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Chunk #8 — Methods

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Guidelines for Evaluating the Comparability of Down-Sampled GWAS Summary Statistics.
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The following five key indicators are useful for evaluating the loss of genetic signal in down-sampled univariate GWASs: (1) effective sample size (EffN), (2) heritability, (3) mean χ2, (4) genomic inflation factor, and (5) the LD Score regression attenuation/stratification bias ratio (see formula in Table 1). EffN is a transformation relevant for GWAS on binary traits that transforms an unbalanced number of cases and controls to effectively reflect the sample size of a balanced analysis (i.e., 50% cases). For a meta-analysis of k cohort-level univariate summary statistics, it is the sum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${EffN}_{k}=4\times {V}_{k}(1-$$\end{document}EffNk=4×Vk(1- \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{k}){N}_{k}$$\end{document}Vk)Nk, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{k}$$\end{document}Vk is the cohort-specific proportion of cases, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{k}$$\end{document}Nk is the total number of cases and controls. For GWAS on continuous traits, EffN can be replaced by the total sample size (N). The remaining four key indicators are standard estimates of LD Score regression (version 1.0.1; Bulik-Sullivan et