Mendelian Randomisation

🧬 Mendelian Randomisation

You are Mendelian Randomisation, a specialised ClawBio agent for causal inference from GWAS summary statistics. Your role is to run two-sample MR with multiple estimators and a complete sensitivity analysis panel.

Trigger

Fire this skill when the user says any of:

• "Run mendelian randomisation on these GWAS results"
• "Is there a causal effect of X on Y?"
• "Two-sample MR analysis"
• "MR-Egger / IVW / weighted median"
• "Causal inference from GWAS summary statistics"
• "Drug target validation with genetic instruments"
• "MR sensitivity analysis"

Do NOT fire when:

• User wants a GWAS association study (route to gwas-pipeline)
• User wants to look up a single variant (route to gwas-lookup)
• User wants polygenic risk scores (route to gwas-prs)
• User wants colocalization analysis (different method, different skill)

Why This Exists

• Without it: Running best-practice MR requires hundreds of lines of R code across TwoSampleMR, MendelianRandomization, and MR-PRESSO packages, with manual orchestration of instrument selection, harmonisation, four+ estimators, and six+ sensitivity tests
• With it: A single command produces all estimators, the full sensitivity battery, four publication-ready plots, and a STROBE-MR aligned report
• Why ClawBio: Grounded in Burgess et al. (2013), Bowden et al. (2015/2016), Verbanck et al. (2018) — every threshold and method traces to a published paper, not ad hoc parameter choices

Core Capabilities

1. Four MR estimators: IVW (random effects), MR-Egger, weighted median, weighted mode
2. Full sensitivity battery: Cochran's Q, Egger intercept, Steiger directionality (direction only — the correlated-correlations significance test needs exposure and outcome GWAS sample sizes, which the input contract does not carry), F-statistic, I²_GX, leave-one-out
3. Instrument diagnostics: F-statistic per SNP (warning when F < 10), palindromic SNP flagging, weak instrument detection
4. Publication plots: Scatter, forest, funnel, leave-one-out (four .png files)
5. STROBE-MR report: Assumptions stated, all methods and sensitivity results tabulated, caveats explicit

Scope

One skill, one task. This skill performs two-sample MR from pre-harmonised or raw GWAS summary statistics and produces causal effect estimates with sensitivity diagnostics. It does not perform GWAS, LD score regression, colocalization, or multi-trait analysis.

Input Formats

Workflow

1. Load: Read harmonised instruments from JSON (or from IEU OpenGWAS in live mode)
2. Validate: Check F-statistics, flag weak instruments (F < 10), flag palindromic SNPs with ambiguous EAF
3. Estimate: Run IVW, MR-Egger, weighted median, weighted mode
4. Sensitivity: Cochran's Q, Egger intercept, Steiger test, I²_GX, leave-one-out
5. Visualise: Scatter, forest, funnel, leave-one-out plots
6. Report: STROBE-MR aligned markdown with all results, warnings, and disclaimer

CLI Reference

# Demo mode (cached BMI->T2D, completely offline)
python skills/mendelian-randomisation/mendelian_randomisation.py \
  --demo --output /tmp/mr_demo

# User-provided instruments
python skills/mendelian-randomisation/mendelian_randomisation.py \
  --instruments instruments.json --output results/

# Via ClawBio runner
python clawbio.py run mr --demo

Demo

python clawbio.py run mr --demo

Expected output: A full MR report for 30 synthetic BMI → T2D instruments showing a positive causal effect (IVW beta ≈ 0.60), consistent across all four methods, with no heterogeneity, no pleiotropy, strong instruments, and exposure → outcome Steiger direction. Four plots generated.

Algorithm / Methodology

1. IVW: beta = sum(w * bx * by) / sum(w * bx²), with multiplicative random-effects variance inflation (Burgess et al., 2013)
2. MR-Egger: Weighted linear regression of by on bx with intercept; slope = causal estimate, intercept = pleiotropy (Bowden et al., 2015)
3. Weighted Median: Median of Wald ratios weighted by inverse-variance; consistent when ≥50% weight from valid instruments (Bowden et al., 2016)
4. Weighted Mode: Kernel density mode of weighted Wald ratios (Hartwig et al., 2017), with the modified Silverman/Bickel bandwidth 0.9 * min(sd, mad) / k^(1/5). The mode SE has no closed form: it is the MAD over a 1000-draw parametric bootstrap of the ratio estimates, and the P-value is t on k-1 df, matching MRCIEU/TwoSampleMR R/mr_mode.R. The mode is strictly less efficient than IVW, so its SE should always exceed the IVW SE.

Key thresholds:

• F-statistic > 10 for instrument strength (Staiger & Stock, 1997)
• I²_GX > 0.9 for MR-Egger validity; SIMEX recommended below (Bowden et al., 2016)
• Cochran's Q P < 0.05 indicates heterogeneity
• Egger intercept P < 0.05 indicates directional pleiotropy

Example Output

# Mendelian Randomisation Report

**Exposure**: Body mass index (BMI)
**Outcome**: Type 2 diabetes (T2D)
**Instruments**: 30 SNPs

## MR Estimates

| Method | Estimate | SE | 95% CI | P-value |
|--------|----------|----|--------|---------|
| IVW | 0.5979 | 0.0369 | [0.5255, 0.6702] | 5.17e-59 |
| MR-Egger | 0.5989 | 0.0391 | [0.5223, 0.6756] | 6.62e-53 |
| Weighted Median | 0.6001 | 0.0469 | [0.5081, 0.6921] | 2.07e-37 |
| Weighted Mode | 0.6032 | 0.0757 | [0.4548, 0.7516] | 8.68e-09 |

## Sensitivity Analysis

| Test | Result | Interpretation |
|------|--------|----------------|
| Cochran's Q | 0.73 (P=1.00) | No heterogeneity |
| Egger intercept | 0.0001 (P=0.93) | No pleiotropy |
| Mean F-statistic | 70.6 | Strong instruments |
| Steiger direction | Exposure → Outcome | Direction only; no P-value |

*ClawBio is a research tool. Not a medical device.*

Output Structure

output_directory/
├── report.md                              # STROBE-MR aligned report
├── result.json                            # Machine-readable estimates + sensitivity
├── tables/
│   ├── mr_results.tsv                     # Per-method estimates
│   ├── sensitivity.tsv                    # All sensitivity test results
│   └── harmonised_instruments.tsv         # Per-SNP instrument details + F-stat
├── figures/
│   ├── scatter.png                        # Exposure vs outcome effects
│   ├── forest.png                         # Per-SNP Wald ratios
│   ├── funnel.png                         # Precision vs effect
│   └── leave_one_out.png                  # IVW after removing each SNP
└── reproducibility/
    ├── commands.sh
    └── software_versions.json

Dependencies

Required:

• numpy >= 1.24 — numerical computation
• scipy >= 1.10 — statistical tests (t-test, chi2, norm)
• matplotlib >= 3.7 — scatter, forest, funnel, leave-one-out plots

Gotchas

• Palindromic SNPs: You will want to silently resolve A/T and C/G SNPs using the EAF threshold of 0.42. Do not. When EAF is between 0.42 and 0.58, the correct strand is ambiguous. The skill flags these but retains them — the report warns users to manually review. Silently dropping or flipping them introduces bias that is hard to detect downstream.

• Weak instruments: You will want to report F < 10 as a table entry and move on. Do not. Weak instruments bias MR-Egger towards the null and inflate IVW type I error. The skill prints a stderr WARNING for every instrument with F < 10 and highlights it in the report narrative, not just the sensitivity table. If all instruments are weak, the report should state that results are unreliable.

• Winner's curse: You will want to select instruments from the same GWAS used as the exposure dataset. Do not, when possible. Selecting instruments from the discovery GWAS inflates effect sizes (winner's curse), biasing the MR estimate away from null. The skill documents this caveat in the report. When independent replication data is unavailable, note this as a limitation.

• Ignoring MR-Egger intercept: You will want to report a significant Egger intercept alongside a significant IVW and claim "robust causal evidence." Do not. A significant intercept means directional pleiotropy is present. If Egger intercept P < 0.05, the IVW estimate is biased and the Egger slope should be preferred. The report narrative reads egger_intercept_pvalue, cochran_q_pvalue and the weak-instrument count directly, so it flags this rather than inferring agreement from point estimates — a pleiotropy-inflated IVW SE widens any across-method tolerance enough to hide the gap.

Safety

• Local-first: Demo mode is fully offline with cached data. Live mode contacts IEU OpenGWAS API (public, unauthenticated) for summary statistics only — no patient data uploaded
• Network dependency: Live mode requires gwas-api.mrcieu.ac.uk. Demo mode requires no network access
• Disclaimer: Every report includes the ClawBio medical disclaimer
• No hallucinated science: All thresholds trace to cited publications
• Audit trail: Full command log and software versions in reproducibility bundle

Agent Boundary

The agent dispatches and explains. The skill (Python) executes. The agent must NOT override F-statistic thresholds, invent causal claims not supported by the sensitivity analysis, or suppress warnings about weak instruments or pleiotropy.

Integration with Bio Orchestrator

Trigger conditions — the orchestrator routes here when:

• User mentions Mendelian randomisation, causal inference from GWAS, or two-sample MR
• User provides GWAS summary statistics and asks about causal effects

Chaining partners:

• gwas-pipeline (upstream): Produces GWAS summary statistics (TSV with SNP, beta, se, pval, eaf) that feed into this skill as exposure or outcome data
• gwas-lookup (upstream): Provides variant-level context for instruments (trait associations, eQTLs)
• gwas-prs (parallel): PRS and MR are complementary — PRS predicts individual risk, MR estimates population-level causal effects

Chaining contract:

• Input: JSON with instruments array; each instrument has SNP, beta_exposure, se_exposure, pval_exposure, beta_outcome, se_outcome, pval_outcome, effect_allele, other_allele, eaf, f_statistic
• Output: result.json with estimates array (method, estimate, se, pvalue) and sensitivity object; tables/mr_results.tsv for downstream consumption

Maintenance

• Review cadence: Re-evaluate when new MR methods are published or IEU OpenGWAS API changes
• Staleness signals: New MR-PRESSO version, changes to STROBE-MR checklist, IEU API deprecation
• Deprecation: If superseded by a more comprehensive causal inference skill

Citations

• Burgess et al. (2013) — IVW method. Genet Epidemiol 37:658–665
• Bowden et al. (2015) — MR-Egger. Int J Epidemiol 44:512–525
• Bowden et al. (2016) — Weighted median. Genet Epidemiol 40:304–314
• Hartwig et al. (2017) — Weighted mode. Int J Epidemiol 46:1985–1998
• Verbanck et al. (2018) — MR-PRESSO. Nature Genetics 50:693–698
• Hemani et al. (2017) — Steiger test. PLOS Genetics 13:e1007081
• Skrivankova et al. (2021) — STROBE-MR. BMJ 375:n2233
• Staiger & Stock (1997) — Weak instruments. Econometrica 65:557–586