Mendelian randomization (MR) has become a popular approach to study causal effects by using genetic variants as instrumental variables. We propose a new MR method, GENIUS-MAWII, which simultaneously addresses the two salient phenomena that adversely affect MR analyses: many weak instruments and widespread horizontal pleiotropy. Similar to MR GENIUS (Tchetgen Tchetgen et al., 2021), we achieve identification of the treatment effect by leveraging heteroscedasticity of the exposure. We then derive the class of influence functions of the treatment effect, based on which, we construct a continuous updating estimator and establish its consistency and asymptotic normality under a many weak invalid instruments asymptotic regime by developing novel semiparametric theory. We also provide a measure of weak identification, an overidentification test, and a graphical diagnostic tool. We demonstrate in simulations that GENIUS-MAWII has clear advantages in the presence of directional or correlated horizontal pleiotropy compared to other methods. We apply our method to study the effect of body mass index on systolic blood pressure using UK Biobank.

翻译：孟德尔随机化（MR）已成为一种通过利用遗传变异作为工具变量来研究因果效应的流行方法。本文提出了一种新的MR方法——GENIUS-MAWII，该方法可同时应对影响MR分析的两个显著问题：众多弱工具变量与广泛存在的水平多效性。类似于MR GENIUS（Tchetgen Tchetgen等，2021），我们通过利用暴露变量的异方差性来识别治疗效应。进而，我们推导出治疗效应的影响函数类，并基于此构建连续更新估计量，同时通过发展新的半参数理论，在众多弱且无效的工具变量的渐近框架下，证明了该估计量的一致性和渐近正态性。此外，我们还提供了弱识别度量、过度识别检验及图形诊断工具。模拟研究表明，在存在方向性或相关性水平多效性的情况下，GENIUS-MAWII相较于其他方法具有显著优势。我们应用该方法，利用英国生物银行数据研究了体重指数对收缩压的因果效应。