Palmer Tom M, Holmes Michael V, Keating Brendan J, Sheehan Nuala A
Am J Epidemiol. 2017 Nov 1;186(9):1104-1114. doi: 10.1093/aje/kwx175.
Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors.
孟德尔随机化研究使用基因型作为工具变量，以检验和估计可改变的风险因素对结局的因果效应。当研究人员愿意做出参数假设时，会使用两阶段残差纳入（TSRI）估计量。然而，研究人员目前报告的是这些估计值未经校正的或稳健的异方差标准误。我们在模拟和实际数据示例中比较了线性和逻辑TSRI估计的几种不同形式的标准误。其中，我们考虑了根据纽厄（1987年）、特尔扎（2016年）的方法修改的标准误以及自助法。在我们的模拟中，就覆盖率和I型错误而言，纽厄、特尔扎、自助法以及校正的两阶段最小二乘法（在线性情况下）标准误给出了最佳结果。在实际数据示例中，纽厄标准误分别比线性和逻辑TSRI估计量的未调整标准误大0.5%和2%。我们表明，具有修改后标准误的TSRI估计量在原假设下具有正确I型错误。研究人员应报告具有修改后标准误的TSRI估计值，而不是报告未调整的或稳健的异方差标准误。
