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.
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+.
Before using code patterns, verify installed versions match. If versions differ:
R: packageVersion('<pkg>') then ?function_name to verify parameters
For GitHub-only packages, check the repo HEAD vs the local install date
If code throws errors, introspect the installed package and adapt the example rather than retrying.
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
