Chunk #118 — Materials and methods — Cook’s distance for outlier detection

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Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2.

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Pearson residuals Rij are calculated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ R_{ij} = \frac{(K_{ij} - \mu_{ij})}{\sqrt{V(\mu_{ij})}}, $$ \end{document}Rij=(Kij−μij)V(μij), where μij is estimated by the negative binomial GLM without the LFC prior, and using the variance function V(μ)=μ+αμ2. A method-of-moments estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\alpha _{i}^{\text {rob}}$ \end{document}αirob, using a robust estimator of variance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $s_{i,\text {rob}}^{2}$ \end{document}si,rob2 to provide robustness against outliers, is used here: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\alpha_{i}^{\text{rob}} = \operatorname{max} \left(\frac{s_{i,\text{rob}}^{2} - \bar\mu_{i}}{{\bar\mu_{i}^{2}}}, 0 \right). $$ \end{document}αirob=maxsi,rob2−μ¯iμ¯i2,0.