pIVW: A novel Mendelian Randomization Method Accounting for Weak Instruments and Horizontal Pleiotropy with Applications to the COVID-19 Outcomes

Xu, S.; Fung, W. K.; Liu, Z.

Mendelian randomization (MR) 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, many MR methods including the most popular inverse-variance weighted (IVW) estimator could be biased by the weak IVs that are weakly associated with the exposure. In this article, we develop a novel method called penalized inverse-variance weighted (pIVW) estimator, where we adjust the IVW estimator to account for the weak IVs by a proposed penalization method to prevent the denominator of the pIVW estimator from being close to zero. Moreover, we account for the horizontal pleiotropy|a widespread phenomenon in human genome that could bias the inference for the causal effect|by adjusting the variance estimation of the pIVW estimator. The proposed pIVW estimator can reduce to the debiased IVW (dIVW) estimator|another extension of the the IVW estimator|when the number of IVs and the IV strength increase. More generally, we prove that the pIVW estimator can achieve smaller bias and variance than the dIVW estimator under some regularity conditions. We also illustrate the improved performance of the proposed pIVW estimator over competing MR methods through a comprehensive simulation study. Further, we analyze the causal effects of the obesity-related traits and diseases on the Coronavirus disease 2019 (COVID-19). Notably, we find that hypertensive disease is associated with increased risk of hospitalized COVID-19, while 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. The R package for the pIVW method is publicly available at https://github.com/siqixu/mr.pivw.