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，以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 更不易受水平多效性的影响，并能估计每个暴露对结局的直接效应。然而，MVMR 在弱工具变量（即条件于其他暴露时与某些暴露弱相关的遗传变异）方面面临更大挑战。本文聚焦于利用全基因组关联研究（GWAS）汇总数据的 MVMR。我们提出了一种新的渐近框架，用于分析具有众多弱工具变量的 MVMR 估计量，允许不同线性组合的暴露具有不同程度的工具强度，并正式证明了流行的多变量逆方差加权（MV-IVW）估计量的渐近行为对工具强度高度敏感。随后，我们提出了一种多变量去偏 IVW（MV-dIVW）估计量，该估计量有效减少了 MV-IVW 中由弱工具变量引起的渐近偏倚，并引入其调整版本 MV-adIVW，以提升有限样本下的稳健性。我们建立了所提估计量的理论性质，并将其扩展到处理平衡水平多效性。最后，我们通过在模拟数据集和真实数据集中的表现来验证所提方法的性能。该方法已在 R 包 mr.divw 中实现。