With the fitted model, we inverse estimated the required log total sample size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{ss}$$\end{document}xss with fixed TPR \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${y}_{tpr}$$\end{document}ytpr, log-fold change \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{fc}$$\end{document}xfc, and log absolute cell count change \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{cc}$$\end{document}xcc as:15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{ss}=\frac{-(\alpha +{\beta }_{fc}{x}_{fc}+{\beta }_{fc,cc}{x}_{fc}{x}_{cc}-{y}_{tpr})}{({\beta }_{ss}+{\beta }_{ss,cc}{x}_{cc})}$$\end{document}xss=−(α+βfcxfc+βfc,ccxfcxcc−ytpr)(βss+βss,ccxcc)With this formula, we estimated the sample size for a fixed power of 0.8 across changing log-fold changes between [0.01, 5] and the fraction of cell-type sizes to total cell counts between [0.01, 0.2] for the same fixed FDR levels.
