New Mendelian Randomization Method Analyzes Correlated Outcomes Together

A new statistical framework could make Mendelian randomization more sensitive to the biological connections linking multiple traits, allowing researchers to test a network of outcomes at once rather than analyzing each one in isolation. The method, developed by researchers at Boston University, the US National Heart, Lung, and Blood Institute and the Framingham Heart Study, is designed for a problem increasingly common in modern genetics: one molecular change can influence several genes, proteins or disease-related traits simultaneously. The researchers say their approach improves estimates of causal effects, detects misleading genetic instruments more effectively and offers a sharper way to test whether an exposure has any effect across a group of correlated outcomes. Their findings, published in the European Journal of Epidemiology, could be particularly useful for multi-omics studies, in which DNA sequence, DNA methylation, gene activity and other molecular measurements are analyzed together.

Mendelian randomization is often described as a natural experiment written into the genome. The method uses genetic variants associated with an exposure—such as a molecular marker or a physiological characteristic—as instrumental variables. Because genetic variants are assigned before birth and are generally less influenced by later behavior or disease, they can sometimes help distinguish correlation from causation in observational data. In a conventional analysis, however, each outcome is usually treated separately. That strategy can discard information when outcomes are biologically related and statistically correlated. It can also make the analysis less powerful, because the evidence is divided among multiple tests. “Correlated outcomes” might include the expression levels of several genes controlled by a common regulatory mechanism, or a collection of clinical traits that share underlying biology. The new framework treats those outcomes as a connected system rather than as unrelated endpoints.

The researchers introduce two complementary tools. The first, called multivariate inverse-variance weighted Mendelian randomization, or multivariate MR-IVW, extends a widely used method for combining genetic evidence. In ordinary inverse-variance weighting, estimates from individual genetic instruments are weighted according to their precision: variants with smaller uncertainty contribute more to the overall result. The multivariate version additionally models the covariance among outcome estimates. In practical terms, it knows that measurements of two related genes may rise and fall together, and it adjusts the calculation accordingly. The method uses multivariate meta-analysis, a statistical technique that combines several outcomes while retaining information about their correlations. This “borrowing of strength” can reduce noise and improve the accuracy of the estimated causal effects, provided that the covariance structure is estimated appropriately.

The second tool, multivariate MR-PRESSO, addresses one of the most persistent hazards in Mendelian randomization: horizontal pleiotropy. A genetic variant is a useful instrument only when its effect on an outcome operates through the exposure being studied. But some variants affect several biological pathways directly. Such variants can distort a causal estimate, even when the exposure-outcome association appears convincing. Existing MR-PRESSO analyses can identify instruments that behave unusually for one outcome at a time. The multivariate extension evaluates the pattern across all outcomes simultaneously. It uses Mahalanobis distance, which measures how far a vector of observations lies from the expected multivariate pattern while accounting for correlations among variables. An instrument can therefore be flagged not merely because it looks extreme for one gene, but because its combined effects across several genes are inconsistent with the causal model.

To test the performance of the methods, the team conducted extensive simulations in which the underlying causal effects, correlations among outcomes and levels of pleiotropy could be controlled. The simulations showed that multivariate MR-IVW consistently produced lower bias and lower mean squared error than the corresponding univariate approach. Bias is the systematic tendency of an estimator to miss the true value, while mean squared error combines that bias with random variation and is a standard measure of overall estimation quality. The advantage became especially striking when outcomes were strongly correlated. In a global hypothesis test involving two outcomes with a correlation of 0.8, the multivariate MR-IVW method detected an effect in 95 percent of relevant simulated cases, compared with 52 percent for the univariate method. At the same time, the researchers report that false-positive rates remained controlled, an essential safeguard when greater sensitivity can otherwise produce spurious discoveries.

The simulations also revealed a substantial gain in the detection of problematic genetic instruments. With four correlated outcomes and balanced pleiotropy—when a variant’s unintended effects push in opposing directions—the multivariate MR-PRESSO procedure identified outlying single-nucleotide polymorphisms in roughly 85 to 90 percent of simulated cases. The comparable univariate analysis detected them only 35 to 40 percent of the time. This difference matters because pleiotropic variants can be difficult to recognize when their effects are modest for any individual outcome. Across several outcomes, however, those small deviations may form a distinctive multivariate signature. Mahalanobis distance captures that joint departure, increasing the chance that a researcher will investigate or remove an instrument before it biases the final conclusion. The method does not eliminate the assumptions of Mendelian randomization, but it provides a more systematic stress test for them.

The researchers next applied their methods to a real multi-omics question involving DNA methylation at a genomic site known as cg11294513 and the expression of five zinc-finger genes. DNA methylation is a chemical modification in which methyl groups are added to DNA, often near regulatory regions. It can influence whether genes are active, although its effects depend on genomic location, cell type and surrounding molecular context. Zinc-finger proteins are a large family of proteins that can bind DNA and help regulate gene activity, making them important components of cellular control systems. The analysis combined data from the Framingham Heart Study with gene-expression information from the Genotype-Tissue Expression project, or GTEx. Together, these resources allowed the team to examine whether genetically predicted variation in methylation at cg11294513 was causally related to the activity of the five genes.

The multivariate analysis found significant causal effects of methylation at cg11294513 on all five zinc-finger gene-expression outcomes. The joint approach also identified additional heterogeneous instruments that were not detected when the genes were analyzed individually. In this context, heterogeneity means that the genetic instruments do not all support a single coherent causal pattern; some may be influenced by alternative pathways or may behave differently because of biological complexity. Identifying those instruments is crucial before interpreting a molecular association as causal. The finding does not by itself establish that changing methylation at cg11294513 would produce a specific health benefit, nor does it demonstrate that the five genes form a single linear pathway. Rather, it shows how a coordinated statistical analysis can reveal a shared regulatory signal and expose genetic evidence that deserves closer examination.

The approach arrives as genetic studies increasingly move beyond one-exposure, one-outcome questions. Large association studies now measure thousands of molecular traits, while researchers seek to understand how regulatory changes propagate through cells and eventually contribute to disease. Analyzing each outcome independently can create a maze of separate significance tests, reduce statistical power and obscure patterns that are visible only at the system level. Multivariate MR-IVW offers a way to estimate several related effects together, while multivariate MR-PRESSO provides a corresponding method for identifying instruments that do not fit the overall pattern. The framework may therefore be valuable in studies of gene regulation, multimorbidity and other settings where biological outcomes are intrinsically linked. Its usefulness will depend on reliable estimates of outcome correlations, strong and valid genetic instruments, and careful attention to the possibility that the same participants or datasets contribute to multiple measurements.

The authors provide R code for the multivariate MR-PRESSO method and their simulation study, while the multivariate MR-IVW analysis was implemented using the mvmeta package, which supports fixed-effects and random-effects multivariate meta-analysis. These resources could make the methods easier to evaluate and adapt, but the statistical gains should not be mistaken for a replacement for experimental validation. Mendelian randomization remains dependent on core assumptions: the genetic instruments must be associated with the exposure, must not be related to important confounders, and must influence the outcomes primarily through the exposure rather than through independent pathways. Correlated outcomes can strengthen inference when modeled correctly, but they can also amplify errors if the correlation structure or causal model is wrong. Even so, by turning the relationships among multiple outcomes from a nuisance into usable information, the new framework offers a potentially powerful upgrade for the next generation of causal genetic research—one capable of following biological signals across an entire molecular network instead of stopping at a single gene.