\usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p}_{a}^{{\rm{NULL}}}$$\end{document}paNULL and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p}_{a}^{{\rm{ALT}}}$$\end{document}paALT are the probabilities of locus a carrying zero or at least one causal variant, respectively. The term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${q}_{{jl}}$$\end{document}qjl is the probability that the model with l axes of genetic variation best fit the data. We selected the model with the largest posterior probability for each variant as the best-fitting model to capture the genetic effect heterogeneity. Variants in which the zero component model was selected (that is, all models with at least one component were rejected) were considered to have homogeneous effects across ancestry. Among the remaining variants, we considered which one of the meta-regression models (that is, 1–4 components) best described the extent of effect heterogeneities based on the posterior probabilities for each model. In addition, we required that strongly heterogeneous variants had an MDS component effect that was significantly different from zero and were polymorphic in two or more ancestry-stratified cohorts to ease interpretation of heterogeneous effects. For example, a variant in which the model with two components best fit the data was considered at least weakly heterogeneous. If this variant
