Mendelian randomization uses genetic variants as instrumental variables to make causal inferences about the effects of modifiable risk factors on diseases from observational data. One of the major challenges in Mendelian randomization is that many genetic variants are only modestly or even weakly associated with the risk factor of interest, a setting known as many weak instruments. Many existing methods, such as the popular inverse-variance weighted (IVW) method, could be biased when the instrument strength is weak. To address this issue, the debiased IVW (dIVW) estimator, which is shown to be robust to many weak instruments, was recently proposed. However, this estimator still has non-ignorable bias when the effective sample size is small. In this paper, we propose a modified debiased IVW (mdIVW) estimator by multiplying a modification factor to the original dIVW estimator. After this simple correction, we show that the bias of the mdIVW estimator converges to zero at a faster rate than that of the dIVW estimator under some regularity conditions. Moreover, the mdIVW estimator has smaller variance than the dIVW estimator.We further extend the proposed method to account for the presence of instrumental variable selection and balanced horizontal pleiotropy. We demonstrate the improvement of the mdIVW estimator over the dIVW estimator through extensive simulation studies and real data analysis.

翻译：孟德尔随机化利用遗传变异作为工具变量，从观察性数据中推断可改变风险因素对疾病的因果效应。孟德尔随机化面临的主要挑战之一是，许多遗传变异仅与感兴趣的风险因素有中等甚至微弱关联，这种情形被称为“多弱工具变量”。许多现有方法，如常用的逆方差加权（IVW）方法，在工具变量强度较弱时可能存在偏倚。为解决此问题，近年提出了对多弱工具变量具有稳健性的去偏IVW（dIVW）估计量。然而，当有效样本量较小时，该估计量仍存在不可忽略的偏倚。本文通过将原始dIVW估计量乘以一个修正因子，提出一种修正的去偏IVW（mdIVW）估计量。我们证明，经过此简单修正后，在若干正则条件下，mdIVW估计量的偏倚收敛到零的速度快于dIVW估计量。此外，mdIVW估计量的方差也小于dIVW估计量。我们进一步扩展了所提方法，以考虑工具变量选择和平衡水平多效性的存在。通过广泛的模拟研究和实际数据分析，我们展示了mdIVW估计量相对于dIVW估计量的改进效果。