> For the complete documentation index, see [llms.txt](https://docs.nested-knowledge.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.nested-knowledge.com/review-workflow/synthesis/navigate-synthesis-outputs/quantitative-synthesis/meta-analytical-methods.md). # Meta-Analytical Methods This page documents exactly how Nested Knowledge computes the pooled estimates and network meta-analysis (NMA) results shown in [Quantitative Synthesis](/review-workflow/synthesis/navigate-synthesis-outputs/quantitative-synthesis.md) and [Explore NMA](/review-workflow/synthesis/navigate-synthesis-outputs/quantitative-synthesis/explore-nma.md). ### What's Analyzed Any study included in Screening (adjudicated, if dual screening) with Meta-Analytical Extraction marked **Complete** is analyzed. If dual extraction is configured for the nest, only adjudicated data is used. ### Summary (Pooled Estimates) Any study with one or more extracted arms is included in the summary table — rows correspond to individual study arms or an intervention while columns are estimates (per-arm, or pooled across a whole intervention) for the data element being analyzed. * **Continuous (mean & SD) and dichotomous data** are pooled using the **Inverse Variance** method. Where random effects are specified, between-study variance uses the **DerSimonian–Laird** estimator. * **Dichotomous data with a 0 event count** receives a conditional **Haldane–Anscombe correction**. * **Continuous data with a missing SD** has that SD imputed. * All inferential statistics at the arm and intervention level use normal approximations, logit-transformed for dichotomous data. * Data elements with a mean but no configured SD get an arithmetic mean only — no inferential statistics are computed for these. * **Medians** are pooled as a Weighted Median of Medians (McGrath et al.). ### Network Meta-Analysis (NMA) Any multi-arm study with two or more extracted arms is eligible for NMA. If your intervention grouping assigns the same intervention to two or more arms in a study, those arms are pooled; if it assigns the same intervention to every arm in a study, that study is discarded from the NMA. Only continuous data (with mean & SD configured) or dichotomous data are eligible; arms missing an SD are discarded. Before analysis, the intervention graph is broken into connected components, each analyzed as a separate NMA, with results then combined for display. No effect estimate is produced between interventions belonging to different connected components — if two treatments were never linked by any direct or indirect chain of comparisons in your data, they won't get one. * **Direct effects** are Mean Differences (continuous) or Odds Ratios (dichotomous) between all pairs of within-study arms. * **Consistent indirect effects** use the Aitken estimator (Senn et al.), with a pairwise-effect weighting correction for multi-arm (3+) studies (Rücker et al., 2014; full Aitken detail in Rücker et al., 2012). * Between-study variance under random effects uses the **DerSimonian–Laird** estimator. * All inferential statistics — at both the study level (used in forest plots) and the intervention level — use normal approximations, logit-transformed for dichotomous data, applied to the consistent treatment effects. * **Intervention rankings** use P-scores (Rücker and Schwarzer, 2015). * **Zero-event corrections:** a 0 value in dichotomous data (for example, a 0 event rate in one arm) receives a continuity correction of 0.5 across all zero-containing cells, so the study can still contribute an effect size and variance without skewing results. * **Funnel plots** are generated from all contrasts available on the selected intervention, using "comparison-adjusted" effects (Chaimani et al.) that center direct effects at a common value so trend and symmetry analysis is possible on the same plot. ### Where These Methods Come From Every computation is implemented as a transcription — with documented, minor modifications — of peer-reviewed methods from the open-source R packages **meta**, **metafor**, **metamedian** (Summary), and **netmeta** (NMA). Because the R packages are open source, Nested Knowledge's own modifications are too, published in the JavaScript package **shukra**: pooled estimates in its [pooling module](https://github.com/holub008/shukra/blob/master/src/pooling.js), NMA in its [nma module](https://github.com/holub008/shukra/blob/master/src/nma.js). Every method in shukra is tested for equality against the upstream R packages' own results — the [pooling tests](https://github.com/holub008/shukra/blob/master/test/test_pooling.js) and [NMA tests](https://github.com/holub008/shukra/blob/master/test/test_nma.js) are publicly auditable alongside the code itself. ### FAQs
I'm not a statistician. Do I need to read this page? No. [Quantitative Synthesis](/review-workflow/synthesis/navigate-synthesis-outputs/quantitative-synthesis.md) and [Explore NMA](/review-workflow/synthesis/navigate-synthesis-outputs/quantitative-synthesis/explore-nma.md) are written for a general reader; this page exists for anyone who specifically needs to verify, cite, or defend the underlying statistics — for a manuscript's methods section, a regulatory submission, or a peer reviewer's question.
Can I verify these methods myself? Yes — every computation is implemented in the open-source shukra package, tested directly against the peer-reviewed R packages it's built from. See the links above.
Does this apply to Qualitative Synthesis too? No — this page covers only the numeric, statistical side of Quantitative Synthesis. Qualitative Synthesis doesn't perform any statistical analysis; see [Qualitative Synthesis](/review-workflow/synthesis/navigate-synthesis-outputs/qualitative-synthesis.md) for how that output works instead.
### Next Steps
:chart-line:
Quantitative Synthesis		View the Summary and Distribution results.Quantitative Synthesis
:chart-line:
Explore NMA		Read NMA results and forest plots.Explore NMA
:chart-scatter:
Extraction for Meta-Analysis		Configure the data extracted for these computations.Meta-Analytical Extraction
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