A Modified Debiased Inverse-Variance Weighted Estimator in Two-Sample Summary-Data Mendelian Randomization

Mendelian randomization uses genetic variants as instrumental variables to estimate the causal effect of exposure on outcome from observational data. A common challenge in Mendelian randomization is that many genetic variants are only modestly or even weakly associated with the exposure of interest, a setting known as many weak instruments. Conventional methods, such as the popular inverse-variance weighted (IVW) estimator, could be heavily biased toward zero when the instrument strength is weak. To address this issue, the debiased IVW (dIVW) estimator and the penalized IVW (pIVW) estimator, which are shown to be robust to many weak instruments, were recently proposed. However, we find that the dIVW estimator tends to produce an exaggerated estimate of the causal effect, especially when the effective sample size is small. Although the pIVW estimator has better statistical properties, it is slightly more complex, and the idea behind this method is also a bit less intuitive. Therefore, we propose a modified debiased IVW (mdIVW) estimator that directly multiplies a shrinkage factor with the original dIVW estimator. After this simple modification, we prove that the mdIVW estimator not only has second-order bias with respect to the effective sample size, but also has smaller variance and mean squared error than the preceding two estimators. We then 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 competing ones through extensive simulation studies and real data analysis.