Mendelian randomization (MR) is an instrumental variable (IV) approach to infer causal relationships between exposures and outcomes with genome-wide association studies (GWAS) summary data. However, the multivariable inverse-variance weighting (IVW) approach, which serves as the foundation for most MR approaches, cannot yield unbiased causal effect estimates in the presence of many weak IVs. In this paper, we prove that the bias of the multivariable IVW estimate is a product of weak instrument and estimation error biases, where the latter is linearly composed of measurement error and confounder biases with a trade-off due to sample overlap among multiple GWAS cohorts. To address this problem, we propose a novel multivariable MR approach, MR using Bias-corrected Estimating Equation (MRBEE), which can infer unbiased causal relationships with many weak IVs. Asymptotic behaviors of multivariable IVW and MRBEE are investigated under moderate conditions, showing that MRBEE outperforms multivariable IVW in terms of unbiasedness and asymptotic validity. We apply MRBEE to examine myopia and confirm that schooling and driving time are causal factors for myopia. A novel locus of myopia is identified in the subsequent whole-genome pleiotropy test.

翻译：孟德尔随机化（MR）是一种利用全基因组关联研究（GWAS）汇总数据推断暴露与结局之间因果关系的工具变量（IV）方法。然而，作为大多数MR方法基础的多变量逆方差加权（IVW）方法，在存在大量弱IV时无法得到无偏的因果效应估计。本文证明，多变量IVW估计的偏倚是弱工具偏倚与估计误差偏倚的乘积，其中后者由测量误差偏倚和混杂偏倚线性组合而成，且因多个GWAS队列间的样本重叠而存在权衡。为解决此问题，我们提出一种新型多变量MR方法——基于偏倚校正估计方程的MR（MRBEE），该方法能在多弱IV条件下推断无偏因果关系。在适度条件下研究了多变量IVW和MRBEE的渐近行为，表明MRBEE在无偏性和渐近有效性方面均优于多变量IVW。我们将MRBEE应用于近视研究，证实了教育年限和驾车时间是近视的因果因素，并在后续的全基因组多效性检验中识别出一个新的近视位点。