Detect and adjust for horizontal pleiotropy in two-sample Mendelian randomization by distinguishing uncorrelated (UHP) from correlated (CHP) pleiotropy and choosing among Egger, MR-PRESSO, MR-RAPS, CAUSE, LHC-MR, LCV, MR-Clust, MR-Mix, and contamination-mixture methods. Use when validating an MR causal claim, running the STROBE-MR sensitivity battery, suspecting a shared heritable confounder, working under weak-instrument or polygenic-exposure regimes, or reconciling discordant estimates across robust methods.
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Detect and adjust for horizontal pleiotropy in two-sample Mendelian randomization by distinguishing uncorrelated (UHP) from correlated (CHP) pleiotropy and choosing among Egger, MR-PRESSO, MR-RAPS, CAUSE, LHC-MR, LCV, MR-Clust, MR-Mix, and contamination-mixture methods. Use when validating an MR causal claim, running the STROBE-MR sensitivity battery, suspecting a shared heritable confounder, working under weak-instrument or polygenic-exposure regimes, or reconciling discordant estimates across robust methods.
tool_type
r
primary_tool
TwoSampleMR
Version Compatibility
Reference examples tested with: TwoSampleMR 0.5.11+, MendelianRandomization 0.9.0+, MR-PRESSO 1.0+, CAUSE 1.2.0+, MR-Clust 0.1.0+, MRMix 0.1+, mr.raps 0.4.1+ (GitHub), LHC-MR 0.0.0.9000+ (GitHub), LCV (script-based, no version tag), simex 1.8+.
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Pleiotropy Detection in Mendelian Randomization
"Validate my MR result against pleiotropic bias" -> Decompose violations of the exclusion-restriction assumption into uncorrelated horizontal pleiotropy (UHP, addressable by Egger / median / mode / MR-PRESSO) and correlated horizontal pleiotropy (CHP, addressable only by CAUSE / LHC-MR / LCV), then run a method battery whose assumptions span both regimes.
InSIDE = INstrument Strength Independent of Direct Effect (Bowden 2015 IJE 44:512). Plain English: across SNPs, the per-SNP pleiotropic effect alpha and per-SNP instrument-exposure effect gamma are treated as independent random variables. CHP is the case where they covary because both flow from a shared upstream genetic factor.
The trap (Morrison 2020 Nat Genet 52:740): IVW, MR-Egger, MR-PRESSO, and GSMR are all blind to CHP. Under a shared heritable confounder they each return a plausible-looking corrected causal estimate that is systematically biased in the direction of the confounder. The MR-PRESSO global test does not flag CHP because correlated pleiotropy is not an outlier pattern, it is a population mean shift in the alpha distribution conditional on gamma.
Operational rule: If genetic correlation rg(exposure, outcome) is high (LDSC >= 0.3) or biology strongly suggests a shared upstream factor, the IVW / Egger / PRESSO triple is insufficient. Add CAUSE (preferred when sig SNPs >= 100) or LHC-MR (preferred for polygenic genome-wide IVs).
Operational Decision Flow (4 Steps)
Compute genetic correlation (LDSC). Run ldsc.py --rg <exposure.sumstats.gz>,<outcome.sumstats.gz> (see causal-genomics/genetic-correlation). If |rg| > 0.3, CHP is plausible -> flag for Step 3 escalation. If the LDSC rg standard error spans zero broadly, treat low-rg evidence as weak rather than confirming absence of CHP.
Standard battery. IVW (random-effects when Cochran Q p < 0.05) + MR-Egger (with NOME I^2_GX check) + weighted median + weighted mode + MR-PRESSO (NbDistribution >= 10000 for stringent reporting). Report all five with point estimate, SE, p, 95% CI, and n_SNPs_used. Compute Egger I^2_GX; apply SIMEX if I^2_GX < 0.9 (see examples/simex_egger_correction.R).
CHP escalation. Trigger when rg > 0.3 OR PRESSO global p < 0.05 with > 50% nominal outliers OR Egger / median / mode disagree by > 2 SE. Run CAUSE (if >= 100 significant SNPs after pruning) or LHC-MR (any N; uses genome-wide sumstats). Report ELPD delta + z + q (CHP fraction) + gamma (CHP-adjusted causal estimate).
Triangulate. Pre-MR Steiger filter; bidirectional MR (examples/bidirectional_mr.R); LCV gcp; LDSC rg report. Consensus across methods supports a publication-ready claim. Disagreement requires narrowing the scope (e.g., subgroup, cis-MR, time-varying analysis) rather than reporting a single point estimate.
Algorithmic Taxonomy
Method
Models
UHP-robust
CHP-robust
Min #SNPs
Fails when
Citation
Inverse-variance weighted (IVW)
Weighted regression through origin
Balanced UHP only
No
3
Directional UHP; CHP; weak IV bias; heterogeneity
Burgess 2013 Genet Epidemiol 37:658
MR-Egger intercept + slope
IVW + free intercept
Directional UHP
No
>=10 for power
NOME violated (I^2_GX < 0.9); <10 SNPs; CHP
Bowden 2015 IJE 44:512
Weighted median
Median of Wald ratios
Up to 50% invalid
No
>=10
>50% invalid; CHP
Bowden 2016 Genet Epidemiol 40:304
Weighted mode (MBE)
Mode of estimate density
Plurality valid
Partial
>=10
Multimodal estimates from CHP clusters
Hartwig 2017 IJE 46:1985
Cochran Q
Heterogeneity across Wald ratios
Total heterogeneity flag, not direction-specific
No
3
Cannot distinguish UHP from heterogeneity from CHP
Del Greco M F 2015 Stat Med 34:2926
MR-PRESSO
Detect + remove UHP outliers via RSS-out
Yes (assumes majority valid)
No
>=4
>50% pleiotropic; any CHP; small n
Verbanck 2018 Nat Genet 50:693
GSMR + HEIDI-outlier
Outlier removal via single-instrument estimate heterogeneity
Yes
No
>=10
CHP (HEIDI-outlier is heterogeneity-driven)
Zhu 2018 Nat Commun 9:224
MR-RAPS
Profile likelihood with overdispersion + Huber/Tukey loss
Heritability low; non-Gaussian effect distribution
O'Connor & Price 2018 Nat Genet 50:1728
Methodology evolves; verify against the Burgess & Thompson textbook (2nd ed 2021), Hemani 2018 (basic four-method battery), and Sanderson 2022 Nat Rev Methods Primers 2:6 before locking a sensitivity battery.
Decision Tree by Scenario
Scenario
Primary estimator
Sensitivity / triangulation
Many strong IVs, no biological shared trait suspected
IVW + Egger + weighted median + weighted mode + PRESSO
Triangulate with cis-MR; family-based MR if available
Per-Method Failure Modes
MR-Egger NOME violation
Trigger: I^2_GX = (Q_GX - df) / Q_GX is below 0.9, indicating measurement-error attenuation of the Egger slope (NOME = "no measurement error" in the exposure GWAS effect sizes).
Mechanism: MR-Egger regresses outcome effects on exposure effects with a free intercept. Imprecise exposure effects (high beta.exposure SE relative to beta.exposure variability across instruments) introduce regression dilution that pulls the Egger slope toward the null and inflates the intercept.
Symptom: Egger slope much closer to zero than IVW, weighted median, and weighted mode estimates; large Egger SE.
Fix: Apply SIMEX correction (Bowden 2016 IJE 45:1961; Cook & Stefanski 1994 JASA 89:1314 SIMEX framework) using the simex package on the Egger regression, treating beta.exposure SE as measurement error. See examples/simex_egger_correction.R. Alternative: use MR-RAPS, which models the exposure-effect error explicitly via profile likelihood and does not suffer the NOME failure.
MR-PRESSO majority-outlier breakdown
Trigger: More than 50% of instruments are pleiotropic (UHP), e.g. when instrument set was loosely selected (genome-wide significant but unfiltered).
Mechanism: MR-PRESSO's global RSS-out statistic and outlier detection both assume a majority-valid set; outliers are defined relative to that majority. With a pleiotropic majority, PRESSO removes the valid minority.
Symptom: PRESSO-corrected estimate is similar in magnitude (and sign) to the uncorrected estimate even after dropping nominally "outlier" SNPs; distortion-test p-value paradoxically non-significant; few or no outliers detected despite obvious global-test significance.
Fix: Do not trust PRESSO corrected estimate. Re-examine instrument selection (drop loose p-thresholds, prune LD harder); switch to CAUSE or LHC-MR; consider weighted-mode estimator which is plurality-valid rather than majority-valid.
MR-PRESSO false negative under CHP
Trigger: Strong shared heritable confounder (high rg) producing CHP. Confirmed by significant LDSC rg or LCV gcp.
Mechanism: Correlated pleiotropy is a population-level mean shift in alpha conditional on gamma; it is not an outlier pattern. PRESSO's RSS-out distance is invariant under such a mean shift, so the global test is not powered against CHP.
Symptom: PRESSO global p > 0.05 (no detected pleiotropy) while a CHP-aware method (CAUSE, LHC-MR) returns a substantially different (often null) causal estimate.
Fix: When CHP is plausible, ALWAYS run CAUSE or LHC-MR in addition to PRESSO; do not rely on PRESSO global non-significance as evidence of no pleiotropy.
MR-Egger underpowered with few SNPs
Trigger: Fewer than 10 instruments.
Mechanism: Egger's intercept variance is driven by the spread of beta.exposure across instruments; with few SNPs the intercept CI is so wide that even strongly pleiotropic data give non-significant intercepts.
Fix: Report intercept point estimate and CI rather than a binary "pleiotropy present / absent" verdict; do not use Egger as the only sensitivity method when SNP count is low; weight evidence toward weighted-median, weighted-mode, and CAUSE / LHC-MR.
Steiger filter inverted by exposure measurement error (Hemani 2017)
Trigger: Exposure is imprecisely measured (lower heritability ascertained in the exposure GWAS) and outcome is well-measured.
Mechanism: Steiger compares r^2_GX vs r^2_GY per SNP. Measurement error in the exposure underestimates r^2_GX; well-measured outcome captures r^2_GY accurately. Per-SNP, the inequality can flip even when the true causal direction is exposure -> outcome.
Symptom: A large fraction of instruments fail Steiger (steiger_dir == FALSE) in a direction that conflicts with biological plausibility.
Fix: Interpret Steiger as one signal among many, not a hard gate; cross-check with bidirectional MR; verify exposure GWAS heritability and sample size; switch to LHC-MR which models both directions jointly and accounts for heritability.
CAUSE underpowered with few significant SNPs
Trigger: Fewer than 100 genome-wide-significant instruments (p < 5e-8) after harmonization and LD pruning.
Mechanism: CAUSE fits a Bayesian mixture model over a shared-factor (CHP) component, a shared-causal component, and a null component. Posterior identification of the mixture weights requires substantial signal across many SNPs.
Symptom: CAUSE delta_ELPD CI crosses zero; Pareto-k diagnostic flags unstable points; posterior intervals on q (CHP fraction) span [0, 1].
Fix: Use LCV gcp for genome-wide directional inference (does not require many significant SNPs); use LHC-MR if heritability and sumstats are available; or report CAUSE alongside an explicit caveat about its underpowered regime.
LCV gcp under non-Gaussian effect distributions
Trigger: Highly polygenic trait with substantial sparsity in true effects (mixture of large-effect and zero-effect loci).
Mechanism: LCV assumes a bivariate normal model for effect sizes after LDSC adjustment. Sparse architectures (e.g. immune traits with HLA dominance) violate this and bias gcp estimates.
Symptom: LCV gcp point estimate appears extreme but heritability LDSC z-scores are modest; partitioned heritability shows extreme HLA enrichment.
Fix: Exclude HLA region from LDSC inputs; complement with CAUSE / LHC-MR; report gcp with awareness of the polygenicity caveat.
Plurality-valid (largest valid subset is most common estimate)
Hartwig 2017 IJE 46:1985
CAUSE min #SNPs
>=100 p < 5e-8 SNPs after pruning
Morrison 2020 Nat Genet 52:740 (Supplement)
CAUSE delta_ELPD criterion
one-sided p < 0.05; z = delta_elpd / se(delta_elpd); z > 1.96 standard; z > 3.0 stringent
Morrison 2020 Nat Genet
LDSC rg suggesting CHP
>= 0.3 flags need for CAUSE / LHC-MR
Operational rule; see causal-genomics/genetic-correlation
Steiger r^2 difference
Reverse-causal flag at any per-SNP r2_GY > r2_GX
Hemani 2017 PLoS Genet 13:e1007081
Standard sensitivity battery
IVW + Egger + median + mode + PRESSO + Steiger + LOO
Hemani 2018 eLife 7:e34408 / STROBE-MR 2021
LCV gcp interpretation thresholds (0, 0.5, 0.6, 1) are tabulated in usage-guide.md.
Standard Sensitivity Battery (Working Reference)
Goal: Run the canonical UHP-focused MR sensitivity suite on harmonized two-sample data.
Approach: Compute IVW + Egger + median + mode side-by-side; test Egger intercept and heterogeneity; run MR-PRESSO with >=5000 distributions for publication or >=10000 for stringent reporting; apply Steiger filter; leave-one-out; report all estimates.
Full working pipeline incl SIMEX, MR-RAPS, contamination mixture, and STROBE-MR table: examples/sensitivity_battery.R.
CAUSE for CHP-Aware Estimation
Goal: Distinguish causal from shared-factor (correlated horizontal pleiotropy) explanations of an exposure-outcome association.
Approach: Fit nuisance parameters (LD pruning + rho_GWAS sample-overlap correction) on a random SNP set; fit the sharing and causal posterior; compare ELPD (expected log predictive density) via Pareto-k smoothed importance sampling.
Full posterior extraction + reporting: examples/cause_analysis.R.
Interpreting CAUSE output:
q: posterior CHP fraction; 0 = no CHP, 1 = all instruments operate via the shared factor
eta: shared-factor effect on Y (the "confounder pathway" magnitude)
gamma: posterior causal effect of E on Y after partialling out CHP; report median + 95% credible interval
delta_ELPD (sharing - causal): negative -> causal model preferred; z = delta_elpd / se(delta_elpd); z > 1.96 standard, z > 3.0 stringent; one-sided p reported alongside posterior gamma
Pareto-k > 0.7 indicates unstable posterior on those points; if more than 10% of points are unstable, treat the posterior as unreliable; remediation: add more SNPs (loosen p-threshold one notch then re-prune in LD) or re-fit excluding flagged outliers
CAUSE requires sumstats from both exposure and outcome GWAS in matched effect-allele coding. The pruning step typically retains 100-5000 signature SNPs at LD r^2 < 0.01 in a 1 Mb window; nuisance estimation should use a larger random SNP subset (>= 100,000 genome-wide SNPs) to fit rho (sample overlap) stably.
over.dispersion = TRUE always for MR (horizontal-pleiotropy variance is real, not noise; turning this off underestimates SE)
loss.function = 'huber' (default; outlier-resistant; suited to mild to moderate UHP)
loss.function = 'tukey' (more aggressive; downweights extreme outliers more; choose when many obvious outliers suspected)
loss.function = 'l2' (non-robust; equivalent to weighted least squares; do not use when UHP suspected)
Tukey is preferable when leave-one-out reveals 2+ SNPs single-handedly shifting the IVW estimate by > 1 SE.
MR-Clust for Mechanism Heterogeneity
Goal: When a single causal estimate is misleading because instruments operate through multiple causal mechanisms (e.g. LDL on CHD via multiple lipoprotein subfractions), identify clusters of instruments with similar per-SNP Wald ratios.
Clusters with cluster_class = 'null' are pleiotropy-only instruments. Per-cluster IVW estimates may differ substantially; biological annotation of the SNPs in each cluster (pathway, target gene) is the interpretation step.
LHC-MR Workflow
Goal: Jointly estimate forward causal effect, reverse causal effect, and the heritable-confounder contribution from genome-wide sumstats (not just significant SNPs).
LHC-MR is computationally heavy (hours on full sumstats) but among the most rigorous CHP-aware estimators when both GWAS are well-powered. Output includes axx, ayy, hxy (confounder effect on each trait), and bidirectional alpha_xy, alpha_yx.
Choosing CAUSE vs LHC-MR (Darrous 2021):
Condition
Preferred method
>= 100 genome-wide significant SNPs after pruning
CAUSE (Bayesian; CHP-explicit; mature posterior diagnostics)
Polygenic exposure with few significant loci
LHC-MR (uses genome-wide signal, not just significant SNPs)
Severe sample overlap between exposure and outcome GWAS
LHC-MR (jointly models overlap); CAUSE's rho correction is exposed to misspecification at high overlap
Bidirectionality of central interest
LHC-MR (jointly estimates alpha_xy and alpha_yx); CAUSE only models forward
Limited compute / quick turnaround
CAUSE (minutes to hours); LHC-MR may be > 24h on full sumstats
When both apply, report both with the agreement / disagreement explicit in the discussion.
Bidirectional MR Procedure
Forward MR: instrument exposure E, test effect on outcome Y (primary)
Reverse MR: instrument outcome Y, test effect on exposure E (using outcome-direction instruments)
Steiger pre-filter both directions:steiger_filtering(dat); drop SNPs where outcome r^2 > exposure r^2 before primary IVW
LCV gcp orthogonal check: genome-wide directional inference independent of the instrument set
Working code: examples/bidirectional_mr.R.
Interpretation cheat-sheet:
Forward p
Reverse p
Reading
significant
non-significant
Forward causal claim strengthened
non-significant
significant
Re-examine instrument-exposure assignment; the "outcome" may causally drive the "exposure"
significant
significant
Feedback loop, shared confounder, or reciprocal causation; resolve with LHC-MR
non-significant
non-significant
No evidence of causation in either direction
When forward and reverse both clear Steiger and both IVW p < 0.05, run LHC-MR jointly rather than reporting two univariable estimates.
LCV (Latent Causal Variable)
LCV uses LDSC-merged genome-wide sumstats and reports gcp (genetic causality proportion) on [-1, 1]. It is a complement to, not a replacement for, MR; gcp ~ 0 with high LDSC rg implies pure genetic correlation without partial causation.
Report per-cluster estimates; do not summarize as a single effect
Steiger fails on a substantial fraction of instruments
Reverse causation OR exposure measurement error
Run bidirectional MR; check exposure GWAS heritability; LHC-MR
MR-PRESSO global p < 0.05 but corrected estimate similar to uncorrected
>50% pleiotropic OR CHP masquerading as UHP
Re-prune instruments; switch to weighted-mode / CAUSE / LHC-MR
Operational rule for publication: Report IVW (primary), Egger slope + intercept, weighted median, weighted mode, MR-PRESSO global + distortion + corrected, Cochran Q, Steiger directionality, F-statistic distribution, I^2_GX (for Egger validity), and at least one CHP-aware method (CAUSE or LHC-MR) when rg >= 0.3 or biology suggests shared upstream. Failure to report a CHP-aware result when CHP is plausible is a reviewer-flagged red flag since 2020.
Anticipated Reviewer Pushback
Pushback
Standard response
"Was CHP checked for?"
LDSC rg reported (causal-genomics/genetic-correlation); if rg > 0.3, CAUSE or LHC-MR ran; q posterior reported
"Why CAUSE and not LHC-MR?"
CAUSE preferred when >= 100 significant SNPs available (Morrison 2020). LHC-MR preferred when significant-SNP set is small or polygenic, using genome-wide sumstats (Darrous 2021)
"Egger NOME?"
I^2_GX computed; if 0.6 <= I^2_GX < 0.9, SIMEX correction applied; if < 0.6, Egger dropped in favor of MR-RAPS
"PRESSO doesn't catch CHP?"
Confirmed (Morrison 2020); CAUSE / LHC-MR reported alongside PRESSO for that reason
"Steiger filter applied pre-MR or post?"
Pre-MR: SNPs failing per-SNP Steiger directionality dropped before primary IVW
"Why no replication cohort?"
Two-sample design uses independent exposure and outcome cohorts; if same biobank, MRlap used or noted as a limitation
"Why not just trust the IVW?"
IVW assumes balanced UHP and no CHP; both violated routinely; sensitivity battery is the standard since STROBE-MR 2021
"Effect size is implausibly large"
Re-examine F-statistic distribution for weak IV bias; check Winner's curse; consider Wald ratio at a single strong instrument as sanity check
STROBE-MR Reporting (Skrivankova 2021)
Item
Required content
1-3
Title / abstract / background indicates this is an MR study; pre-registered protocol
4-7
Study design, data sources, instrument selection criteria (p-threshold, LD clumping, MAF)
Primary MR method + all sensitivity methods + CHP-aware method when relevant
18-19
Pleiotropy tests, Steiger, heterogeneity
20
Discussion of remaining assumption violations; limitations
Sub-items (30 total) detail per-method reporting. The full statement (JAMA 326:1614) and explanation (BMJ 375:n2233) are now reviewer-required at most cardiovascular and psychiatric journals since 2022.
Common Errors
Error / symptom
Cause
Solution
MR-PRESSO crashes with Not enough intrumental variables
Fewer than 4 SNPs
Need >=4 for PRESSO; for cis-MR with few SNPs use colocalization
Egger intercept p < 0.05 but I^2_GX = 0.5
NOME violated; intercept is artifactually inflated
SIMEX-correct or do not trust Egger; use MR-RAPS instead
