Meta-analysis of multiple outcomes: a multilevel approach
Open accessAbstract
In meta-analysis, dependent effect sizes are very common. An example is where in one or more studies the effect of an intervention is evaluated on multiple outcome variables for the same sample of participants. In this paper, we evaluate a three-level meta-analytic model to account for this kind of dependence, extending the simulation results of Van den Noortgate, López-López, Marín-Martínez, and Sánchez-Meca Behavior Research Methods, 45, 576-594 (2013) by allowing for a variation in the number of effect sizes per study, in the between-study variance, in the correlations between pairs of outcomes, and in the sample size of the studies. At the same time, we explore the performance of the approach if the outcomes used in a study can be regarded as a random sample from a population of outcomes. We conclude that although this approach is relatively simple and does not require prior estimates of the sampling covariances between effect sizes, it gives appropriate mean effect size estimates, standard error estimates, and confidence interval coverage proportions in a variety of realistic situations.
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Fit indices were used to confirm that three-step meta-analytic models were necessary to account for effect size dependency within studies for depression, anxiety, and suicidality outcomes.
“Fit indices were used to confirm that three-step meta-analytic models were necessary to account for any effect size dependency within studies for the models where depression, anxiety, and suicidality were outcomes (van den Noortgate et al., 2015).”
From Prospective Longitudinal Associations Between Adverse Childhood Experiences and Adult Mental Health Outcomes: Systematic Review and Meta-Analysis (2026) · cites this paper as van den Noortgate et al., 2015
The Conclusions (page not provided) say that multiple outcomes per study can produce dependent effect sizes and that a three-level approach can account for this. The paper does not report fit indices confirming that such models were necessary for depression, anxiety, and suicidality outcomes in the citing study. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe three-level meta-analysis increases statistical power compared to the traditional meta-analytic approach.
“increases statistical power compared to the traditional meta-analytic approach”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
The Conclusions (page unavailable) say that three-level meta-analysis makes efficient use of all available effect sizes, and the section on varying outcomes reports larger standard errors when fewer effect sizes are available. But the paper does not establish that it has greater statistical power than the traditional approach. Its direct comparison instead finds that the traditional two-level model can underestimate standard errors when outcomes are dependent. (LLM, conf=0.79)
Experimental — accuracy not yet measuredThe three-level meta-analysis facilitates the analysis of more moderators than is possible in traditional meta-analysis.
“and facilitates the analysis of more moderators than is possible in traditional meta-analysis.”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
The Conclusions say the three-level model can include outcome and study characteristics as predictors, as well as interactions with moderator variables. The paper also says aggregating effect sizes within studies can make it impossible to test moderators based on outcome characteristics. These passages support an advantage for certain moderators, but not the broader claim that three-level meta-analysis permits more moderators than traditional meta-analysis in general. Page numbers were not available in our copy. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe current study used three-level meta-analysis, which accounts for the statistical dependency among effect sizes within studies and allows for the inclusion of more than one effect size per study.
“the current study also used three-level meta-analysis, which accounts for the statistical dependency among effect sizes within studies, and therefore allows for the inclusion of more than one effect size per study.”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
The three-level meta-analysis allows all dependent effect sizes extracted from the same study to be included, preserving all available information.
“The major advantage of the three-level approach is that all (dependent) effect sizes extracted from the same study can be included in the analysis, which preserves all available information.”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
A three-level meta-analysis was applied to deal with the interdependency of effect sizes.
“A three-level approach to meta-analysis was therefore applied in order to deal with the interdependency of effect sizes (Van den Noortgate et al. 2014).”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
The three-level meta-analysis accounts for both within- and between-study variability.
“Moreover, three-level meta-analysis accounts for both withinand between-study variability”
From The Effects of Youth Mentoring Programs: A Meta-analysis of Outcome Studies (2019) · cites this paper as Van den Noortgate et al. 2014
A three-level meta-analytic model was adopted in which effect sizes are nested within experiments, explicitly taking dependencies into account.
“We thus adopted a three-level meta-analytic model in which effect sizes are nested within experiments, so we explicitly took the dependencies in our data into account in the model63,64.”
From When combinations of humans and AI are useful: A systematic review and meta-analysis (2024) · cites this paper as [63]
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- Authors
- Van den Noortgate, W., López-López, J. A., Marín-Martínez, F., & Sánchez-Meca, J.
- Affiliations
- University of Bristol (GB)
- Venue
- Behavior Research Methods
- Published
- 2014-11-01
- Volume
- 47
- Issue
- 4
- Pages
- 1274-1294
- ISSN
- 1554-351X (ISSN-L)
- 1554-3528
- OpenAlex
- W2039842580
- Cited by
- 450
- References
- 46
- Citations by year
- 2026: 51 · 2025: 55 · 2024: 50 · 2023: 59 · 2022: 51 · 2021: 45 · 2020: 35 · 2019: 38 · 2018: 34 · 2017: 19 · 2016: 10 · 2015: 2 · 2013: 1
- FWCI
- 33.64
- Type
- book chapter
- Language
- en
- Open access
- green
- lirias.kuleuven.be
- Licence
- other-oa
- www.springer.com/tdm (tdm)
- Locations
- Behavior Research Methods (publishedVersion)
- PubMed (publishedVersion)
- Lirias (KU Leuven) (submittedVersion, other-oa)
- Funders
- Vlaams Supercomputer Centrum
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Keywords
- multilevel meta-analysis, multiple outcomes, dependent effect sizes, three-level model, study heterogeneity, simulation study, confidence interval coverage
- MeSH terms
- Computer Simulation, Data Interpretation, Statistical, Humans, Reference Standards, Sampling Studies, Meta-Analysis as Topic, Treatment Outcome, Sample Size
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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