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Statistical Analysis for Scrnaseq Data

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Statistical Analysis for Scrnaseq Data Statistical analysis for scRNAseq data Cathy Maugis-Rabusseau [email protected] C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 1 / 52 Plan 1 Introduction 2 Feature selection / extraction 3 Dimension reduction 4 Single cell clustering 5 Pseudotime analysis 6 Differential analysis C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 2 / 52 scRNA-seq data n cells, G genes: n ≤ G or n ≈ G =) high dimensionality Measures: xij = expression of the gene j for the cell i 2 N Technical and biological noise High variability Zero-inflated data =) "sparsity" (≥ 80% of zeros per raw, dropouts) C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 3 / 52 Biological questions Are there distinct subpopulations of cells? For each cell type, what are the marker genes? How visualize the cells? Are there continuums of differentiation / activation cell states? ... Rostom et al, FEBS 2017 C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 4 / 52 Statistical analysis Clustering of cells Variable (gene) selection in learning or differential analysis (hypothesis testing) Reduction dimension Network inference ... Rostom et al, FEBS 2017 C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 5 / 52 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) https://bioconductor.org/packages/release/bioc/html/sincell.html C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 6 / 52 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) [Poirion et al., 2016] C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 6 / 52 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) [Poirion et al., 2016] [Wolf et al., 2018] SCANPY https://github.com/theislab/Scanpy C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 6 / 52 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) [Poirion et al., 2016] [Wolf et al., 2018] SCANPY [Guo et al., 2015] SINCERA:A Single-Cell RNA-Seq Analytic Pipeline https://github.com/xu-lab/SINCERA https://research.cchmc.org/pbge/sincera.html Fig 1. Schematic Workflow. The analytic pipeline consists of three main components: pre-processing, cell type identification, and cell type specific gene signature and driving force identification. doi:10.1371/journal.pcbi.1004575.g001 addressing rare cell types that are not forming clusters with other cells by adjusting ds y 1 i ð Þ¼ in a separate study. The cell specificity filter is defined by a cell specificity index s, which is modified from the C.Maugis-Rabusseau (IMT/INSA) ti Statistical analysis for scRNAseq data 6 / 52 calculation of tissue specificity index in [42]. Es min Es x s ij À ð i Þ ij ¼ max Es min Es ð i ÞÀ ð i Þ Ns 1 1 x s ð Þ j 1 ij ts ¼ ð À Þ i ¼ X qs 1 À s fi s ti denotes the cell speci city of gene i in sample s, Eij is the expression of gene i in cell j in s, PLOS Computational Biology | DOI:10.1371/journal.pcbi.1004575 November 24, 2015 4 / 28 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) [Poirion et al., 2016] [Wolf et al., 2018] SCANPY [Guo et al., 2015] SINCERA: [Lun et al., 2016] Workflow Package : simpleSingleCell https://bioconductor.org/packages/release/workflows/html/simpleSingleCell.html C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 6 / 52 Some bio-info-stat. pipelines/workflows [Juliá et al., 2015] Sincell (Bioconductor/R package) [Poirion et al., 2016] [Wolf et al., 2018] SCANPY [Guo et al., 2015] SINCERA: [Lun et al., 2016] Workflow Package : simpleSingleCell [Satija et al., 2015] SEURAT: https://satijalab.org/seurat/ ... C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 6 / 52 Plan 1 Introduction 2 Feature selection / extraction 3 Dimension reduction 4 Single cell clustering 5 Pseudotime analysis 6 Differential analysis C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 7 / 52 Feature (gene) extraction Simple filtering criteria : see e.g [Lun et al., 2016],[Soneson and Robinson, 2018] Filtering of lowly expressed genes: genes expressed in <τ % of cells genes with a mean average of expression <τ Dropout-based feature selection M3Drop, [Andrews and Hemberg, 2018] Based on the Michaelis-Menten function S Pdropout = 1 − KM + S where S = mean expression Pdropout = dropout rate MLE to obtain the global KM across all genes C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 8 / 52 Highly Variable Genes (HVG) [Brennecke et al., 2013] Fits a quadratic model (gamma generalized linear model) to the relationship between mean expression and the coefficient of variation squared (CV2) χ2 test is used to find genes signif. above the curve Implemented in M3Drop package C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 9 / 52 Highly Variable Genes (HVG) [Brennecke et al., 2013] [Kim et al., 2015] Uses spike-ins to estimate parameters related to technical variance and estimates gene-specific biological variability by substracting the estimated technical variance from the total variance. C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 9 / 52 Highly Variable Genes (HVG) [Brennecke et al., 2013] [Kim et al., 2015] [Vallejos et al., 2015] BASiCS = Bayesian Analysis of Single-Cell Sequencing Data Models spike-ins and endogenous genes simultaneously as two Poisson-Gamma hierarchical models C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 9 / 52 Highly correlated genes Gene-gene correlation: Calculate the gene-gene correlation matrix ρ = (ρij )i;j=1;:::;G Evaluate the correlation magnitude for each gene : ρ~i = maxjρij j j Take the top few thousand genes having the highest correlation magnitude PCA loadings: Select the genes with high PCA loadings ... Non adapted for batch effects C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 10 / 52 Plan 1 Introduction 2 Feature selection / extraction 3 Dimension reduction 4 Single cell clustering 5 Pseudotime analysis 6 Differential analysis C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 11 / 52 Objectives Minimize curse of dimensionality Allow visualization Reduce computational time .... But attention to the interpretations after! C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 12 / 52 Principal component analysis (PCA) C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 13 / 52 Principal component analysis (PCA) Diagonalization of the covariance (or correlation) matrix Linear transformations: meta-variables = linear combinations of the genes Capture the dimensions with higher variance Fast deterministic procedure Sparse-PCA : PCA + gene selection C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 13 / 52 Extensions of PCA for scRNAseq data [Pierson and Yau, 2015] : ZIFA (Zero Inflated Factor Analysis) Deals with the large number of zero-values in scRNASeq data Relationship between the dropout rate p0 and the mean level of non-zero expression (log read count) µ: 2 p0 = exp(−λµ ) ZIFA adopts a latent variable model and uses an EM algorithm for the parameter estimation Python software : https://github.com/epierson9/ZIFA [Risso et al., 2017] : ZINB-WaVE = Zero-Inflated Negative Binomial Model for RNA-Seq Data a method similar to PCA based on a zero- inflated negative binomial model instead of a Gaussian model https://bioconductor.org/packages/release/bioc/html/zinbwave.html C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 14 / 52 Extensions of PCA [Lin et al., 2017] CIDR (https://github.com/VCCRI/CIDR) 1 Preliminary, log(xij + 1) 2 Identification of dropout candidates. (CIDR finds a sample-dependent threshold that separates the zero peak from the rest of the expression distribution for each cell) 3 Estimation of the relationship between dropout rate and gene expression levels (non-linear least-squares regression to fit a decreasing logistic function to the data) 4 Calculation of dissimilarity between the imputed gene expression profiles for every pairs of single cells 5 PCoA using the CIDR dissimilarity matrix 6 Clustering (CAH) using the first few principal coordinates C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 15 / 52 Example of t-SNE plot C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 16 / 52 t-SNE Reduce a dataset to 2 dimensions Non-linear dimension reduction technique Want to preserve the neighborhood "Don’t interpret distances in t-SNE plots" https://constantamateur.github.io/2018-01-02-tSNE/ C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 17 / 52 t-SNE Reduce a dataset to 2 dimensions Non-linear dimension reduction technique Want to preserve the neighborhood "Don’t interpret distances in t-SNE plots" G INPUT : X = (x1;:::; xn) with xi 2 R (High dimensional data) 2 OUTPUT: Y = (y1;:::; yn) with yi 2 R ( Low dimensional data) C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 17 / 52 Stochastic Neighbor Embedding (SNE) Converting the high-dimensional Euclidian distances into conditional probabilities (=similarities) Similarity of points in high-dimension exp(−kx − x k2=2σ2) p = i j i Gaussian distrib. jji P 2 2 k6=i exp(−kxi − xk k =2σi ) Similarity of points in low dimension exp(−ky − y k2) = i j qjji P 2 Gaussian distrib. k6=i exp(−kyi − yk k ) Cost function: Kullback-Leibler divergence X X X pjji C(Y) = KL(P jQ ) = p ln i i jji q i i j jji Minimize the cost function using gradient descent C.Maugis-Rabusseau (IMT/INSA) Statistical analysis for scRNAseq data 18 / 52 Symmetric SNE Pairwise similarities: exp(−kx − x k2=2σ2) = i j pij P 2 2 Gaussian distrib. k6=l exp(−kxk − xl k =2σ ) exp(−ky − y k2) = i j qij P 2 Gaussian distrib.
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