The Egger intercept (EI) test is a widely used tool to detect horizontal pleiotropy in two-sample summary-data Mendelian randomization. A significant EI test suggests that either the average pleiotropic effect differs from zero (i.e., directional pleiotropy) or the InSIDE (Instrument Strength Independent of Direct Effect) assumption is violated (i.e., correlated pleiotropy) or both. As such, the EI test provides an assessment of the validity of the instrumental variable assumptions, with a non-zero EI indicating that the commonly used inverse-variance weighted (IVW) estimator will be biased. However, the EI test may exhibit inaccurate type one error rates due to biased estimation in Egger regression caused by the measurement error and winner's curse. In this article, we propose a modified EI (MEI) test based on a bias-corrected EI estimator under the null hypothesis of no directional or correlated pleiotropy, leveraging the recently developed rerandomized IVW estimator. We then prove the asymptotic properties of the MEI test under realistic conditions. Like the EI test, we find that the power of the MEI test is also affected by the orientation of SNPs. To enhance the robustness of power, we further combine the MEI test statistics obtained under two specific allele coding schemes. Both simulation and real data studies show that the combined test outperforms the EI test in terms of type one error control and power.

翻译：Egger截距检验是两样本汇总数据孟德尔随机化中广泛用于检测水平多效性的工具。若Egger截距检验显著，则表明平均多效性效应不为零（即方向性多效性）、InSIDE假设不成立（即相关多效性），或两者兼有。因此，Egger截距检验可评估工具变量假设的有效性——非零的Egger截距意味着常用的逆方差加权估计量将存在偏倚。然而，由于测量误差和赢家诅咒导致的Egger回归偏倚估计，该检验可能呈现不精确的第一类错误率。本文基于零假设（无方向性或多效性相关）下的偏倚校正Egger截距估计量，利用近期发展的重随机化逆方差加权估计量，提出改良Egger截距检验。随后我们在现实条件下证明该检验的渐近性质。与标准Egger截距检验类似，我们发现改良检验的统计功效同样受SNP方向性影响。为增强功效稳健性，我们进一步整合两种特定等位基因编码方案下的改良检验统计量。模拟研究与真实数据分析均表明，联合检验在第一类错误控制与统计功效两方面均优于标准Egger截距检验。