MR-PRESSO

Performs a global test evaluating whether horizontal pleiotropy exists across all genetic instruments simultaneously. The test compares the observed residual sum of squares (RSS) from instrumental variable regression against a simulated null distribution generated under the assumption of no pleiotropy. A significant p-value indicates that at least one variant exhibits pleiotropic effects, violating the exclusion restriction assumption of Mendelian randomization.

Identifies specific outlier variants by calculating the contribution of each individual genetic instrument to the overall residual sum of squares. For each variant, the method computes the observed RSS when that variant is excluded and compares it to the expected distribution. Variants with disproportionately large contributions are flagged as pleiotropic outliers and can be systematically removed to obtain unbiased causal estimates.

Quantifies the magnitude of bias introduced by detected outliers by comparing the causal effect estimate before and after outlier removal. The distortion test calculates the proportional change in the causal estimate and assesses its statistical significance. A significant distortion indicates that the pleiotropic variants meaningfully biased the original Mendelian randomization results, justifying their exclusion from the analysis.

Generates an empirical null distribution through Monte Carlo simulations rather than relying on asymptotic approximations. The method simulates instrumental variable analyses under the null hypothesis of no horizontal pleiotropy, preserving the observed linkage disequilibrium structure and instrument-exposure associations. This non-parametric approach provides robust statistical inference even when the number of instruments is small or the distributional assumptions of parametric tests are violated.

Operates as a post-hoc diagnostic within the inverse-variance weighted (IVW) meta-analysis framework. After performing standard IVW Mendelian randomization, MR-PRESSO evaluates the validity of the underlying assumptions. If outliers are detected and removed, the method recalculates the IVW causal estimate using only the retained, non-pleiotropic instruments, providing a corrected effect size that is robust to violations of the exclusion restriction.

Applies Bonferroni correction or other multiple testing adjustments when evaluating individual variant contributions to account for the inflated Type I error rate from testing many instruments simultaneously. This ensures that variants are only flagged as outliers when there is strong statistical evidence, reducing the risk of erroneously discarding valid instruments and preserving statistical power for the corrected causal estimate.

The core violation that MR-PRESSO is designed to detect. Horizontal pleiotropy occurs when a genetic variant affects the outcome through pathways independent of the exposure, violating the exclusion restriction assumption of Mendelian randomization.

• Distinction from vertical pleiotropy: Vertical pleiotropy operates through the exposure (mediator chain), which does not bias MR estimates
• Detection challenge: Pleiotropic variants can distort causal estimates in unpredictable directions
• MR-PRESSO's approach: Identifies outlier variants whose causal estimates deviate significantly from the expected distribution

The foundational fixed-effect meta-analysis method that MR-PRESSO builds upon. IVW combines causal effect estimates from multiple genetic instruments by weighting each variant's estimate by the inverse of its variance.

• Assumption: All instruments are valid (no horizontal pleiotropy)
• Vulnerability: Highly sensitive to even a few pleiotropic variants
• MR-PRESSO relationship: MR-PRESSO can be viewed as IVW with outlier removal, restoring unbiased estimation when the no-pleiotropy assumption is violated

An alternative pleiotropy-robust method that takes a fundamentally different approach from MR-PRESSO. MR-Egger fits a weighted linear regression with an unconstrained intercept that captures average directional pleiotropy.

• Key assumption: Instrument strength independent of direct effects (InSIDE) — pleiotropic effects must be uncorrelated with instrument-exposure associations
• Trade-off: Less statistical power than IVW or MR-PRESSO when pleiotropy is absent
• Complementarity: Often used alongside MR-PRESSO in sensitivity analyses to triangulate evidence

The Residual Sum of Squares observed — the core test statistic computed by MR-PRESSO. It quantifies the total deviation of individual variant causal estimates from the overall causal estimate.

• Calculation: Sum of squared differences between each variant's Wald ratio estimate and the aggregate causal estimate
• Distribution: Under the null hypothesis of no pleiotropy, RSSobs follows a chi-squared distribution
• Global test: A significantly large RSSobs indicates the presence of horizontal pleiotropy somewhere among the instruments

The second stage of the MR-PRESSO procedure that evaluates whether removing detected outliers meaningfully changes the causal estimate. This prevents unnecessary correction when outliers exist but have negligible impact.

• Mechanism: Compares the causal estimate before and after outlier removal
• Interpretation: A significant distortion test indicates that pleiotropic variants were materially biasing results
• Practical value: Distinguishes between statistically detectable pleiotropy and practically important pleiotropy

A complementary sensitivity analysis often reported alongside MR-PRESSO results. Each genetic variant is iteratively removed, and the causal effect is re-estimated to assess the influence of individual instruments.

• Visualization: Typically displayed as a forest plot showing estimates with each variant omitted
• Comparison to MR-PRESSO: Leave-one-out is descriptive; MR-PRESSO provides formal statistical tests for outlier identification
• Combined use: Leave-one-out plots help researchers visually confirm that MR-PRESSO-identified outliers are indeed the influential variants