Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates

Methods have been developed for Mendelian randomization that can obtain consistent causal estimates under weaker assumptions than the standard instrumental variable assumptions. The median-based estimator and MR-Egger are examples of such methods. However, these methods can be sensitive to genetic variants with heterogeneous causal estimates. Such heterogeneity may arise from over-dispersion in the causal estimates, or specific variants with outlying causal estimates. In this paper, we develop three extensions to robust methods for Mendelian randomization with summarized data: 1) robust regression (MM-estimation); 2) penalized weights; and 3) Lasso penalization. Methods using these approaches are considered in two applied examples: one where there is evidence of over-dispersion in the causal estimates (the causal effect of body mass index on schizophrenia risk), and the other containing outliers (the causal effect of low-density lipoprotein cholesterol on Alzheimer’s disease risk). Through an extensive simulation study, we demonstrate that robust regression applied to the inverse-variance weighted method with penalized weights is a worthwhile additional sensitivity analysis for Mendelian randomization to provide robustness to variants with outlying causal estimates. The results from the applied examples and simulation study highlight the importance of using methods that make different assumptions to assess the robustness of findings from Mendelian randomization investigations with multiple genetic variants.已有研究开发出可在比标准工具变量假设更为宽松的假设条件下，获得稳健因果效应估计的孟德尔随机化（Mendelian randomization, MR）方法，基于中位数的估计量与MR-Egger便是这类方法的典型代表。然而此类方法对存在因果估计异质性的遗传变异较为敏感，该类异质性可能源于因果估计的过度离散，或是特定遗传变异存在异常的因果估计值。本文针对汇总数据孟德尔随机化的稳健分析方法，提出三类拓展方案：1）稳健回归（MM-estimation）；2）惩罚权重法；3）Lasso惩罚法。我们将上述三类方法应用于两个实际分析案例：其一存在因果估计过度离散的证据（体重指数对精神分裂症发病风险的因果效应），其二则存在异常值遗传变异（低密度脂蛋白胆固醇对阿尔茨海默病发病风险的因果效应）。通过大规模模拟研究，我们证实：将稳健回归与惩罚权重结合应用于逆方差加权法，是孟德尔随机化中一项极具价值的补充敏感性分析手段，可使方法对存在异常因果估计值的遗传变异具备更强稳健性。本次实际案例与模拟研究的结果均表明：针对包含多个遗传变异的孟德尔随机化分析，采用不同假设前提的方法评估研究结果的稳健性，具有重要意义。