Wang Kai, Alberding Steven Y
Department of Biostatistics, University of Iowa, Iowa City, Iowa, USA.
Stat Med. 2024 Dec 30;43(30):5791-5802. doi: 10.1002/sim.10279. Epub 2024 Nov 18.
The success of a Mendelian randomization (MR) study critically depends on the validity of the assumptions underlying MR. We focus on detecting heterogeneity (also known as horizontal pleiotropy) in two-sample summary-data MR. A popular approach is to apply Cochran's statistic method, developed for meta-analysis. However, Cochran's statistic, including its modifications, is known to lack power when its degrees of freedom are large. Furthermore, there is no theoretical justification for the claimed null distribution of the minimum of the modified Cochran's statistic with exact weighting ( ), although it seems to perform well in simulation studies.
The principle of our proposed method is straightforward: if a set of variables are valid instruments, then any linear combination of these variables is still a valid instrument. Specifically, this principle holds when these linear combinations are formed using eigenvectors derived from a variance matrix. Each linear combination follows a known normal distribution from which a value can be calculated. We use the minimum value for these eigenvector-based linear combinations as the test statistic. Additionally, we explore a modification of the modified Cochran's statistic by replacing the weighting matrix with a truncated singular value decomposition.
Extensive simulation studies reveal that the proposed methods outperform Cochran's statistic, including those with modified weights, and MR-PRESSO, another popular method for detecting heterogeneity, in cases where the number of instruments is not large or the Wald ratios take two values. We also demonstrate these methods using empirical examples. Furthermore, we show that does not follow, but is dominated by, the claimed null chi-square distribution. The proposed methods are implemented in an R package iGasso.
Dimension reduction techniques are useful for generating powerful tests of heterogeneity in MR.
孟德尔随机化（MR）研究的成功关键取决于MR所依据假设的有效性。我们专注于在两样本汇总数据MR中检测异质性（也称为水平多效性）。一种常用方法是应用为荟萃分析开发的Cochran's Q统计方法。然而，已知Cochran's Q统计量（包括其修正形式）在自由度较大时缺乏检验效能。此外，对于具有精确加权的修正Cochran's Q统计量最小值所宣称的零分布，虽然在模拟研究中似乎表现良好，但却没有理论依据。
我们提出的方法原理很简单：如果一组变量是有效的工具变量，那么这些变量的任何线性组合仍然是有效的工具变量。具体而言，当使用从方差矩阵导出的特征向量形成这些线性组合时，该原理成立。每个线性组合都遵循已知的正态分布，从中可以计算出一个P值。我们将这些基于特征向量的线性组合的最小P值用作检验统计量。此外，我们通过用截断奇异值分解替换加权矩阵来探索对修正Cochran's Q统计量的一种修改。
广泛的模拟研究表明，在工具变量数量不大或Wald比取两个值的情况下，所提出的方法优于Cochran's Q统计量（包括那些具有修正权重的统计量）以及另一种检测异质性的常用方法MR - PRESSO。我们还通过实证例子展示了这些方法。此外，我们表明P值并不遵循所宣称的零卡方分布，而是受其支配。所提出的方法在R包iGasso中实现。
降维技术对于在MR中生成强大的异质性检验很有用。
