Multivariable Mendelian randomization (MVMR) uses genetic variants as instrumental variables to infer the direct effect of multiple exposures on an outcome. Compared to univariable Mendelian randomization, MVMR is less prone to horizontal pleiotropy and enables estimation of the direct effect of each exposure on the outcome. However, MVMR faces greater challenges with weak instruments -- genetic variants that are weakly associated with some exposures conditional on the other exposures. This article focuses on MVMR using summary data from genome-wide association studies (GWAS). We provide a new asymptotic regime to analyze MVMR estimators with many weak instruments, allowing for linear combinations of exposures to have different degrees of instrument strength, and formally show that the popular multivariable inverse-variance weighted (MV-IVW) estimator's asymptotic behavior is highly sensitive to instruments' strength. We then propose a multivariable debiased IVW (MV-dIVW) estimator, which effectively reduces the asymptotic bias from weak instruments in MV-IVW, and introduce an adjusted version, MV-adIVW, for improved finite-sample robustness. We establish the theoretical properties of our proposed estimators and extend them to handle balanced horizontal pleiotropy. We conclude by demonstrating the performance of our proposed methods in simulated and real datasets. We implement this method in the R package mr.divw.

翻译：多变量孟德尔随机化（MVMR）利用遗传变异作为工具变量，推断多个暴露因素对结局的直接效应。与单变量孟德尔随机化相比，MVMR不易受到水平多效性的影响，并能估计每个暴露对结局的直接效应。然而，MVMR面临更严峻的弱工具变量挑战——即某些遗传变异在控制其他暴露条件后与部分暴露的关联较弱。本文聚焦于基于全基因组关联研究（GWAS）汇总数据的MVMR方法。我们提出一种新的渐近框架以分析含大量弱工具变量的MVMR估计量，该框架允许不同线性组合的暴露具有不同强度的工具变量，并严格证明了广泛应用的多变量逆方差加权（MV-IVW）估计量的渐近行为对工具变量强度高度敏感。进而提出一种多变量无偏逆方差加权（MV-dIVW）估计量，有效降低了MV-IVW中弱工具变量导致的渐近偏倚，并引入其调整版本MV-adIVW以提升有限样本稳健性。我们建立了所提估计量的理论性质，并将其扩展至处理平衡水平多效性。最后通过模拟数据集和真实数据集验证了所提方法的性能。该方法已在R包mr.divw中实现。