DESeq2 offers tests for composite null hypotheses of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal {H}_{0}: |\beta _{\textit {ir}}| \le \theta $ \end{document}ℋ0:|βir|≤θ to find genes whose LFC significantly exceeds a threshold θ>0. The composite null hypothesis is replaced by two simple null hypotheses: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal {H}_{0a}: \beta _{\textit {ir}} = \theta $ \end{document}ℋ0a:βir=θ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal {H}_{0b}: \beta _{\textit {ir}} = -\theta $ \end{document}ℋ0b:βir=−θ. Two-tailed P values are generated by integrating a normal distribution centered on θ with standard deviation SE(βir) from |βir| toward ∞. The value of the integral is then multiplied by 2 and thresholded at 1. This procedure controls type-I error even when βir=±θ, and is equivalent to the standard DESeq2P value when θ=0.
