Mendelian Randomization Selection

MR rests on three core assumptions that genetic variants must satisfy to serve as valid instruments:

• Relevance (IV1): The genetic variant must be robustly associated with the exposure or risk factor of interest, typically confirmed through genome-wide significant associations (p < 5×10⁻⁸)
• Independence (IV2): The variant must not be associated with any confounders of the exposure-outcome relationship, leveraging Mendel's law of random assortment as a natural randomization mechanism
• Exclusion Restriction (IV3): The variant must affect the outcome only through the exposure, with no horizontal pleiotropy—direct effects on the outcome bypassing the exposure pathway

Violation of these assumptions, particularly through unbalanced pleiotropy, can bias causal estimates and requires sensitivity analyses.

The two-sample MR framework separates exposure and outcome data into independent, non-overlapping cohorts, dramatically expanding the scope of causal inference:

• Exposure GWAS: Summary-level association statistics between genetic variants and the risk factor are extracted from a large, publicly available genome-wide association study
• Outcome GWAS: Corresponding variant-outcome associations are obtained from a separate consortium or biobank, such as FinnGen or UK Biobank
• Harmonization: Effect alleles are aligned across datasets, and palindromic variants with ambiguous strand orientation are carefully resolved or excluded

This design enables causal estimation for exposures that were never directly measured in the outcome cohort, unlocking retrospective analysis of existing summary data.

The inverse-variance weighted method is the primary causal estimator in MR, combining Wald ratio estimates from multiple independent genetic instruments:

• Each variant provides a ratio estimate: the SNP-outcome association divided by the SNP-exposure association
• These individual estimates are meta-analyzed using fixed-effects IVW, weighting each variant's contribution by the inverse of its outcome association variance
• Under the assumption that all instruments are valid with no pleiotropy, IVW yields an unbiased, maximally efficient causal effect estimate

When pleiotropy is present, the fixed-effects IVW can produce biased results, motivating the use of random-effects IVW or robust regression alternatives like MR-Egger.

A suite of complementary methods tests the robustness of MR findings against horizontal pleiotropy, where genetic variants influence the outcome through pathways independent of the exposure:

• MR-Egger Regression: Allows an intercept term to capture directional pleiotropy; a non-zero intercept signals bias, while the slope provides a pleiotropy-corrected causal estimate under the InSIDE assumption
• Weighted Median Estimator: Provides consistent causal estimates even when up to 50% of the weight comes from invalid instruments, offering robustness to widespread pleiotropy
• MR-PRESSO: Detects and removes outlier variants that contribute disproportionately to heterogeneity, then recalculates the causal effect
• Cochran's Q Test: Quantifies heterogeneity across individual variant estimates; significant Q statistics indicate potential pleiotropy or instrument invalidity

Concordance across these methods strengthens causal claims, while discordance signals the need for cautious interpretation.

Advanced MR designs address reverse causation and confounding by multiple correlated exposures:

• Bidirectional MR: Performs two independent analyses—first testing if the exposure causes the outcome, then reversing the roles to test if the outcome causes the exposure. This disentangles the direction of effect and identifies feedback loops
• Multivariable MR (MVMR): Simultaneously estimates the direct causal effect of multiple correlated exposures on an outcome by including all their genetic instruments in a single regression model. This is critical when exposures are highly correlated, such as lipid fractions (LDL, HDL, triglycerides)
• MVMR requires instruments that are conditionally associated with each exposure given the others, assessed through conditional F-statistics to avoid weak instrument bias

These extensions transform MR from a single-exposure tool into a framework for dissecting complex causal networks.

Colocalization tests whether the same causal variant drives both the exposure and outcome associations, distinguishing true causal relationships from confounding by linkage disequilibrium:

• Bayesian Colocalization (coloc): Computes posterior probabilities for five mutually exclusive hypotheses, with H4 representing a shared causal variant. A posterior probability of H4 > 0.75–0.80 is typically considered strong evidence
• SusieR with Sum of Single Effects: A variable selection framework that identifies distinct credible sets of causal variants, enabling fine-mapping and colocalization in regions with multiple independent signals
• Colocalization is essential when MR uses cis-acting variants (e.g., gene expression instruments), where linkage disequilibrium contamination is most severe

Integrating colocalization with MR provides orthogonal evidence that the genetic instrument operates through the hypothesized exposure, not a correlated neighbor.

The foundational econometric framework underlying Mendelian randomization. An instrumental variable must satisfy three core assumptions: it must be associated with the exposure, not associated with confounders, and affect the outcome only through the exposure (exclusion restriction). In MR, genetic variants—typically single nucleotide polymorphisms (SNPs)—serve as instruments. The two-stage least squares (2SLS) estimator first regresses the exposure on the instruments, then regresses the outcome on the predicted exposure values. Violations of IV assumptions, particularly horizontal pleiotropy, require sensitivity analyses like MR-Egger regression or the weighted median estimator.

GWAS is the prerequisite data source for Mendelian randomization. These large-scale studies scan millions of genetic variants across thousands of individuals to identify SNP-trait associations at genome-wide significance (p < 5×10⁻⁸). For MR, researchers extract summary-level GWAS statistics—beta coefficients, standard errors, and p-values—for the exposure and outcome traits. Key considerations include ensuring non-overlapping samples between exposure and outcome GWAS to avoid bias, and selecting independent instruments by clumping SNPs based on linkage disequilibrium (LD) thresholds (typically r² < 0.001 within 10,000 kb windows).

Horizontal pleiotropy—when a genetic variant affects the outcome through pathways independent of the exposure—is the primary threat to MR validity. Detection and correction methods include:

• MR-Egger regression: Allows an intercept term to capture directional pleiotropy; a non-zero intercept indicates violation
• Weighted median estimator: Provides consistent estimates when at least 50% of the weight comes from valid instruments
• MR-PRESSO: Detects and removes outlier instruments that contribute disproportionately to heterogeneity
• Cochran's Q statistic: Quantifies heterogeneity across individual variant causal estimates
• Leave-one-out analysis: Iteratively removes each SNP to identify influential variants

Beyond MR, causal discovery methods learn causal structures directly from observational data without pre-specified instruments. Algorithms like PC (Peter-Clark) and FCI (Fast Causal Inference) use conditional independence tests to construct directed acyclic graphs (DAGs). LiNGAM (Linear Non-Gaussian Acyclic Model) exploits non-Gaussianity to identify causal directions. For high-dimensional biomarker data, restricted structural equation models and causal Bayesian networks can complement MR by discovering novel causal pathways. These methods differ from MR in that they do not require genetic instruments but rely on stronger distributional assumptions.

Colocalization tests whether the same causal variant drives both the exposure and outcome GWAS signals, distinguishing shared causal variants from mere genomic proximity due to linkage disequilibrium. The COLOC method uses Bayesian posterior probabilities to evaluate five mutually exclusive hypotheses, with H4 representing a shared causal variant. A posterior probability > 0.75 for H4 is typically considered strong evidence of colocalization. This analysis strengthens MR findings by confirming that the genetic instrument for the exposure is the same variant influencing the outcome, ruling out confounding by nearby variants in LD.

A study design that performs MR in both directions—testing whether the exposure causes the outcome and whether the outcome causes the exposure. This requires separate sets of genetic instruments for each trait, extracted from independent GWAS. Bidirectional MR helps disentangle reverse causation from true causal directionality. For example, in biomarker research, bidirectional MR can determine whether elevated C-reactive protein causes cardiovascular disease or is merely a consequence of it. Consistent evidence in one direction but not the other strengthens causal inference and informs therapeutic targeting strategies.