Outlier Detection With MR-PRESSO

Why use MR-PRESSO?

With multiple genetic variants as instruments, their individual outcome associations may not all agree with a single causal effect. A variant can have a direct association with the outcome that is not mediated by the exposure: horizontal pleiotropy. Some variants may produce especially large residuals from the inverse-variance weighted (IVW) fit. MR-PRESSO (Mendelian Randomization Pleiotropy RESidual Sum and Outlier) uses simulation to test for such residual patterns, identify variants that look like outliers, and assess how much the estimated causal effect changes when those variants are removed.

These are diagnostic and sensitivity-analysis steps, not an automatic way to make an MR estimate valid. A large residual can reflect pleiotropy, but it can also arise from sampling variability, an incorrect variant association, or a model that does not describe the data. The interpretation of any correction therefore depends on the assumptions that connect residuals to invalid instruments.

Model and assumptions

Consider a single exposure and \(J\) approximately independent genetic variants. For variant \(j\), let \(\hat\beta_{Xj}\) be its estimated association with the exposure and \(\hat\beta_{Yj}\) its estimated association with the outcome; let \(SE(\hat\beta_{Yj})\) be the standard error of the outcome association. In the usual univariable MR-PRESSO setup, the IVW slope is fitted through the origin, treating the exposure-association estimates as fixed. The residual for variant \(j\) at a fitted causal slope \(\hat\theta\) is \(\hat\beta_{Yj}-\hat\beta_{Xj}\hat\theta\).

The simulation null is that the outcome associations follow a common causal slope, with variation consistent with their sampling errors. In a simple univariable description, simulated outcome associations are drawn around \(\hat\beta_{Xj}\hat\theta\), using the outcome-association standard errors. The simulated data are refitted, and their residual statistics provide reference distributions for the tests. Thus, the tests are not merely a comparison with a fixed chi-squared cutoff.

This setup makes assumptions important. Variants should be independent, or their dependence must be handled appropriately; ordinary MR-PRESSO use is generally based on LD-pruned variants. The exposure-association estimates are treated as known, so material measurement error in them can distort residuals and tests. The test also relies on the simulated null being an adequate description of sampling variation. Interpreting a flagged residual as horizontal pleiotropy further requires that data problems and other forms of model misspecification are not its explanation.

MR-PRESSO is most informative when invalid variants are exceptional outliers and most of the instruments give a reasonable reference fit. It is not a general detector of every form of pleiotropy. In particular, pleiotropic effects that shift all variants in a similar way, or track instrument strength, need not appear as isolated residuals. The earlier material on direct and correlated pleiotropy helps distinguish these possibilities conceptually; a residual test alone cannot establish which mechanism generated a pattern.

What the three tests report

For the global test, the observed statistic is the weighted residual sum of squares from the IVW fit:

A large value means the variants collectively fit a common slope poorly relative to their reported outcome-association uncertainty. To obtain a simulation p-value, compare the observed statistic with the statistics from \(B\) simulated data sets. For example, an empirical tail estimate can be calculated as \((1+r)/(B+1)\), where \(r\) is the number of simulated statistics at least as large as the observed one. A small global-test p-value is evidence against the simulated no-pleiotropy fit; it does not identify the source of the misfit.

The outlier test asks which variant or variants contribute unusually large residuals. The software evaluates variant-level residual evidence against simulated data and accounts for testing multiple variants. A hand calculation of one variant’s residual can show why it is suspicious, but it does not replace the simulated, multiplicity-adjusted outlier test. The distortion test then compares the IVW estimate using all variants with the estimate after outlier removal. Its p-value asks whether the observed change is unusual under its simulation procedure; it does not test whether the corrected estimate is the true causal effect.

Outlier removal and a change in conclusion

Removing a variant is defensible only if there is a reason to interpret its unusual residual as an invalid instrument rather than random error or a data problem. Even then, the removal does not prove that the remaining variants satisfy the instrumental-variable assumptions. It is prudent to report estimates with and without flagged variants, describe the selection rule, and explain why the excluded variant is plausibly problematic. The distortion test quantifies whether the change is noteworthy under its simulation model; it does not certify the post-removal analysis.

Assumptions, diagnostics, and limits

A practical reading of MR-PRESSO results should separate three questions: whether the overall fit is unusual, whether particular variants are outliers, and whether removing them materially changes the estimate. Check that the number of usable, independent variants is adequate for the fitted model and the tests; with very few instruments, there is little information for simulation-based diagnosis. Also check allele alignment, association estimates, standard errors, and the plausibility of treating exposure associations as fixed. A very small simulation count makes tail p-values coarse; with \(B\) simulations, the smallest nonzero empirical p-value under the formula above is \(1/(B+1)\).

A global-test rejection without a clear outlier can indicate several moderately unusual residuals rather than one removable variant. Conversely, a non-significant global test is not proof that all instruments are valid: the test may have low power, especially with few variants or imprecise associations. Large residuals may also reflect an incorrect standard error, dependence between variants, allele-coding errors, or a poorly specified model. Investigate such possibilities before interpreting an outlier as pleiotropy.

MR-PRESSO complements rather than replaces other approaches. IVW supplies the fitted slope whose residuals are assessed. MR-Egger models an intercept that can capture a different pattern of average pleiotropy but relies on its own assumptions. Weighted median and mode methods use different robustness conditions. MR-PRESSO’s distinctive target is residual outliers relative to a common-slope fit; none of these approaches guarantees protection when its assumptions fail. The later material on radial Mendelian randomization examines a different way to express and inspect variant contributions, so an MR-PRESSO outlier should not be treated as a complete influence analysis.

Common mistake