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，基于观察数据对可改变风险因素对疾病的影响进行因果推断。孟德尔随机化面临的主要挑战之一是，许多遗传变异与感兴趣的风险因素仅存在中等甚至弱关联，这一设定被称为“多弱工具变量”。许多现有方法，例如流行的逆方差加权（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，近期提出了对多弱工具变量具有鲁棒性的去偏逆方差加权（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。本文通过在原dIVW估计量基础上乘以一个修正因子，提出了一种改进的去偏逆方差加权（mdIVW）估计量。我们证明，经过这一简单修正后，在某些正则条件下，mdIVW估计量的偏倚收敛于零的速度快于dIVW估计量。此外，mdIVW估计量的方差小于dIVW估计量。我们进一步将所提方法扩展至考虑工具变量选择和平衡水平多效性的情况。通过广泛的模拟研究和真实数据分析，我们展示了mdIVW估计量相较于dIVW估计量的改进效果。