Analyses biostatistiques de données RNA-seq

Transcription

1 Analyses biostatistiques de données RNA-seq Ignacio Gonzàlez, Annick Moisan & Nathalie Villa-Vialaneix Toulouse, 18/19 mai 2017 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

2 Outline 1 Exploratory analysis Introduction Experimental design Data exploration and quality assessment 2 Normalization Raw data filtering Interpreting read counts 3 Differential Expression analysis Hypothesis testing and correction for multiple tests Differential expression analysis for RNAseq data Interpreting and improving the analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

3 Outline 1 Exploratory analysis Introduction Experimental design Data exploration and quality assessment 2 Normalization Raw data filtering Interpreting read counts 3 Differential Expression analysis Hypothesis testing and correction for multiple tests Differential expression analysis for RNAseq data Interpreting and improving the analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

4 A typical transcriptomic experiment IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

5 A typical transcriptomic experiment IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

6 A typical RNA-seq experiment 1 collect samples 2 generate libraries of cdna fragments 3 affect material to one lane in one flow cell IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

7 Steps in RNAseq data analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

8 Part I: Experimental design IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

9 Confounded effects: a simple example Basic experiment: find differences between control/treated plants control group plant treated group plant IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

10 Confounded effects: a simple example Basic experiment: find differences between control/treated plants control group plant treated group plant A bad experimental design: grow all control group plants in one field and grow all treated group plants in another field Field 1 Field 2 because you can not differentiate between differences due to the field and differences due to the treatment confounded effects IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

11 Confounded effects: a simple example Basic experiment: find differences between control/treated plants control group plant treated group plant A good experimental design: grow half control group plants (chosen at random) and half treated group plants in one field (and the rest in the other field) Field 1 Field 2 differences due to the field and differences due to the treatment can be estimated separately IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

12 Confounded effects: a simple example Basic experiment: find differences between control/treated plants control group plant treated group plant In summary, what is a good experimental design? Experimental design are usually not as simple as this example: they can include multiple experimental factors (day of experiment, flow cell,... ) and multiple covariates (sex, parents,... ). The experimental design must be carefully thought before starting the experiment and confounded effects must be searched for in a systematic manner. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

13 Effect & Variation 2 conditions, 2 genes whose expression distribution is: first gene: different median levels between the two groups but large variance: differences may be non significant second gene: different median levels between the two groups but very small variance: differences may be significant IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

14 Source of variation in RNA-seq experiments 1 at the top layer: biological variations (i.e., individual differences due to e.g., environmental or genetic factors) 2 at the middle layer: technical variations (library preparation effect) 3 at the bottom layer: technical variations (lane and cell flow effects) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

15 Source of variation in RNA-seq experiments 1 at the top layer: biological variations (i.e., individual differences due to e.g., environmental or genetic factors) 2 at the middle layer: technical variations (library preparation effect) 3 at the bottom layer: technical variations (lane and cell flow effects) lane effect < cell flow effect < library preparation effect biological effect IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

16 Advised policy for biological/technical replicates biological replicates: different biological samples, processed separately (advised: 3 per condition) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

17 Advised policy for biological/technical replicates biological replicates: different biological samples, processed separately (advised: 3 per condition) technical replicates: same biological material but independent replications of the technical steps (from library preparation; advised: 2 per biological replicate) but 6 biological replicates are better than 3 biological replicates 2 technical replicates! See [Liu et al., 2014] for further discussions. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

18 In summary: a simple two-condition experimental design for RNA-seq Typical RNA-seq design: independent samples are sequenced into different lanes (lane effect cannot be estimated but within sample comparison is preserved) RNA extraction Library preparation Lane 1 Lane 2 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

19 In summary: a simple two-condition experimental design for RNA-seq Typical RNA-seq design: independent samples are sequenced into different lanes (lane effect cannot be estimated but within sample comparison is preserved) RNA extraction Library preparation Lane 1 Lane 2 Example with 2 biological replicates per condition and 4 technical replicates per biological replicate: Flow cell 1 Flow cell 2 Flow cell 3 Flow cell C 11 C 21 T 11 T 21 C 12 C 22 T 12 T 22 C 13 C 23 T 13 T 23 C 14 C 24 T 14 T 24 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

20 In summary: a simple two-condition experimental design for RNA-seq Multiplex RNA-seq design: DNA fragments are barcoded so that multiple samples can be included in the same lane Barcode adapters RNA extraction Library preparation and barcoding Pooling Lane 1 Lane 2 Barcoded adapters IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

21 In summary: a simple two-condition experimental design for RNA-seq Multiplex RNA-seq design: DNA fragments are barcoded so that multiple samples can be included in the same lane Barcode adapters RNA extraction Library preparation and barcoding Pooling Lane 1 Lane 2 Barcoded adapters Example with 2 biological replicates per condition and 4 technical replicates per biological replicate, splitted on 4 flow cells: Flow cell 1 Flow cell 2 Flow cell 3 Flow cell C 111 C 121 C 131 C 141 C 112 C 122 C 132 C 142 C 113 C 123 C 133 C 143 C 114 C 124 C 134 C 144 C 211 C 221 C 231 C 241 C 212 C 222 C 232 C 242 C 213 C 223 C 233 C 243 C 214 C 224 C 234 C 244 T 111 T 121 T 131 T 141 T 112 T 122 T 132 T 142 T 113 T 123 T 133 T 143 T 114 T 124 T 134 T 144 T 211 T 221 T 231 T 241 T 212 T 222 T 232 T 242 T 213 T 223 T 233 T 243 T 214 T 224 T 234 T 244 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

22 Part II: Exploratory analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

23 Some features of RNAseq data What must be taken into account? discrete, non-negative data (total number of aligned reads) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

24 Some features of RNAseq data What must be taken into account? discrete, non-negative data (total number of aligned reads) skewed data IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

25 Some features of RNAseq data What must be taken into account? discrete, non-negative data (total number of aligned reads) skewed data overdispersion (variance mean) black line is variance = mean IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

26 Dataset used in the examples Dataset pasilla The dataset pasilla comes from the R package pasilla available on Bioconductor It can be installed using source(" bioconductor. org/ bioclite.r") bioclite(" pasilla") directly use the function data in R (the library DESeq is required to extract the count data): library( pasilla); library( DESeq) data(" pasillagenes") head( counts( pasillagenes)) or import the text file included in the package which contains the counts datafile=system.file("extdata/pasilla_gene_counts.tsv", package =" pasilla") rawcounttable =read. table( dfile, header =TRUE, row. names =1) head( rawcount) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

27 Dataset used in the examples Description of the data: experiment on Drosophila melanogaster [Brooks et al., 2010] count data obtained from FASTQ files produced by second generation sequencing techniques (Illumina) details on the way the count table was obtained are given in the package s vignette IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

28 Dataset used in the examples Description of the data: experiment on Drosophila melanogaster [Brooks et al., 2010] count data obtained from FASTQ files produced by second generation sequencing techniques (Illumina) details on the way the count table was obtained are given in the package s vignette Before any further processing, the data must be explored by visualization methods and statistical methods that provide simplified summary of the data. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

29 Count distribution The count distribution (i.e., the number of times a given count is obtained in the data) can be visualized with histograms count control1 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

30 Count distribution The count distribution (i.e., the number of times a given count is obtained in the data) can be visualized with histograms count 5000 log 2(count + 1) control control1 This distribution is highly skewed and it is better visualized using a log 2 transformation before it is displayed. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

31 Count distribution The count distribution (i.e., the number of times a given count is obtained in the data) can be visualized with histograms count 5000 log 2(count + 1) control control1 This distribution is highly skewed and it is better visualized using a log 2 transformation before it is displayed. library size The library size is the sum of all counts in a given sample. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

32 Count distribution within samples The count distributions within each sample can be compared using parallel boxplots (on the log 2 transformed data): 15 log 2 (count + 1) 10 5 Condition control treated 0 control1 control2 control3 control4 treated1 treated2 treated3 It is expected that, within a given condition (i.e., control or treated ), the count distributions between the different samples are similar. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

33 Check reproducibility between samples MA plots can be used to visualize reproducibility between samples of an experiment (and thus check if normalization is needed). They plot the log-fold change (M-values) against the log-average (A-values): A-values: average log counts between two samples: M-values: log of ratio between counts between two samples: Mg = log2 (Kgj ) log2 (Kgj 0 ) Ag = log2 (Kgj ) + log2 (Kgj 0 ) 2 where Kgj stands for the counts for gene g in sample j. IG, AM, NV2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

34 Check reproducibility between samples MA plots can be used to visualize reproducibility between samples of an experiment (and thus check if normalization is needed). They plot the log-fold change (M-values) against the log-average (A-values): control1 vs control2 control1 vs control3 control1 vs control4 control2 vs control3 control2 vs control4 control3 vs control M A IG, AM, NV2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

35 Check similarity between samples Similarities between samples can be visualized with a AHC and a heatmap: perform ascending hierarchical classification (AHC) using Euclidean distance between samples: δ(j, j ) = ( g log2 (K gj ) log 2 (K gj ) ) 2 visualize the strength of the similarity with heatmap. Color key control3 : paired end control4 : paired end treated2 : paired end treated3 : paired end control1 : single end control2 : single end treated1 : single end : single end : single end : single end : paired end : paired end IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64 : paired end : paired end

36 Search for the main structures in the data: PCA PCA (on log 2 counts) can be used to project data into a small dimensional space and search for unexpected experimental effects in the data. In DESeq, the function plotpca performs PCA on the top genes with the highest variance. control : paired end control : single end treated : paired end treated : single end 10 PC PC1 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

37 Search for the main structures in the data: MDS MDS (on log 2 counts) can also be used to project data into a small dimensional space. Unlike PCA (which aims at providing the projection with the largest variance), its aim is to preserve the distances during the projection. In edger, the function plotmds performs MDS on the top genes with the highest variance. reated : paired end treated : paired end treated : single e Dimension trol : paired end control : paired end control : single end control : single end when using the Euclidean distance between counts for MDS, it is equivalent to PCA Dimension 1 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

38 Outline 1 Exploratory analysis Introduction Experimental design Data exploration and quality assessment 2 Normalization Raw data filtering Interpreting read counts 3 Differential Expression analysis Hypothesis testing and correction for multiple tests Differential expression analysis for RNAseq data Interpreting and improving the analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

39 Raw data filtering Filtering consists in removing genes with low expression. Different strategies can be used: [Sultan et al., 2008]: filter out genes with a total read count smaller than a given threshold; [Bottomly et al., 2011]: filter out genes with zero count in an experimental condition; [Robinson and Oshlack, 2010]: filter out genes such that the number of samples with a CPM value (for this gene) smaller than a given threshold is larger than the smallest number of samples in a condition. With CPM: Count Per Million (i.e., raw count divived by library size, this strategy takes into account differences in library sizes). IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

40 Raw data filtering Filtering consists in removing genes with low expression. Different strategies can be used: [Sultan et al., 2008]: filter out genes with a total read count smaller than a given threshold; [Bottomly et al., 2011]: filter out genes with zero count in an experimental condition; [Robinson and Oshlack, 2010]: filter out genes such that the number of samples with a CPM value (for this gene) smaller than a given threshold is larger than the smallest number of samples in a condition. With CPM: Count Per Million (i.e., raw count divived by library size, this strategy takes into account differences in library sizes). More sophisticated filtering To account for the fact that lowly expressed genes are almost never found differentially expressed, a more sophisticated filtering can be performed. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

41 Part III: Normalization IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

42 Purpose of normalization identify and correct technical biases (due to sequencing process) to make counts comparable types of normalization: within sample normalization and between sample normalization IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

43 Within sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts for gene B are twice larger than counts for gene A because: IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

44 Within sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts for gene B are twice larger than counts for gene A because: gene B is expressed with a number of transcripts twice larger than gene A gene A gene B IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

45 Within sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts for gene B are twice larger than counts for gene A because: both genes are expressed with the same number of transcripts but gene B is twice longer than gene A gene A gene B IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

46 Within sample normalization Purpose of within sample comparison: enabling comparisons of genes from a same sample Sources of variability: gene length, sequence composition (GC content) These differences need not to be corrected for a differential analysis and are not really relevant for data interpretation. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

47 Between sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts in sample 3 are much larger than counts in sample 2 because: IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

48 Between sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts in sample 3 are much larger than counts in sample 2 because: gene A is more expressed in sample 3 than in sample 2 gene A in sample 2 gene A in sample 3 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

49 Between sample normalization Example: (read counts) sample 1 sample 2 sample 3 gene A gene B counts in sample 3 are much larger than counts in sample 2 because: gene A is expressed similarly in the two samples but sequencing depth is larger in sample 3 than in sample 2 (i.e., differences in library sizes) gene A in sample 2 gene A in sample 3 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

50 Between sample normalization Purpose of between sample comparison: enabling comparisons of a gene in different samples Sources of variability: library size,... These differences must be corrected for a differential analysis and for data interpretation. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

51 Principles for sequencing depth normalization Basics 1 choose an appropriate baseline for each sample 2 for a given gene, compare counts relative to the baseline rather than raw counts IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

52 Principles for sequencing depth normalization Basics 1 choose an appropriate baseline for each sample 2 for a given gene, compare counts relative to the baseline rather than raw counts In practice: Raw counts correspond to different sequencing depths control treated Gene Gene Gene : : : : : : : : : Gene G IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

53 Principles for sequencing depth normalization Basics 1 choose an appropriate baseline for each sample 2 for a given gene, compare counts relative to the baseline rather than raw counts In practice: A correction multiplicative factor is calculated for every sample control treated Gene Gene Gene : : : : : : : : : Gene G C j IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

54 Principles for sequencing depth normalization Basics 1 choose an appropriate baseline for each sample 2 for a given gene, compare counts relative to the baseline rather than raw counts In practice: Every counts is multiplied by the correction factor corresponding to its sample Gene C j Gene x IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

55 Principles for sequencing depth normalization Basics 1 choose an appropriate baseline for each sample 2 for a given gene, compare counts relative to the baseline rather than raw counts Consequences: Library sizes for normalized counts are roughly equal. control treated Gene Gene Gene : : : : : : : : : Gene G Lib. size x 10 5 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

56 Principles for sequencing depth normalization Definition If K gj is the raw count for gene g in sample j then, the normalized counts is defined as: K gj = K gj s j in which s j = C 1 j is the scaling factor for sample j. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

57 Principles for sequencing depth normalization Definition If K gj is the raw count for gene g in sample j then, the normalized counts is defined as: K gj = K gj s j in which s j = C 1 j is the scaling factor for sample j. Three types of methods: distribution adjustment method taking length into account the effective library size concept IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

58 Distribution adjustment Total read count adjustment [Mortazavi et al., 2008] s j = 1 N N l=1 D l in which N is the number of samples and D j = g K gj. D j raw counts normalized counts log 2(count + 1) Samples Sample 1 Sample 2 edger: cpm(..., normalized. lib. sizes=true) rank(mean) gene expression IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

59 Distribution adjustment Total read count adjustment [Mortazavi et al., 2008] (Upper) Quartile normalization [Bullard et al., 2010] s j = Q (p) j 1 N l=1 Q(p) l in which Q (p) is a given quantile (generally 3rd quartile) of the count j distribution in sample j. raw counts normalized counts raw counts normalized counts log 2(count + 1) 10 Samples Sample 1 Sample 2 log 2(count + 1) 10 Samples Sample 1 Sample rank(mean) gene expression rank(mean) gene expression edger: calcnormfactors(..., method = " upperquartile", p = 0.75) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

60 Method using gene lengths (intra & inter sample normalization) RPKM: Reads Per Kilobase per Million mapped Reads Assumptions: read counts are proportional to expression level, transcript length and sequencing depth s j = D jl g in which L g is gene length (bp). edger: rpkm(..., gene.length =...) Unbiaised estimation of number of reads but affect variability [Oshlack and Wakefield, 2009]. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

61 Relative Log Expression (RLE) [Anders and Huber, 2010], edger - DESeq - DESeq2 Method: 1 compute a pseudo-reference sample: geometric mean across samples N R g = K gj (geometric mean is less sensitive to extreme values than standard mean) j=1 1/N 15 log 2(count + 1) 10 5 Samples Sample 1 Sample rank(mean) gene expression IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

62 Relative Log Expression (RLE) [Anders and Huber, 2010], edger - DESeq - DESeq2 Method: 1 compute a pseudo-reference sample 2 center samples compared to the reference K gj = K gj R g with R g = N K gj j=1 1/N 4 count / geo. mean 3 2 Samples Sample 1 Sample rank(mean) gene expression IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

63 Relative Log Expression (RLE) [Anders and Huber, 2010], edger - DESeq - DESeq2 Method: 1 compute a pseudo-reference sample 2 center samples compared to the reference 3 calculate normalization factor: median of centered counts over the genes s j = median } g { Kgj factors multiply to 1: s j = ( s j 1 exp N N l=1 log( s l) ) count / geo. mean Samples Sample 1 Sample rank(mean) gene expression with and K gj = K gj R g N R g = K gj j=1 1/N IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

64 Relative Log Expression (RLE) [Anders and Huber, 2010], edger - DESeq - DESeq2 Method: 1 compute a pseudo-reference sample 2 center samples compared to the reference 3 calculate normalization factor: median of centered counts over the genes log 2(count + 1) Samples Sample 1 Sample 2 ## with edger calcnormfactors(..., method =" RLE") ## with DESeq estimatesizefactors (...) rank(mean) gene expression IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

65 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

66 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed remove extreme data for fold-changed (M) and average intensity (A) ( ) ( ) Kgj Kgr M g (j, r) = log 2 log D 2 A g (j, r) = 1 [ ( ) ( )] Kgj Kgr log j D r log D 2 j D r select as a reference sample, the sample r with the upper quartile closest to the average upper quartile M(j,r) Trimmed values None M- vs A-values IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64 A(j,r)

67 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed remove extreme data for fold-changed (M) and average intensity (A) ( ) ( ) Kgj Kgr M g (j, r) = log 2 log D 2 A g (j, r) = 1 [ ( ) ( )] Kgj Kgr log j D r log D 2 j D r 2 1 Trim 30% on M-values M(j,r) 0 1 Trimmed values None 30% of Mg IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64 A(j,r)

68 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed remove extreme data for fold-changed (M) and average intensity (A) ( ) ( ) Kgj Kgr M g (j, r) = log 2 log D 2 A g (j, r) = 1 [ ( ) ( )] Kgj Kgr log j D r log D 2 j D r 2 1 Trim 5% on A-values M(j,r) 0 1 Trimmed values None 30% of Mg 5% of Ag IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64 A(j,r)

69 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed M(j,r) A(j,r) Trimmed values None 30% of Mg 5% of Ag On remaining data, calculate the weighted mean of M-values: w g (j, r)m g (j, r) TMM(j, r) = with w g (j, r) = g:not trimmed g:not trimmed ( Dj K gj D j K gj w g (j, r) + D r K gr D r K gr ). IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

70 Trimmed Mean of M-values (TMM) [Robinson and Oshlack, 2010], edger Assumptions behind the method the total read count strongly depends on a few highly expressed genes most genes are not differentially expressed Correction factors: s j = 2 TMM(j,r) factors multiply to 1: s j = ( s j 1 exp N N l=1 log( s l) ) calcnormfactors(..., method =" TMM") IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

71 Comparison of the different approaches [Dillies et al., 2013], (6 simulated datasets) Purpose of the comparison: finding the best method for all cases is not a realistic purpose find an approach which is robust enough to provide relevant results in all cases Method: comparison based on several criteria to select a method which is valid for multiple objectives IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

72 Comparison of the different approaches [Dillies et al., 2013], (6 simulated datasets) Effect on count distribution: RPKM and TC are very similar to raw data. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

73 Comparison of the different approaches [Dillies et al., 2013], (6 simulated datasets) Effect on differential analysis (DESeq v. 1.6): Inflated FPR for all methods except for TMM and DESeq (RLE). IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

74 Comparison of the different approaches [Dillies et al., 2013], (6 simulated datasets) Conclusion: Differences appear based on data characteristics TMM and DESeq (RLE) are performant in a differential analysis context. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

75 Outline 1 Exploratory analysis Introduction Experimental design Data exploration and quality assessment 2 Normalization Raw data filtering Interpreting read counts 3 Differential Expression analysis Hypothesis testing and correction for multiple tests Differential expression analysis for RNAseq data Interpreting and improving the analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

76 Part IV: Differential expression analysis IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

77 Different steps in hypothesis testing 1 formulate an hypothesis H 0 : H 0 : the average count for gene g in the control samples is the same that the average count in the treated samples which is tested against an alternative H 1 : the average count for gene g in the control samples is different from the average count in the treated samples IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

78 Different steps in hypothesis testing 1 formulate an hypothesis H 0 : H 0 : the average count for gene g in the control samples is the same that the average count in the treated samples 2 from observations, calculate a test statistics (e.g., the mean in the two samples) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

79 Different steps in hypothesis testing 1 formulate an hypothesis H 0 : H 0 : the average count for gene g in the control samples is the same that the average count in the treated samples 2 from observations, calculate a test statistics (e.g., the mean in the two samples) 3 find the theoretical distribution of the test statistics under H 0 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

80 Different steps in hypothesis testing 1 formulate an hypothesis H 0 : H 0 : the average count for gene g in the control samples is the same that the average count in the treated samples 2 from observations, calculate a test statistics (e.g., the mean in the two samples) 3 find the theoretical distribution of the test statistics under H 0 4 deduce the probability that the observations occur under H 0 : this is called the p-value IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

81 Different steps in hypothesis testing 1 formulate an hypothesis H 0 : H 0 : the average count for gene g in the control samples is the same that the average count in the treated samples 2 from observations, calculate a test statistics (e.g., the mean in the two samples) 3 find the theoretical distribution of the test statistics under H 0 4 deduce the probability that the observations occur under H 0 : this is called the p-value 5 conclude: if the p-value is low (usually below α = 5% as a convention), H 0 is unlikely: we say that H 0 is rejected. We have that: α = P H0 (H 0 is rejected). IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

82 Summary of the possible decisions Not reject H 0 Reject H 0 IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

83 Types of errors in tests Reality H 0 is true H 0 is false Decision Do not reject H 0 Correct decision Type II error (True Negative) (False Negative) Reject H 0 Type I error Correct decision (False Positive) (True Positive) P(Type I error) = α (risk) P(Type II error) = 1 β ( β: power) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

84 Why performing a large number of tests might be a problem? Framework: Suppose you are performing G tests at level α. P(at least one FP if H 0 is always true) = 1 (1 α) G Ex: for α = 5% and G = 20, P(at least one FP if H 0 is always true) 64%!!! IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

85 Why performing a large number of tests might be a problem? Framework: Suppose you are performing G tests at level α. P(at least one FP if H 0 is always true) = 1 (1 α) G Ex: for α = 5% and G = 20, P(at least one FP if H 0 is always true) 64%!!! Probability to have at least one false positive versus the number of tests performed when H 0 is true for all G tests 1.00 Probability For more than 75 tests and if H 0 is always true, the probability to have at least one false positive is very close to 100%! IG, AM, NV 2 (INRA) Number of tests Biostatistique RNA-seq Toulouse, 18/19 mai / 64

86 Notation for multiple tests Number of decisions for G independent tests: True null False null Total hypotheses hypotheses Rejected U V R Not rejected G 0 U G 1 V G R Total G 0 G 1 G IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

87 Notation for multiple tests Number of decisions for G independent tests: True null False null Total hypotheses hypotheses Rejected U V R Not rejected G 0 U G 1 V G R Total G 0 G 1 G Instead of the risk α, control: familywise error rate (FWER): FWER = P(U > 0) (i.e., probability to have at least one false positive decision) false discovery rate (FDR): FDR = E(Q) with U/R if R > 0 Q = 0 otherwise IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

88 Adjusted p-values Settings: p-values p 1,..., p G (e.g., corresponding to G tests on G different genes) Adjusted p-values adjusted p-values are p 1,..., p G such that Rejecting tests such that p g < α P(U > 0) α or E(Q) α IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

89 Adjusted p-values Settings: p-values p 1,..., p G (e.g., corresponding to G tests on G different genes) Adjusted p-values adjusted p-values are p 1,..., p G such that Rejecting tests such that p g < α P(U > 0) α or E(Q) α Calculating p-values 1 order the p-values p (1) p (2)... p (G) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

90 Adjusted p-values Settings: p-values p 1,..., p G (e.g., corresponding to G tests on G different genes) Adjusted p-values adjusted p-values are p 1,..., p G such that Rejecting tests such that p g < α P(U > 0) α or E(Q) α Calculating p-values 1 order the p-values p (1) p (2)... p (G) 2 calculate p (g) = a g p (g) with Bonferroni method: a g = G (FWER) with Benjamini & Hochberg method: a g = G/g (FDR) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

91 Adjusted p-values Settings: p-values p 1,..., p G (e.g., corresponding to G tests on G different genes) Adjusted p-values adjusted p-values are p 1,..., p G such that Rejecting tests such that p g < α P(U > 0) α or E(Q) α Calculating p-values 1 order the p-values p (1) p (2)... p (G) 2 calculate p (g) = a g p (g) with Bonferroni method: a g = G (FWER) with Benjamini & Hochberg method: a g = G/g (FDR) 3 if adjusted p-values p (g) are larger than 1, correct p (g) min{ p (g), 1} IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

92 Fisher s exact test for contingency tables After normalization, one may build a contingency table like this one: treated control Total gene g n ga n gb n g other genes N A n ga N B n gb N n g Total N A N B N Question: is the number of reads of gene g in the treated sample significatively different than in the control sample? IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

93 Fisher s exact test for contingency tables After normalization, one may build a contingency table like this one: treated control Total gene g n ga n gb n g other genes N A n ga N B n gb N n g Total N A N B N Question: is the number of reads of gene g in the treated sample significatively different than in the control sample? Method Direct calculation of the probability to obtain such a contingency table (or a more extreme contingency table) with: independency between the two columns of the contingency tables; the same marginals ( Total ). IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

94 Example of results obtained with the Fisher test Genes declared significantly differentially expressed are in pink: 6 3 log 2 fold change 0 3 Main remark: more conservative for genes with a low expression mean log 2 expression IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

95 Example of results obtained with the Fisher test Genes declared significantly differentially expressed are in pink: 6 3 log 2 fold change 0 3 Main remark: more conservative for genes with a low expression mean log 2 expression Limitation of Fisher test Highly expressed genes have a very large variance! As Fisher test does not estimate variance, it tends to detect false positives among highly expressed genes do not use it! IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

96 Basic principles of tests for count data: 2 conditions and replicates Notations: for gene g, K 1 g1,..., K 1 gn 1 (condition 1) and K 2 g1,..., K 2 gn 2 (condition 2) choose an appropriate distribution to model count data (discrete data, overdispersion) estimate its parameters for both conditions conclude by calculating p-value IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

97 Basic principles of tests for count data: 2 conditions and replicates Notations: for gene g, K 1 g1,..., K 1 gn 1 (condition 1) and K 2 g1,..., K 2 gn 2 (condition 2) choose an appropriate distribution to model count data (discrete data, overdispersion) K k gj NB(s k j λ gk, φ g ) in which: s k is library size of sample j in condition k j λ gk is the proportion of counts for gene g in condition k φ g is the dispersion of gene g (supposed to be identical for all samples) estimate its parameters for both conditions conclude by calculating p-value IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

98 Basic principles of tests for count data: 2 conditions and replicates Notations: for gene g, K 1 g1,..., K 1 gn 1 (condition 1) and K 2 g1,..., K 2 gn 2 (condition 2) choose an appropriate distribution to model count data (discrete data, overdispersion) K k gj NB(s k j λ gk, φ g ) in which: s k is library size of sample j in condition k j λ gk is the proportion of counts for gene g in condition k φ g is the dispersion of gene g (supposed to be identical for all samples) estimate its parameters for both conditions λ g1 λ g2 φ g conclude by calculating p-value IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

99 Basic principles of tests for count data: 2 conditions and replicates Notations: for gene g, K 1 g1,..., K 1 gn 1 (condition 1) and K 2 g1,..., K 2 gn 2 (condition 2) choose an appropriate distribution to model count data (discrete data, overdispersion) K k gj NB(s k j λ gk, φ g ) in which: s k is library size of sample j in condition k j λ gk is the proportion of counts for gene g in condition k φ g is the dispersion of gene g (supposed to be identical for all samples) estimate its parameters for both conditions λ g1 λ g2 φ g conclude by calculating p-value Test H0 : {λ g1 = λ g2 } IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

100 First method: Exact Negative Binomial test [Robinson and Smyth, 2008] Normalization is performed to get equal size librairies s K 1 g K 1 gn 1 NB(sλ g1, φ g /n 1 ) (and similarly for the second condition) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

101 First method: Exact Negative Binomial test [Robinson and Smyth, 2008] Normalization is performed to get equal size librairies s K 1 g K 1 gn 1 NB(sλ g1, φ g /n 1 ) (and similarly for the second condition) 1 λ g1 and λ g2 are estimated (mean of the distributions) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

102 First method: Exact Negative Binomial test [Robinson and Smyth, 2008] Normalization is performed to get equal size librairies s K 1 g K 1 gn 1 NB(sλ g1, φ g /n 1 ) (and similarly for the second condition) 1 λ g1 and λ g2 are estimated (mean of the distributions) 2 φ g is estimated independently of λ g1 and λ g2, using different approaches to account for small sample size IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

103 First method: Exact Negative Binomial test [Robinson and Smyth, 2008] Normalization is performed to get equal size librairies s K 1 g K 1 gn 1 NB(sλ g1, φ g /n 1 ) (and similarly for the second condition) 1 λ g1 and λ g2 are estimated (mean of the distributions) 2 φ g is estimated independently of λ g1 and λ g2, using different approaches to account for small sample size 3 The test is performed similarly as for Fisher test (exact probability calculation according to estimated paramters) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

104 Estimating the dispersion parameter φ g Some methods: DESeq, DESeq2: φ g is a smooth function of λ g = λ g1 = λ g2 dge <- estimatedispersion( dge) dispersion gene est fitted final 5e 01 5e+00 5e+01 5e+02 mean of normalized counts edger: estimate a common dispersion parameter for all genes and use it as a prior in a Bayesian approach to estimate a gene specific dispersion parameter dge <- estimatecommondisp( dge) dge <- estimatetagwisedisp( dge) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

105 Perform the test Some methods: DESeq, DESeq2: exact (DESeq) or approximate (Wald and LR in DESeq2) tests res <- nbinomwaldtest( dge) results( res) res <- nbinomlr( dge) results( res) edger: exact tests res <- exacttest( dge) toptags( res) (comparison between methods in [Zhang et al., 2014]) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

106 More complex experiments: GLM Framework: K gj NB(µ gj, φ g ) with log(µ gj ) = log(s j ) + log(λ gj ) in which: s j is the library size for sample j; IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

107 More complex experiments: GLM Framework: in which: K gj NB(µ gj, φ g ) with log(µ gj ) = log(s j ) + log(λ gj ) s j is the library size for sample j; log(λ gj ) is estimated (for instance) by a Generalized Linear Model (GLM): log(λ gj ) = λ 0 + x j β g in which x j is a vector of covariates. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

108 More complex experiments: GLM Framework: in which: K gj NB(µ gj, φ g ) with log(µ gj ) = log(s j ) + log(λ gj ) s j is the library size for sample j; log(λ gj ) is estimated (for instance) by a Generalized Linear Model (GLM): log(λ gj ) = λ 0 + x j β g in which x j is a vector of covariates. GLM allows to decompose the effects on the mean of different factors their interactions IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

109 More complex experiments: GLM in practice edger dge <- estimatedisp(dge, design) fit <- glmfit(dge, design) res <- glmrt(fit,...) toptags( res) DESeq, DESeq2 dge <- newcountdataset( counts, design) dge <- estimatesizefactors( dge) dge <- estimatedispersions( dge) fit <- fitnbinomglms(dge, count ~...) fit0 <- fitnbinomglms(dge, count ~ 1) res <- nbinomglmtest(fit, fit0) p. adjust(res, method = " BH") IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

110 Alternative approach: linear model for count data [Law et al., 2014], limma Basic idea: 1 data are transformed so that they are approximately normally distributed tcount <- voom( counts, design) 2 a linear (Gaussian) model is fitted (with a Bayesian approach to improve FDR [McCarthy and Smyth, 2009]): K gj N(µ gj, σ 2 g) with E( Kgj ) = β 0 + x j β g fit <- lmfit( tcount, design) fit <- ebayes( fit) toptables(fit,...) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

111 Part V: Interpreting differential analysis results IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

112 Overview of the results: MA-plot DESeq, DESeq2 plotma(..., main="deseq", ylim=c(-4,4)) plotma(..., main="deseq2", ylim=c(-4,4)) DESeq DESeq2 log 2 fold change log fold change e 01 5e+00 5e+01 5e+02 5e+03 mean of normalized counts 5e 01 5e+00 5e+01 5e+02 5e+03 mean expression (the last one includes a prior on log 2 fold change which results in more moderated estimates for low count genes) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

113 Overview of the results: MA-plot edger plotsmear(..., de.tags =...) logfc Average logcpm IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

114 Fold change and p-value: the Volcano plot p-value versus fold change (both log scaled) scatterplot. Significant genes are in red: 2 fold + 2 fold log 10 pvalue pval = log 2 fold change IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

115 Gene clustering Prior clustering: transform data to obtain counts with similar variance DESeq, DESeq2 variancestabilizingtransformation (...) DESeq2 rlog(...) edger cpm(..., prior. count =2, log=true) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

116 Gene clustering On transformed data, use e.g., heatmap: Color key B_3 B_2 B_1 A_3 Samples A_2 A_1 gene495 gene816 gene723 gene888 gene202 gene843 gene828 gene837 gene841 gene295 gene970 gene883 gene423 gene222 gene844 gene174 gene704 gene253 gene275 gene751 gene433 gene66 gene78 gene793 gene533 gene596 gene935 gene721 gene978 gene201 gene76 gene20 gene437 gene672 gene39 gene215 gene957 gene242 gene532 gene852 gene737 gene711 gene535 gene305 gene718 gene774 gene322 gene538 gene520 gene283 gene886 gene61 gene166 gene147 gene303 gene160 gene584 gene442 gene947 gene203 gene397 gene355 gene229 gene586 gene728 gene990 gene59 gene878 gene833 gene785 gene337 gene759 gene367 gene782 gene566 gene470 gene68 gene929 gene967 gene545 Genes which is useful to visualize which genes are over/under-expressed in one condition. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

117 Standard property of usual DE analyses DESeq log 2 fold change e 01 5e+00 5e+01 5e+02 5e+03 mean of normalized counts Remark: low read counts have a too large variance to be found differentially expressed. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

118 Standard property of usual DE analyses DESeq log 2 fold change e 01 5e+00 5e+01 5e+02 5e+03 mean of normalized counts Remark: low read counts have a too large variance to be found differentially expressed. Consequence: filtering out these genes before the DE analysis because it improves the power of the test because of multiple test correction. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

119 Example Filtering out the 40% genes that have the lowest overall counts does not affect much low p-values: frequency pass do not pass 0 1 but leads to find new DE genes that were previously discarded by multiple test correction. IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

120 Filtering in practice HTSFilter cdsfilt <- HTSFilter(..., plot=false)$ filtereddata res <- nbinomtest( cdsfilt) log 2 fold change e 01 5e+00 5e+01 5e+02 5e+03 mean of normalized counts IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64

121 In summary... (with edger) preparation of the design of the experiment sequencing count data exploratory analysis (hist, boxplot...) creating an R object with count data (DGEList) a DGEList object normalization (calcnormfactors) a DGEList object with normalization factors fitting the model (estimatedisp) a DGEList object with dispersion estimates filtering low count genes (HTSFilter) a DGEList object without filtering test (exacttest or glmfit/glmlrt) a DGEExact or DGELRT object exploratory analysis (toptags, plotsmear...) IG, AM, NV 2 (INRA) Biostatistique RNA-seq Toulouse, 18/19 mai / 64