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The paper claims that related outcome traits share enough invalid instruments with a primary trait that borrowing them via a coheterogeneity-ranked auxiliary trait yields more robust Mendelian randomization estimates—more power and better t

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2026-08-01 21:22 UTC pith:EEXULWIQ

load-bearing objection The coheterogeneity statistic and IB-Mode are real contributions, but the unvalidated data-driven selection of the auxiliary trait is the gap to fix before this is fully convincing. the 2 major comments →

arxiv 2607.16086 v1 pith:EEXULWIQ submitted 2026-07-17 stat.ME

Improving Mendelian Randomization Analysis by Instrument Borrowing from Auxiliary Outcome Traits

Anagh Chattopadhyay , Nilanjan Chatterjee This is my paper
classification stat.ME MSC 62F1262G0762P10
keywords Mendelian randomizationpleiotropyinstrument borrowingcoheterogeneityinvalid instrumentsmultivariate mode estimationoutlier detectionsummary statistics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that pleiotropy across related outcome traits, normally a nuisance, can be repurposed to improve Mendelian randomization (MR). It introduces a 'coheterogeneity' statistic that uses summary statistics to measure how much two outcomes share invalid instruments for a given exposure, with proven consistency and asymptotic normality. Building on this, it extends MR-Mode and MR-PRESSO into bivariate 'instrument borrowing' methods, IB-Mode and IB-PRESSO, that jointly use an auxiliary outcome. Simulations and re-analyses of established causal and non-causal hypotheses show that borrowing instruments from a well-chosen auxiliary trait increases power and controls type I error better than single-trait analyses, with gains growing as the overlap of invalid instruments grows.

Core claim

The central claim is that pleiotropy across outcome traits—normally a curse—can be capitalized on to improve MR. The paper shows that for related outcomes, the valid and invalid instruments for an exposure substantially overlap, and that a new statistic, ρ_CH, can detect this overlap from GWAS summary data alone. The authors extend MR-Mode and MR-PRESSO to the bivariate setting (IB-Mode and IB-PRESSO) and demonstrate, via extensive simulations and applications to 48 known exposure–outcome hypotheses, that borrowing instruments from a well-chosen auxiliary trait yields more power and better type I error control than analyzing the primary trait alone. In the real-data analysis, IB-Mode is the

What carries the argument

The coheterogeneity statistic ρ_CH—the debiased, precision-weighted correlation of Wald-ratio deviations between two outcomes for the same exposure—is the selection engine. The paper proves its consistency and asymptotic normality (Theorem 1) and shows (Lemma 1) that under a polygenic random-effect model it converges to a parameter that grows with the overlap D_ov of invalid instruments. IB-Mode then generalizes MR-Mode by maximizing a bivariate kernel density of the two outcomes' Wald ratios, so that the mode is anchored by instruments valid for both traits; IB-PRESSO replaces univariate outlier detection with a bivariate Mahalanobis-distance test. The auxiliary trait is chosen as the one w

Load-bearing premise

The load-bearing premise is that the coheterogeneity statistic ρ_CH tracks how much two outcomes share invalid instruments; the paper proves this only under a specific random-effect model with independent direct effects, and acknowledges that heterogeneous causal effects or shared causal pathways could make ρ_CH reflect something other than shared invalid instruments.

What would settle it

A simulation with two outcomes sharing no invalid instruments but with an exposure whose causal effect differs across instruments through an unobserved mediator would produce a high ρ_CH; IB-Mode applied to such a pair should then show worse bias than MR-Mode, breaking the claimed monotone relationship.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If correct, MR analyses can be made more robust by borrowing instruments from auxiliary traits, leading to more reliable causal claims in areas like drug-target validation.
  • The coheterogeneity statistic is itself a tool for mapping shared-confounding structure across traits per exposure, usable beyond MR for tasks like constructing causal directed acyclic graphs.
  • IB-Mode maintains type I error at least as well as MR-Mode and improves power, with gains growing with the overlap of invalid instruments.
  • IB-PRESSO mostly improves efficiency (up to roughly 210% gain in some real-data comparisons) while somewhat reducing bias of MR-PRESSO, though type I error can still be inflated in hard scenarios.
  • The framework extends naturally to other MR methods: MR-Mix, MR-ConMix, and MR-cML can be adapted to bivariate borrowing, and more than two traits may be leveraged for additional robustness.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The coheterogeneity statistic could double as a diagnostic for whether a proposed confounder is shared: if ρ_CH is high only for certain exposure–outcome pairs, that suggests exposure-specific shared pathways, which could guide biological hypothesis generation.
  • The monotonicity in Lemma 1 is proven only under a specific random-effect model with independent direct-effect errors; a natural extension would be to test whether ρ_CH remains monotone under heterogeneous causal effects or correlated pleiotropy, since the Discussion concedes these could break the link.
  • A practical extension would be to use ρ_CH to pre-screen auxiliary traits in a large biobank automatically and to weight multiple auxiliaries rather than picking the top one, potentially improving power further.
  • The IB framework implicitly assumes the exposure's causal effect on the primary trait is the target; an extension to 'borrowing' across multiple exposures might combine benefits but would require careful handling of cross-exposure confounding.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper proposes a framework for Mendelian randomization (MR) that borrows information from an auxiliary outcome trait when the auxiliary and primary traits share invalid instruments for a given exposure. A new coheterogeneity statistic, ρ_CH, is introduced to quantify shared horizontal pleiotropic structure, with asymptotic theory (Theorem 1, Lemma S2, Theorem 2) and a monotonicity result linking ρ_CH to the overlap of invalid instruments under a specific random-effect model (Lemma 1). The authors then extend MR-Mode and MR-PRESSO into IB-Mode and IB-PRESSO, which use bivariate ratio distributions or bivariate residuals to improve mode estimation and outlier detection. Simulation studies compare the IB methods against standard MR approaches under various levels of instrument overlap, and real-data analyses on cardiometabolic traits, including positive and negative controls and the vitamin D controversy, are used to argue that IB-Mode improves type I error control and power.

Significance. If the central claims hold, the coheterogeneity statistic would be a useful diagnostic for shared pleiotropic structure, and the IB framework could make MR more robust by leveraging frequently available multi-trait GWAS data. The paper contains substantial methodological development: rigorous asymptotic proofs in the appendix, publicly available code (IBMR package), extensive simulations, and a real-data application with positive and negative controls. The main caveat is that the recommended workflow for selecting auxiliary traits is not validated end-to-end in simulations, which is a load-bearing issue for the real-data conclusions about type I error control. Overall, the contribution is significant but currently incomplete with respect to its own stated workflow.

major comments (2)
  1. [§4, Algorithm 1 (lines 8–11) and §2.3.1] The suggested workflow selects the auxiliary trait by the largest |ρ_CH| estimated from the same primary-outcome data used for the final MR inference. However, all simulation studies feed a pre-specified auxiliary trait with known D_ov into IB-Mode/IB-PRESSO; no simulation runs the full selection pipeline over a candidate pool. The bootstrap inference in §2.3.1 resamples bivariate Wald ratios conditional on the already-selected trait and does not re-run trait selection. Selection based on max |ρ_CH| induces a conditioning event involving Y1's sampling noise, so the reported p-values and confidence intervals are not adjusted for selection. Consequently, the real-data claim that 'IB-Mode is the most robust method' for type I error control is not directly supported by evidence from the exact procedure being recommended. A simulation experiment that includes multiple candidate auxiliaries an
  2. [Lemma 1, Appendix A.5, and Discussion] The monotonic relationship between ρ_CH and D_ov is derived under the paper's random-effect simulation model (independent direct-effect errors, known confounder structure, no heterogeneous causal effects). The Discussion acknowledges that heterogeneous causal effects of the exposure can also generate coheterogeneity. If the selected auxiliary shares causal pathways or heterogeneous components rather than invalid instruments, then borrowing may not improve—and could harm—the primary MR estimate. This is a load-bearing assumption for auxiliary-trait selection. The authors should either extend the simulation study to include scenarios with heterogeneous causal effects (or shared mediated pathways) and assess whether IB methods still control type I error, or clearly restrict the scope of the selection criterion to settings where invalid-instrument overlap is the dominant source of coheteroge
minor comments (4)
  1. [§4, Figure 4B and Figure S11] The text states there are 17 exposure–outcome pairs in the 'correlated but with unclear causality or conflicting evidence' category, but Figure 4B and Figure S11 label this category as 'corr (N=15)'. The count should be reconciled.
  2. [Figure 2] The 'optimal power' comparison selects the tuning parameter φ for each method as the largest value that maintains type I error ≤ 5% in null simulations. Since the recommended default is φ = 1, reporting only the oracle-selected φ may overstate the practical power gain. Presenting results at φ = 1 alongside the optimal-selection results would clarify the achievable benefit.
  3. [§2.3.2] The definition of the IB-PRESSO residual uses a robust covariance matrix via minimum covariance determinant, but the text does not state how the robust covariance estimate is computed when K is small. A brief clarification or reference would be helpful.
  4. [Throughout] The notation 'IB-MODE' is used in figures and tables while the text uses 'IB-Mode'. Capitalization should be made consistent.

Circularity Check

0 steps flagged

No significant circularity: coheterogeneity statistic and IB estimators are independently defined and validated; the unmodeled selection step is a post-selection gap, not a definitional loop.

full rationale

The derivation chain is self-contained rather than circular. The coheterogeneity estimator (Eqs. 1–2) is defined as a debiased, precision-weighted correlation of centered Wald-ratio deviations; Theorem 1 proves consistency and asymptotic normality under explicit regularity conditions in Appendix A.3, with a delta-method variance estimator. Lemma 1 does not define rho_CH in terms of D_ov; it derives a limiting expression under a stated variance-component model and shows monotonicity in D_ov as a property of that model. Simulations evaluate rho_CH against known D_ov and compare IB methods with external benchmarks, including positive/negative controls from Morrison et al. and vitamin D RCTs, so the central claims are not fitted inputs renamed as predictions. Self-citations (Qi & Chatterjee 2019/2021; Qi et al. 2024) are used as simulation scaffolding, background pleiotropy evidence, or benchmark comparisons; none supplies a load-bearing uniqueness or ansatz assumption. The paper itself flags the main caveat in the Discussion: "if certain exposures have heterogeneous causal effects, the coheterogeneity measure can also capture overlap among traits with respect to the same causal components," and Algorithm 1 selects auxiliaries from the same primary data while simulations pre-specify the auxiliary. That is a post-selection inference limitation, not circularity: no equation reduces to its own input and no fitted parameter is relabeled as a prediction.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

No new physical entities; the coheterogeneity parameter is a statistical estimand, not a proposed physical mechanism. The free-parameter ledger is light because the method's central machinery is derived from GWAS summary statistics rather than fitted constants.

free parameters (1)
  • KDE bandwidth scaling φ = 1 (default; authors recommend φ=1 for IB-Mode)
    Smoothing parameter in the weighted bivariate kernel density mode estimator; controls bias/variance trade-off and type I error. In simulations, φ was varied and selected per scenario to equalize type I before comparing power (Section 3, Fig 2).
axioms (5)
  • domain assumption Zero-modal pleiotropy assumption for MR-Mode/IB-Mode: the modal pleiotropic effect across instruments is zero.
    Section 2.3.1; inherited from Hartwig et al. 2017 (ref 22). If the mode of pleiotropy is not zero, IB-Mode is biased.
  • domain assumption Related outcome traits share a substantial fraction of valid/invalid instruments (large D_ov) in relation to a given exposure.
    Core hypothesis in the Introduction and Fig S1; if D_ov is small, borrowing cannot help and may hurt.
  • ad hoc to paper ρ_CH is monotonically related to D_ov under the paper's random-effect polygenic architecture (Lemma 1, Appendix A.5).
    This is established under the simulation model in Section 3 with independence of direct-effect errors and known confounder partition; outside that model, e.g. with heterogeneous causal effects, the monotonicity need not hold (Discussion).
  • domain assumption Regularity conditions (C1)-(C6): K_N=o(N), independent summary statistics across SNPs, |βX,k| bounded below, bounded pleiotropy, τ_l bounded away from zero, and variance limit (Appendix A.3).
    Needed for Theorem 1; C3 (strong instruments) fails in weak-instrument regimes, although Lemma S2 relaxes it.
  • domain assumption Cross-trait sampling covariance σ12,k can be recovered from the intercept of bivariate LD-score regression (A.2, eq 6).
    Used to debias C12 for overlapping outcome samples; relies on LDSC intercept identifying Nsρ12/sqrt(N1N2).

pith-pipeline@v1.3.0-alltime-deepseek · 35619 in / 12975 out tokens · 122652 ms · 2026-08-01T21:22:30.422413+00:00 · methodology

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read the original abstract

Mendelian randomization (MR) is a widely used approach for inferring causal effects of exposures on outcomes using genetic variants as instrumental variables; however, existing methods remain vulnerable to bias and/or loss of power in the presence of invalid instruments. We hypothesize that closely related outcome traits are likely to have a large overlap in underlying valid instruments in relation to a given exposure and that instrument borrowing (IB) across such traits can therefore yield more robust MR inference. To operationalize this idea, we first introduce a novel coheterogeneity statistic and its asymptotic theory under different paradigms which can be used to identify secondary outcome traits that are likely to share valid instruments with the primary trait. We then propose extensions of two popular methods, MR-Mode and MR-PRESSO, that improve MR inference for the primary trait, taking advantage of a secondary trait. Extensive simulation studies demonstrate that the proposed coheterogeneity statistic has expected finite-sample properties and IB-based methods consistently outperform their standard counterparts, with gains increasing as the degree of overlap in valid instruments across outcome traits grows. Applications to established positive and negative control hypotheses suggest that IB-based methods offer improved control of type I error and increased power. We further illustrate the practical utility of these methods by revisiting the long-debated hypothesis on the causal effect of vitamin D on cardiometabolic traits.

Figures

Figures reproduced from arXiv: 2607.16086 by Anagh Chattopadhyay, Nilanjan Chatterjee.

Figure 1
Figure 1. Figure 1: Sampling distribution of the coheterogeneity statistics and coverage of 95% confidence interval. Left: Ridge density plots of ρˆ (N) CH across replications with different sample sizes (N). Right: Empirical coverage of nominal 95% confidence intervals for ρˆ (N) CH across sample sizes N (with the corresponding mean number of selected instruments K). The horizontal red line marks 95% nominal coverage. ρCH. W… view at source ↗
Figure 2
Figure 2. Figure 2: Power comparison between MR-Mode and IB-Mode methods across diverse simulation scenarios. For each method and scenario setting, the largest value for the tuning parameter ϕ that maintains the Type-I error rate at or below 5% is selected using simulation experiments under null. The statistical power of the two methods at the respective optimal ϕ are then evaluated through simulations under alternative hypot… view at source ↗
Figure 3
Figure 3. Figure 3: Type-I error and power of different MR methods. Simulations are conducted under models where invalid instruments arise due to hidden heritable confounders leading to violation of the InSIDE assumption. The overlap in underlying invalid instruments across two outcome traits due to shared confounders is assumed to be Dov = 0.75. Additionally, invalid instruments are allowed to have directional pleiotropic ef… view at source ↗
Figure 4
Figure 4. Figure 4: Data analysis results for MR analysis involving cardiometabolic traits and 48 exposure-outcome causal hypotheses (A) Heatmaps representing values for coheterogeneity statistics for two representative exposures (BMI and LDL) across selected outcome traits. Statistically significant (p-value < 0.001) are indicated by **. (B) Proportion of positive findings (p-value < 0.001) according to different MR methods … view at source ↗

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Reference graph

Works this paper leans on

54 extracted references

  1. [1]

    Mendelian randomization: prospects, potentials, and limitations

    G. D. Smith and S. Ebrahim. “Mendelian randomization: prospects, potentials, and limitations”. In:International journal of epidemiology33.1 (2004), pp. 30–42

    2004

  2. [2]

    Mendelian randomization studies of cancer risk: a literature review

    B. L. Pierce, P. Kraft, and C. Zhang. “Mendelian randomization studies of cancer risk: a literature review”. In:Current epidemiology reports5 (2018), pp. 184–196

    2018

  3. [3]

    Type 2 diabetes, metabolic traits, and risk of Heart failure: a mendelian randomization study

    I. R. Mordi, R. T. Lumbers, C. N. Palmer, E. R. Pearson, N. Sattar, M. V. Holmes, and C. C. Lang. “Type 2 diabetes, metabolic traits, and risk of Heart failure: a mendelian randomization study”. In: Diabetes Care44.7 (2021), pp. 1699–1705

    2021

  4. [4]

    Mendelian randomization studies on coronary artery disease: a systematic review and meta-analysis

    S. Silva, S. Fatumo, and D. Nitsch. “Mendelian randomization studies on coronary artery disease: a systematic review and meta-analysis”. In:Systematic reviews13.1 (2024), p. 29

    2024

  5. [5]

    Association between circulating inflammatory markers and adult cancer risk: a Mendelian randomization analysis

    J. Yarmolinsky, J. W. Robinson, D. Mariosa, V. Karhunen, J. Huang, N. Dimou, N. Murphy, K. Burrows, E. Bouras, K. Smith-Byrne, et al. “Association between circulating inflammatory markers and adult cancer risk: a Mendelian randomization analysis”. In:EBioMedicine100 (2024)

    2024

  6. [6]

    Socioeconomic status, personality, and major mental disorders: a bidirectional Mendelian randomization study

    Q. Xu, H. Li, and D. Zhu. “Socioeconomic status, personality, and major mental disorders: a bidirectional Mendelian randomization study”. In:Schizophrenia10.1 (2024), p. 49. 16

    2024

  7. [7]

    Does better education mitigate risky health behavior? A mendelian randomization study

    J. Viinikainen, A. Bryson, P. B¨ ockerman, J. T. Kari, T. Lehtim¨ aki, O. Raitakari, J. Viikari, and J. Pehkonen. “Does better education mitigate risky health behavior? A mendelian randomization study”. In:Economics & Human Biology46 (2022), p. 101134

    2022

  8. [8]

    Mediating factors in the association of maternal educational level with pregnancy outcomes: a Mendelian Randomization Study

    T. Rogne, D. Gill, Z. Liew, X. Shi, V. H. Stensrud, T. I. L. Nilsen, and S. Burgess. “Mediating factors in the association of maternal educational level with pregnancy outcomes: a Mendelian Randomization Study”. In:JAMA Network Open7.1 (2024), e2351166–e2351166

    2024

  9. [9]

    Network Mendelian randomization study: exploring the causal pathway from insomnia to type 2 diabetes

    W. Xiuyun, L. Jiating, X. Minjun, L. Weidong, W. Qian, and L. Lizhen. “Network Mendelian randomization study: exploring the causal pathway from insomnia to type 2 diabetes”. In:BMJ Open Diabetes Research and Care10.1 (2022), e002510

    2022

  10. [10]

    Mendelian randomization: a novel approach for the prediction of adverse drug events and drug repurposing opportunities

    V. M. Walker, G. Davey Smith, N. M. Davies, and R. M. Martin. “Mendelian randomization: a novel approach for the prediction of adverse drug events and drug repurposing opportunities”. In: International journal of epidemiology46.6 (2017), pp. 2078–2089

    2017

  11. [11]

    Mendelian randomization for studying the effects of perturbing drug targets

    D. Gill, M. K. Georgakis, V. M. Walker, A. F. Schmidt, A. Gkatzionis, D. F. Freitag, C. Finan, A. D. Hingorani, J. M. Howson, S. Burgess, et al. “Mendelian randomization for studying the effects of perturbing drug targets”. In:Wellcome open research6 (2021), p. 16

    2021

  12. [12]

    Finding genetically-supported drug targets for Parkinson’s disease using Mendelian randomization of the druggable genome

    C. S. Storm, D. A. Kia, M. M. Almramhi, S. Bandres-Ciga, C. Finan, A. D. Hingorani, and N. W. Wood. “Finding genetically-supported drug targets for Parkinson’s disease using Mendelian randomization of the druggable genome”. In:Nature communications12.1 (2021), p. 7342

    2021

  13. [13]

    A comprehensive evaluation of methods for Mendelian randomization using realistic simulations and an analysis of 38 biomarkers for risk of type 2 diabetes

    G. Qi and N. Chatterjee. “A comprehensive evaluation of methods for Mendelian randomization using realistic simulations and an analysis of 38 biomarkers for risk of type 2 diabetes”. In:International journal of epidemiology50.4 (2021), pp. 1335–1349

    2021

  14. [14]

    A global overview of pleiotropy and genetic architecture in complex traits

    K. Watanabe, S. Stringer, O. Frei, M. Umi´ cevi´ c Mirkov, C. de Leeuw, T. J. Polderman, S. van der Sluis, O. A. Andreassen, B. M. Neale, and D. Posthuma. “A global overview of pleiotropy and genetic architecture in complex traits”. In:Nature genetics51.9 (2019), pp. 1339–1348

    2019

  15. [15]

    Genome-wide large-scale multi-trait analysis characterizes global patterns of pleiotropy and unique trait-specific variants

    G. Qi, S. B. Chhetri, D. Ray, D. Dutta, A. Battle, S. Bhattacharjee, and N. Chatterjee. “Genome-wide large-scale multi-trait analysis characterizes global patterns of pleiotropy and unique trait-specific variants”. In:Nature communications15.1 (2024), p. 6985

    2024

  16. [16]

    Specificity, length, and luck: How genes are prioritized by rare and common variant association studies

    J. P. Spence, H. Mostafavi, M. Ota, N. Milind, T. Gjorgjieva, C. J. Smith, Y. B. Simons, G. Sella, and J. K. Pritchard. “Specificity, length, and luck: How genes are prioritized by rare and common variant association studies”. In:bioRxiv(2024), pp. 2024–12

    2024

  17. [17]

    Detection and interpretation of shared genetic influences on 42 human traits

    J. K. Pickrell, T. Berisa, J. Z. Liu, L. S´ egurel, J. Y. Tung, and D. A. Hinds. “Detection and interpretation of shared genetic influences on 42 human traits”. In:Nature genetics48.7 (2016), pp. 709–717

    2016

  18. [18]

    A plethora of pleiotropy across complex traits

    P. M. Visscher and J. Yang. “A plethora of pleiotropy across complex traits”. In:Nature genetics 48.7 (2016), pp. 707–708

    2016

  19. [19]

    10 years of GW AS discovery: biology, function, and translation

    P. M. Visscher, N. R. Wray, Q. Zhang, P. Sklar, M. I. McCarthy, M. A. Brown, and J. Yang. “10 years of GW AS discovery: biology, function, and translation”. In:The American Journal of Human Genetics101.1 (2017), pp. 5–22

    2017

  20. [20]

    Detection of widespread horizontal pleiotropy in causal relationships inferred from Mendelian randomization between complex traits and diseases

    M. Verbanck, C.-Y. Chen, B. Neale, and R. Do. “Detection of widespread horizontal pleiotropy in causal relationships inferred from Mendelian randomization between complex traits and diseases”. In:Nature genetics50.5 (2018), pp. 693–698

    2018

  21. [21]

    Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression

    J. Bowden, G. Davey Smith, and S. Burgess. “Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression”. In:International journal of epi- demiology44.2 (2015), pp. 512–525

    2015

  22. [22]

    Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption

    F. P. Hartwig, G. Davey Smith, and J. Bowden. “Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption”. In:International journal of epidemiology 46.6 (2017), pp. 1985–1998

    2017

  23. [23]

    Mendelian randomization analysis using mixture models for robust and efficient estimation of causal effects

    G. Qi and N. Chatterjee. “Mendelian randomization analysis using mixture models for robust and efficient estimation of causal effects”. In:Nature communications10.1 (2019), p. 1941

    2019

  24. [24]

    A robust and efficient method for Mendelian randomization with hundreds of genetic variants

    S. Burgess, C. N. Foley, E. Allara, J. R. Staley, and J. M. Howson. “A robust and efficient method for Mendelian randomization with hundreds of genetic variants”. In:Nature communications11.1 (2020), p. 376. 17

    2020

  25. [25]

    Robust multivariable Mendelian randomization based on constrained maximum likelihood

    Z. Lin, H. Xue, and W. Pan. “Robust multivariable Mendelian randomization based on constrained maximum likelihood”. In:The American Journal of Human Genetics110.4 (2023), pp. 592–605

    2023

  26. [26]

    A comparison of robust Mendelian randomization methods using summary data

    E. A. Slob and S. Burgess. “A comparison of robust Mendelian randomization methods using summary data”. In:Genetic epidemiology44.4 (2020), pp. 313–329

    2020

  27. [27]

    Mendelian randomization analysis with multiple genetic variants using summarized data

    S. Burgess, A. Butterworth, and S. G. Thompson. “Mendelian randomization analysis with multiple genetic variants using summarized data”. In:Genetic epidemiology37.7 (2013), pp. 658–665

    2013

  28. [28]

    Meta-analysis in clinical trials

    R. DerSimonian and N. Laird. “Meta-analysis in clinical trials”. In:Controlled clinical trials7.3 (1986), pp. 177–188

    1986

  29. [29]

    An atlas of genetic correlations across human diseases and traits

    B. Bulik-Sullivan, H. K. Finucane, V. Anttila, A. Gusev, F. R. Day, P. -R. Loh, R. Consortium, P. G. Consortium, G. C. for Anorexia Nervosa of the Wellcome Trust Case Control Consortium 3, L. Duncan, et al. “An atlas of genetic correlations across human diseases and traits”. In:Nature genetics47.11 (2015), pp. 1236–1241

    2015

  30. [30]

    Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects

    H. Xue, X. Shen, and W. Pan. “Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects”. In:The American Journal of Human Genetics108.7 (2021), pp. 1251–1269

    2021

  31. [31]

    Multivariate estimation with high breakdown point

    P. J. Rousseeuw. “Multivariate estimation with high breakdown point”. In:Mathematical statistics and applications8.283-297 (1985), p. 37

    1985

  32. [32]

    MendelianRandomization: an R package for performing Mendelian randomization analyses using summarized data

    O. O. Yavorska and S. Burgess. “MendelianRandomization: an R package for performing Mendelian randomization analyses using summarized data”. In:International journal of epidemiology46.6 (2017), pp. 1734–1739

    2017

  33. [33]

    Multi-response Mendelian randomization: Identification of shared and distinct exposures for multimorbidity and multiple related disease outcomes

    V. Zuber, A. Lewin, M. G. Levin, A. Haglund, S. Ben-Aicha, C. Emanueli, S. Damrauer, S. Burgess, D. Gill, and L. Bottolo. “Multi-response Mendelian randomization: Identification of shared and distinct exposures for multimorbidity and multiple related disease outcomes”. In:The American Journal of Human Genetics110.7 (2023), pp. 1177–1199

    2023

  34. [34]

    Mendelian randomization accounting for correlated and uncorrelated pleiotropic effects using genome-wide summary statistics

    J. Morrison, N. Knoblauch, J. H. Marcus, M. Stephens, and X. He. “Mendelian randomization accounting for correlated and uncorrelated pleiotropic effects using genome-wide summary statistics”. In:Nature genetics52.7 (2020), pp. 740–747

    2020

  35. [35]

    Million Veteran Program: A mega-biobank to study genetic influences on health and disease

    J. M. Gaziano, J. Concato, M. Brophy, L. Fiore, S. Pyarajan, J. Breeling, S. Whitbourne, J. Deen, C. Shannon, D. Humphries, et al. “Million Veteran Program: A mega-biobank to study genetic influences on health and disease”. In:Journal of clinical epidemiology70 (2016), pp. 214–223

    2016

  36. [36]

    Vitamin D supplementation and prevention of type 2 diabetes

    A. G. Pittas, B. Dawson-Hughes, P. Sheehan, J. H. Ware, W. C. Knowler, V. R. Aroda, I. Brodsky, L. Ceglia, C. Chadha, R. Chatterjee, et al. “Vitamin D supplementation and prevention of type 2 diabetes”. In:New England journal of medicine381.6 (2019), pp. 520–530

    2019

  37. [37]

    Vitamin D supplements and prevention of cancer and cardiovascular disease

    J. E. Manson, N. R. Cook, I. -M. Lee, W. Christen, S. S. Bassuk, S. Mora, H. Gibson, D. Gordon, T. Copeland, D. D’Agostino, et al. “Vitamin D supplements and prevention of cancer and cardiovascular disease”. In:New England Journal of Medicine380.1 (2019), pp. 33–44

    2019

  38. [38]

    Towards optimal doubly robust estimation of heterogeneous causal effects

    E. H. Kennedy. “Towards optimal doubly robust estimation of heterogeneous causal effects”. In: Electronic Journal of Statistics17.2 (2023), pp. 3008–3049

    2023

  39. [39]

    Causal effect heterogeneity

    J. E. Brand and J. S. Thomas. “Causal effect heterogeneity”. In:Handbook of causal analysis for social research. Springer, 2013, pp. 189–213

    2013

  40. [40]

    Systematic review of genomic associations with blood pressure and hypertension in populations with African-Ancestry

    S. Singh, J. Brandenburg, A. Choudhury, F. G´ omez-Oliv´ e, and M. Ramsay. “Systematic review of genomic associations with blood pressure and hypertension in populations with African-Ancestry”. In:Frontiers in genetics12 (2021), p. 699445

    2021

  41. [41]

    Increased arterial blood pressure and vascular remodeling in mice lacking salt-inducible kinase 1 (SIK1)

    A. M. Bertorello, N. Pires, B. Igreja, M. J. Pinho, E. Vorkapic, D. W ˚ ags¨ ater, J. Wikstr¨ om, M. Behrendt, A. Hamsten, P. Eriksson, et al. “Increased arterial blood pressure and vascular remodeling in mice lacking salt-inducible kinase 1 (SIK1)”. In:Circulation Research116.4 (2015), pp. 642–652

    2015

  42. [42]

    Association of CETP gene variants with risk for vascular and nonvascular diseases among Chinese adults

    I. Y. Millwood, D. A. Bennett, M. V. Holmes, R. Boxall, Y. Guo, Z. Bian, L. Yang, S. Sansome, Y. Chen, H. Du, et al. “Association of CETP gene variants with risk for vascular and nonvascular diseases among Chinese adults”. In:JAMA cardiology3.1 (2018), pp. 34–43

    2018

  43. [43]

    Pleiotropic genetic effects contribute to the correlation between HDL cholesterol, triglycerides, and LDL particle size in hypertensive sibships

    I. J. Kullo, M. d. Andrade, E. Boerwinkle, J. P. McConnell, S. L. Kardia, and S. T. Turner. “Pleiotropic genetic effects contribute to the correlation between HDL cholesterol, triglycerides, and LDL particle size in hypertensive sibships”. In:American journal of hypertension18.1 (2005), pp. 99–103. 18

    2005

  44. [44]

    Genetic studies of body mass index yield new insights for obesity biology

    A. E. Locke, B. Kahali, S. I. Berndt, A. E. Justice, T. H. Pers, F. R. Day, C. Powell, S. Vedantam, M. L. Buchkovich, J. Yang, et al. “Genetic studies of body mass index yield new insights for obesity biology”. In:Nature518.7538 (2015), pp. 197–206

    2015

  45. [45]

    The breadth and impact of the Global Lipids Genetics Consortium

    J. S. Dron, P. Natarajan, and G. M. Peloso. “The breadth and impact of the Global Lipids Genetics Consortium”. In:Current Opinion in Lipidology36.2 (2025), pp. 61–70

    2025

  46. [46]

    Genome-wide analysis in over 1 million individuals of European ancestry yields improved polygenic risk scores for blood pressure traits

    J. M. Keaton, Z. Kamali, T. Xie, A. Vaez, A. Williams, S. B. Goleva, A. Ani, E. Evangelou, J. N. Hellwege, L. Yengo, et al. “Genome-wide analysis in over 1 million individuals of European ancestry yields improved polygenic risk scores for blood pressure traits”. In:Nature genetics56.5 (2024), pp. 778–791

    2024

  47. [47]

    Genome-wide association study identifies 143 loci associated with 25 hydroxyvitamin D concentration

    J. A. Revez, T. Lin, Z. Qiao, A. Xue, Y. Holtz, Z. Zhu, J. Zeng, H. Wang, J. Sidorenko, K. E. Kemper, et al. “Genome-wide association study identifies 143 loci associated with 25 hydroxyvitamin D concentration”. In:Nature communications11.1 (2020), p. 1647

    2020

  48. [48]

    The trans-ancestral genomic architecture of glycemic traits

    J. Chen, C. N. Spracklen, G. Marenne, A. Varshney, L. J. Corbin, J. Luan, S. M. Willems, Y. Wu, X. Zhang, M. Horikoshi, et al. “The trans-ancestral genomic architecture of glycemic traits”. In: Nature genetics53.6 (2021), pp. 840–860

    2021

  49. [49]

    Defining the role of common variation in the genomic and biological architecture of adult human height

    A. R. Wood, T. Esko, J. Yang, S. Vedantam, T. H. Pers, S. Gustafsson, A. Y. Chu, K. Estrada, J. Luan, Z. Kutalik, et al. “Defining the role of common variation in the genomic and biological architecture of adult human height”. In:Nature genetics46.11 (2014), pp. 1173–1186

    2014

  50. [50]

    Lab.UK Biobank GWAS results: Round 1 (Rapid GWAS of thousands of phenotypes for 337,000 samples in the UK Biobank)

    N. Lab.UK Biobank GWAS results: Round 1 (Rapid GWAS of thousands of phenotypes for 337,000 samples in the UK Biobank). https : / / www . nealelab . is / uk - biobank. Trait: Birth weight (phenotype code 20022), European ancestry, males and females, N=193,063. 2017

    2017

  51. [51]

    Elsworth.Body Fat Percentage (OpenGWAS ID: ukb-b-8909)

    B. Elsworth.Body Fat Percentage (OpenGWAS ID: ukb-b-8909). https://gwas.mrcieu.ac.uk/ datasets/ukb- b- 8909. MRC-IEU OpenGW AS Project; European ancestry, both sexes, N = 454,633; HG19/GRCh37; derived using PHESANT on UK Biobank. 2018

    2018

  52. [52]

    Elsworth.Ever Smoked (OpenGWAS ID: ukb-b-20261)

    B. Elsworth.Ever Smoked (OpenGWAS ID: ukb-b-20261). https : / / gwas . mrcieu . ac . uk / datasets/ukb- b- 20261. MRC-IEU OpenGW AS Project; European ancestry, both sexes, N = 461,066; HG19/GRCh37; derived using PHESANT on UK Biobank. 2018

    2018

  53. [53]

    Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use

    M. Liu, Y. Jiang, R. Wedow, Y. Li, D. M. Brazel, F. Chen, G. Datta, J. Davila-Velderrain, D. McGuire, C. Tian, et al. “Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use”. In:Nature genetics51.2 (2019), pp. 237–244. 19 Supplementary Information A Supplemental Notes A.1 Notation T ab...

    2019

  54. [54]

    IB-Mode gains are reported at the default bandwidth ϕ= 1and at the more conservative ϕ= 0.5

    (✓: support from method) Exposure Outcome Category IB-Mode IB-PRESSO Inverse variance weighted MR Egger MR-ConMix MR-Mix MR-PRESSO MR-cML Weighted median Weighted modeSmoking Asthma causalBF CAD causal✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓BMI CAD causal✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓DBP CAD causal✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓Height CAD causal✓ ✓ ✓ ✓ ✓ ✓ ✓LDL CAD causal✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓SBP CAD ca...