The recently developed rerandomized inverse variance weighted (RIVW) estimator provides a simple and efficient framework to break the winner's curse in two-sample Mendelian randomization (MR). However, this method has ignored the possible presence of sample structure (e.g., residual population stratification and sample overlap), a common confounding factor in MR studies. Sample structure can not only distort SNP-exposure and SNP-outcome association estimates but also induce correlation between them, leading exposure-side instrument selection to propagate bias to the outcome side. To address this challenge, we propose the bivariate RIVW (BRIVW) estimator that can simultaneously account for the winner's curse and sample structure. The BRIVW estimator extends the RIVW framework by modeling the joint distribution of SNP-exposure and SNP-outcome associations, first adjusting their covariance matrix via linkage disequilibrium score regression to account for sample structure, and then applying randomized instrument selection and Rao-Blackwellization to obtain unbiased post-selection association estimates as well as their covariance matrix. Under appropriate conditions, we show that the BRIVW estimator is consistent and asymptotically normal. Extensive simulations and real data analyses demonstrate that the BRIVW estimator provides more accurate causal effect estimates than existing methods.

翻译：近期发展的重随机化逆方差加权（RIVW）估计量为克服两样本孟德尔随机化（MR）中的赢家诅咒提供了一个简洁高效的框架。然而，该方法忽略了MR研究中常见的混杂因素——样本结构（如残余群体分层和样本重叠）可能存在的干扰。样本结构不仅会扭曲SNP-暴露与SNP-结局的关联估计，还可能诱发二者之间的相关性，导致暴露侧工具变量选择将偏倚传递至结局侧。为应对这一挑战，我们提出了双变量重随机化逆方差加权（BRIVW）估计量，能够同时校正赢家诅咒与样本结构。BRIVW估计量通过建模SNP-暴露与SNP-结局关联的联合分布扩展了RIVW框架：首先通过连锁不平衡评分回归调整其协方差矩阵以校正样本结构，继而应用随机化工具变量选择与Rao-Blackwell化处理，获得无偏的后选择关联估计及其协方差矩阵。在适当条件下，我们证明BRIVW估计量具有一致性与渐近正态性。大量模拟实验与真实数据分析表明，相较于现有方法，BRIVW估计量能提供更准确的因果效应估计。