\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{zx} = \frac{{z_{zx}}}{{\sqrt {2p(1 - p)(n + z_{zx}^2)} }}$$\end{document}b^zx=zzx2p(1-p)(n+zzx2) with p being the allele frequency and n being the sample size). We then applied the clumping algorithm in PLINK28 to select near-independent GWS SNPs for each trait (r2 threshold = 0.05, window size = 1 Mb and P-value threshold = 5 × 10−8) using the 1000G-imputed ARIC data33 (n = 7,703 unrelated individuals) as the reference for LD estimation. As the statistical power of the GSMR analysis increases as the number of instruments, we performed the clumping analysis repeatedly for the SNPs in common between each pair of risk factor and disease data sets to maximize the number of instruments.
