In PRSice-2, to obtain the empirical P-value, the target trait values are permuted across the sample of individuals k times (default = 10,000) and the PRS analysis is repeated on each set of permuted phenotypes. Thus, on each permutation, the “best-fit PRS” is obtained as that most associated with the target trait across the range of P-value thresholds considered, and the empirical P-value is calculated as: (2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{equation*} \mathrm{empirical}\ P\ = \ \frac{{\mathop \sum \nolimits_{n\ = \ 1}^N I({P_n} < {P_o}) + 1}}{{N + 1}}, \end{equation*}\end{document}where N is the number of permutations performed; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$I\left(.\right)$\end{document}is an indicator function, which takes a value of 1 if the P-value of the best-fit PRS of permutation n is smaller than the observed P-value, Po, and 0 otherwise; and where pseudo-counts of 1 are added to the numerator and denominator to avoid empirical P-values of 0 and reflecting (conservatively) counting the observed trait configuration as 1 potential null permutation [22]. While the empirical P-values for association
