once per excluded study and reports the resulting change in the estimate for every study individually, usually as a table or forest-style plot. A Baujat plot uses the same underlying influence calculation but combines it with each study’s separate contribution to heterogeneity in a single two-dimensional scatter, which is what lets you see influence and heterogeneity contribution together rather than reading two separate outputs.

Does a study in the upper-right quadrant of a Baujat plot have to be excluded from the meta-analysis?

No. The plot flags a study for closer scrutiny and for a reported sensitivity analysis; it does not by itself justify exclusion. A study should only be removed from a primary analysis for a pre-specified, methodologically defensible reason (an eligibility error, a data extraction mistake, or a protocol-defined exclusion criterion) — not because it disagrees with the other studies, which is exactly the kind of post-hoc exclusion that sensitivity-analysis reporting standards are designed to prevent.

Can a Baujat plot be used with a fixed-effect model, or only random-effects?

Both. The plot works with either model, though the exact formula for the x-axis heterogeneity contribution differs slightly — a direct Q-statistic contribution under a fixed/equal-effects model, versus a squared Pearson residual under a random-effects model, per the metafor package’s own implementation. The y-axis influence measure (the standardized change in the pooled estimate on exclusion) is conceptually the same under both.

What software produces a Baujat plot?

R’s metafor package has a dedicated baujat() function that takes a fitted meta-analysis model object directly. Equivalent influence-diagnostic tools exist in Stata’s meta suite and in supplementary R packages built on top of metafor, such as dmetar.

How is a Baujat plot different from a funnel plot?

A funnel plot checks for small-study effects and possible publication bias by plotting each study’s effect estimate against its precision. A Baujat plot checks for influential outliers relative to the pooled model by plotting each study’s heterogeneity contribution against its influence on the result. They use similar-looking scatter layouts but diagnose entirely different problems, and a meta-analysis benefits from producing both rather than treating one as a substitute for the other.