dsh-meta-analysis

Pool the effect sizes — with arithmetic you can check line by line.

Effect-size conversion with named formulas, fixed-effect and DerSimonian–Laird random-effects pooling, Q / I² / τ², forest-plot data, Markdown + SARIF, and a light Egger test that refuses to run on fewer than ten studies.

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What it does

• ma_pool — inverse-variance pooling on one analysis scale. Fixed: w = 1/v, pooled Σwθ/Σw, SE = 1/√Σw. Random: DerSimonian–Laird τ², weights 1/(v+τ²). Reports Q, df, p, I², τ², per-study weights and the pooled CI/p at the requested confidence level (level, default 0.95).
• ma_convert — OR⇄logOR, RR⇄logRR (SE from a CI), d⇄r, d⇄OR (logistic approximation), SMD from two means, SE from a CI. Every result names the formula and any approximation.
• ma_report — renderer-agnostic forest data (effect, CI, weight % + pooled row), Markdown, SARIF 2.1.0.
• Egger — only at k ≥ 10: OLS of θᵢ/SEᵢ on 1/SEᵢ; the intercept tests small-study effects. Labelled a screening aid, not proof of reporting bias.

What it does not do

• No model fitting beyond DL. No REML/Paule–Mandel, no meta-regression, no subgroup or leave-one-out automation (the inputs are yours to vary), no trim-and-fill.
• No risk-of-bias judgement. Weights do not encode study quality.
• No data extraction. Effect sizes and SEs must be supplied on one scale; ma_convert helps produce them.
• No plots. Forest data is provided; drawing belongs to the host or another tool.
• No evidence store. This plugin is pure arithmetic: nothing is written to disk, and the README says so instead of pretending there is a REP record.

Formulas

| Quantity | Formula | |---|---| | Fixed pooled | Σwᵢθᵢ / Σwᵢ, wᵢ = 1/vᵢ | | Random pooled | same with wᵢ* = 1/(vᵢ + τ²) | | Q | Σ wᵢ(θᵢ − θ_FE)², df = k−1 | | I² | max(0, (Q − df)/Q) | | τ² (DL) | max(0, (Q − df)/(Σw − Σw²/Σw)) | | SE from CI | (high − low)/(2·z) | | d→r | d/√(d²+4) | | d⇄OR | exp(d·π/√3) / log(OR)·√3/π | | SMD | (m₁−m₂)/s_pooled, SE √(1/n₁+1/n₂+d²/(2(n₁+n₂))) | | Egger | OLS intercept of θᵢ/SEᵢ on 1/SEᵢ, t with df = k−2 |

Normal-tail p uses an A&S 7.1.26 approximation (~1e-7); Φ⁻¹ uses Wichura's AS 241 / PPND16 (~1e-16); χ² and t use regularized incomplete gamma/beta continued fractions (~1e-10). All are implemented in src/math.ts with no dependencies.

Tools

ma_pool

{ studies: [{label, effect, se?, ciLow?, ciHigh?}], model?, level? } → { ok, result }.

ma_convert

{ conversion, value?, low?, high?, level?, mean1?, sd1?, n1?, mean2?, sd2?, n2? } → { ok, result }.

ma_report

{ result, measure? } → { ok, forest, markdown, sarif }.

Error codes

INVALID_INPUT (non-finite values, non-positive SE/OR/RR, |r| ≥ 1, SE/CI disagreement, k < 2).

Compatibility & install

| | | |---|---| | DeepSeek Harness | dsh-v0.2.1-rc.5 (verified 2026-11-08); peer >=0.2.1-0 <0.3.0 \|\| >=0.2.2-0 <0.3.0 | | Node | ^22.19.0 \|\| >=24.9.0 (tested 24.22.1), ESM only | | Peers | @perrylink/dsh-research-core ^0.1.0, @deepseek-ai/cordis ^4.0.5-alpha.1, @deepseek-ai/dsh-tools, @deepseek-ai/schemastery ^3.18.5-alpha.1 | | Runtime dependencies | zero |

dsh plugin --profile <name> add @perrylink/dsh-research-core dsh-meta-analysis
dsh --profile <name> --dump-config | grep dsh-meta-analysis

Configuration

| Key | Default | Meaning | |---|---|---| | enabled | true | false mounts nothing | | model | both | default pooling model (fixed / random / both) | | level | 0.95 | default confidence level |

Evaluation

23 unit tests: special functions against known critical values (χ²(8,2)=0.9817, t(2.306,8)≈0.05, z(1.96)≈0.05, Φ⁻¹(0.975) to 12 decimal places), conversions (logOR+SE, d⇄r, d⇄OR, SMD, impossible inputs), pooling (hand-calculated fixed/random estimates, Q=8, I²=0.75, τ²=0.03 from three studies), the requested confidence level for pooled and study CIs, CI-derived SE and SE/CI disagreement rejection, invalid models/levels/studies, Egger gating at k=10, heterogeneity warnings, tool schemas, malformed-report rejection, end-to-end report, plugin contract, package contract and the enabled/disabled mount contract.

Synthetic meta-analysis benchmark

A separate 20-case, deterministic synthetic benchmark (dataset meta v0.1.0, frozen) lives in the sibling dsh-research-bench repository under data/meta; it is not vendored into this package. Each case supplies studies (effect + SE, or a symmetric CI) and closed-form expected values for fixed/random pooling, Q, df, pQ, I², τ² and Egger presence.

Coverage: 5 homogeneous cases (I²=0, τ²=0), 5 medium- and 4 high-heterogeneity cases (Q>df, τ²>0), 2 zero-effect, 2 negative-effect and 2 small-k cases; k = 2 (4 cases), 5 (5), 10 (6) and 12 (5); 10 equal-SE and 10 unequal-SE designs; SE-only, CI-only and mixed inputs. Egger runs on the 11 cases with k ≥ 10 (including the k=10 boundary) and on none of the 9 below it.

The adapter calls pool(studies, { model: 'both' }) and compares against the generator's independent implementation (no plugin import, no expected value derived from plugin output). 20/20 cases pass; absolute errors:

| Quantity | Max abs error | Mean abs error | Tolerance | |---|---:|---:|---:| | fixed/random effect | 1.11e-16 | 8.33e-18 | 1e-6 | | fixed/random SE | 2.78e-17 | 1.74e-18 | 1e-6 | | fixed/random CI | 2.22e-16 | 3.96e-17 | 1e-6 | | Q | 8.53e-14 | 7.58e-15 | 1e-6 | | τ² | 8.33e-17 | 6.72e-18 | 1e-6 | | I² | 2.22e-16 | 1.94e-17 | 1e-9 | | pQ | 1.67e-15 | 1.96e-16 | 1e-9 |

The benchmark surfaced one real precision limit: the old Acklam Φ⁻¹ was 1.6e-9 off at 95%, and CI-derived SEs amplified it into I² deviations of 1.12e-9 on two cases. normalQuantile now uses AS 241; the largest Q error is 8.5e-14.

pnpm run build
pnpm run bench:meta        # reads ../dsh-research-bench/data/meta (BENCH_DIR overrides)

It writes bench/results-meta.json and bench/results-meta.md (no timestamps; re-running is byte-identical).

Known limitations (v0.1)

• One analysis scale per call; multi-scale harmonisation is the caller's job.
• DL τ² is known to be biased at small k; the plugin warns when k < 5.
• The Egger test assumes a normal distribution of effects and is underpowered below ~10 studies.
• No prediction interval (could be added without changing the interface).

License

Apache-2.0. No third-party runtime code.