A novel penalized inverse‐variance weighted estimator for Mendelian randomization with applications to COVID‐19 outcomes

Mendelian randomization utilizes genetic variants as instrumental variables (IVs) to estimate the causal effect of an exposure variable on an outcome of interest even in the presence of unmeasured confounders. However, the popular inverse‐variance weighted (IVW) estimator could be biased in the presence of weak IVs, a common challenge in MR studies. In this article, we develop a novel penalized inverse‐variance weighted (pIVW) estimator, which adjusts the original IVW estimator to account for the weak IV issue by using a penalization approach to prevent the denominator of the pIVW estimator from being close to zero. Moreover, we adjust the variance estimation of the pIVW estimator to account for the presence of balanced horizontal pleiotropy. We show that the recently proposed debiased IVW (dIVW) estimator is a special case of our proposed pIVW estimator. We further prove that the pIVW estimator has smaller bias and variance than the dIVW estimator under some regularity conditions. We also conduct extensive simulation studies to demonstrate the performance of the proposed pIVW estimator. Furthermore, we apply the pIVW estimator to estimate the causal effects of five obesity‐related exposures on three coronavirus disease 2019 (COVID‐19) outcomes. Notably, we find that hypertensive disease is associated with an increased risk of hospitalized COVID‐19; and peripheral vascular disease and higher body mass index are associated with increased risks of COVID‐19 infection, hospitalized COVID‐19, and critically ill COVID‐19.