Toolkit · 05 of 13

Sensitivity analysis

Leave-one-out and Baujat plots.

What it is

A pooled result can rest on a single study: one very large trial, one with an unusual population, or one at high risk of bias. Sensitivity analysis asks whether the conclusion survives when that study, or that decision, is taken away.

In a leave-one-out analysis the meta-analysis is repeated as many times as there are studies, each time without one of them. If the direction, the statistical significance and the heterogeneity stay the same whichever study is removed, the result is robust.

The Baujat plot shows, for each study, how much it adds to the heterogeneity (horizontal axis) and how much it moves the pooled result (vertical axis). A study far to the right or at the top is the one to look at.

The Baujat plot is not strictly necessary: leave-one-out alone answers whether the result is robust. It is a good complement, because it shows in one picture which studies drive the heterogeneity, and leave-one-out then shows what happens without them.

Worked example14 trials, need for transfusion

	Risk ratio	95% CI	I²
All trials	0.75	0.60-0.94	54%
Without HeLiX	0.70	0.56-0.89	42%
Without Babu 2021	0.80	0.65-0.99	47%

Baujat: HeLiX stands apartit adds the most heterogeneity and influenceLeave-one-out: without either, the benefit remainsthe result is robust

Removing the most influential trials changes the size of the effect a little, never its direction or significance.

When to use it

Use it when

Heterogeneity is relevant (in my reviews, Cochran's Q P < 0.10 or I² > 25%) and you need to know where it comes from.
There are at least 3 studies; with 2, leaving one out leaves a single study.
One study dominates the weight, or differs in design, population or risk of bias.
The protocol pre-specified sensitivity analyses, as Cochrane recommends.

Choose another tool when

You want to drop studies until the result becomes significant: sensitivity analysis tests robustness, it does not choose the result to report.
The question is whether the effect differs between groups of studies: use subgroup analysis.
The concern is small studies or missing studies: use publication bias methods.

Leave-one-out, parameter by parameter

Click a highlighted argument to see what it does and which values to use. Picking a value updates the code.

# m: the model from the binary or continuous tool
l1o <- metainf(m,  = "random")

png("leave-one-out.png",
    width = 5500, height = 1100 + 170 * m$k, res = 500)
forest(l1o,
        = c("studlab", "effect", "ci", "w.random", "I2"),
       leftlabs = c("Study", "RR", "95% CI", "Weight", "I2"),
        = TRUE, print.tau2 = TRUE, print.Q = TRUE,
        = "navyblue",  = "black",
        = 2,
       xlab = "Favors intervention        Favors control")
dev.off()

Baujat plot, parameter by parameter

Click a highlighted argument to see what it does and which values to use.

png("baujat.png", width = 3500, height = 3000, res = 500)
baujat(m,
        = TRUE,
        = 0,  = 0,
        = "navyblue",
       cex.studlab = 0.8)
dev.off()

How to read the results

Leave-one-out

Robust: every row keeps the direction and the significance of the pooled result.
Influential study: omitting it changes the significance, or moves the estimate by more than about 10%.
Source of heterogeneity: omitting it makes I² fall sharply.

Baujat plot

Bottom left: typical studies, little heterogeneity and little influence.
Far right: the study adds heterogeneity; check its population, design and risk of bias.
Top: the study moves the pooled result; confirm with leave-one-out what changes without it.

Reporting

Name the influential study and say what changes without it, in the Results.
The Baujat plot uses common-effect weights, so it describes the data rather than the random-effects result.

In my work

Two figures for the same outcome of a published review with 14 trials: the leave-one-out analysis shows that the result holds without any single trial, and the Baujat plot shows which trials drive the heterogeneity. Click a figure to enlarge it.

Need for transfusion, leave-one-outEvery omission keeps the risk ratio below 1 and significant; I² ranges from 42% to 58%. From JAMA Surg, 2026 ↗

l1o <- metainf(m,                # main model
               pooled = "random") # refit k times

forest(l1o,
       leftcols = c("studlab", "effect", "ci",
                    "w.random", "I2"))  # columns

Need for transfusion, Baujat plotRisk ratio, 14 trials, I² = 54%. HeLiX stands apart: it adds the most heterogeneity and moves the result the most. From JAMA Surg, 2026 ↗

baujat(m,              # the meta-analysis model
       studlab = TRUE, # label the studies
       bg = "navyblue") # point colour

References

Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane; 2024. Chapter 10.14 (sensitivity analyses).
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. Stat Med. 2002;21:2641-2652.
Viechtbauer W, Cheung MWL. Outlier and influence diagnostics for meta-analysis. Res Synth Methods. 2010;1:112-125.
Harrer M, Cuijpers P, Furukawa TA, Ebert DD. Doing Meta-Analysis with R: A Hands-On Guide. Chapman & Hall/CRC; 2021. Chapter 5.
Balduzzi S, Rücker G, Schwarzer G. How to perform a meta-analysis with R: a practical tutorial. Evid Based Ment Health. 2019;22:153-160.