Meta-Analysis — Diagnostics & Primary Pooled Estimation

Table of Contents

• Scope Boundary
• Workflow
• Decision Tree
• Required Inputs
• Code Structure
• Reporting Standards
• Example Dataset
• Method Status
• Minimal Smoke Test
• Cross-Skill Interface

Open-source skill.

Scope Boundary

Use this skill when:

• The inputs are study-level summary statistics and the first need is a transparent pooled estimate with heterogeneity diagnostics.
• A one-effect-size-at-a-time meta-analysis is appropriate before moderator, bias, or multilevel extensions.

Do not use this skill when:

• The project is network meta-analysis, IPD meta-analysis, or evidence synthesis without extractable study-level effects.
• The primary need is publication-bias modeling or meta-regression from the start.

Workflow

Read each step file in workflow/ before executing that step.

Step	Responsibility	Executor	Document	Input	Output
Collect	Collect Inputs	Main Agent	workflow/step01-collect-inputs.md	User input	Structured input summary
Diagnose	Check Distribution	Main Agent	workflow/step02-check-distribution.md	Prior step output	PART 1 code block
Test	Run Primary Test	Main Agent	workflow/step03-run-primary-test.md	Prior step output	PART 2-3 code blocks

Decision Tree

1. EFFECT SIZE TYPE
   ├── Continuous (SMD, MD) → escalc(measure="SMD") or "MD"
   ├── Binary (OR, RR, RD) → escalc(measure="OR") or "RR"/"RD"
   └── Correlation (r) → escalc(measure="ZCOR") Fisher z transform

2. HETEROGENEITY ASSESSMENT
   ├── I² < 25% → low heterogeneity (fixed-effects may suffice)
   ├── 25% ≤ I² ≤ 75% → moderate (random-effects preferred)
   └── I² > 75% → high (random-effects + moderator analysis needed)

Required Inputs

Role	What to collect
Study data	Study ID, effect size, SE (or CI, or N per group + means/SDs)
Effect type	SMD, MD, OR, RR, RD, or r
Moderators	Study-level variables (year, quality, setting) — for recommendation
Model preference	Fixed vs random (or let data decide)

Code Structure

PART 0: Setup & Data Loading
PART 1: Study Table + Forest Plot + Heterogeneity → plot_01_forest.png
PART 2: Pooled Estimates (fixed + random) + Prediction Interval
PART 3: Recommendation Block → text listing additional analyses available

Reporting Standards

1. Pooled effect: "pooled ES = X.XX, 95% CI [X.XX, X.XX], z = X.XX, p"
2. Heterogeneity: "Q(df) = X.XX, p = .XXX; I² = XX.X%; tau² = X.XX"
3. Prediction interval: always alongside CI
4. p-values: "< .001" not "0.000"; exact to 3 decimals otherwise
5. Weights: report study weights in forest plot
6. Degrees of freedom: always with test statistics
7. Sample size: report total N across studies and k (number of studies)
8. Decimal places: 2 for effect sizes, 3 for p-values, 1 for I²

Example Dataset

Constructed example: 10 studies comparing treatment vs control on a continuous outcome (standardized mean difference). NOT a built-in R dataset — create a data frame with study_id, n_treatment, n_control, mean_treatment, mean_control, sd_treatment, sd_control.

R: metafor package. Python: statsmodels or custom inverse-variance.

Method Status

Status	Methods
Implemented in this skill	Effect-size construction, fixed/random pooled estimates, forest plot, heterogeneity metrics, prediction interval
Implemented downstream in vera-data-meta-generating	Publication-bias checks, sensitivity analysis, subgroup analysis, meta-regression, Bayesian and three-level extensions
Out of scope in this open-source baseline	Network meta-analysis, IPD meta-analysis, and evidence-synthesis families not named above

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-meta-reviewing on a 10-study continuous-outcome example with study IDs, group means, SDs, and sample sizes. Produce the standard baseline artifacts."

Cross-Skill Interface

Output:
├── code_r      → .R script
├── code_python → .py script
├── figures/    → 1 PNG (forest plot)
└── recommendations → text block (additional analyses available)

Next step: Invoke vera-data-meta-generating from this skillset to run the full pipeline (additional tests, subgroup analysis, modeling, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.