Differential Analyses With DSS Guide
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Differential analyses with DSS Hao Wu [1em]Department of Biostatistics and Bioinformatics Emory University Atlanta, GA 303022 [1em] hao.wu@emory.edu October 30, 2017 Contents 1 Introduction 2 Using DSS for differential expression analysis 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . 3 2.1 Input data preparation . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Single factor experiment . . . . . . . . . . . . . . . . . . . . . 4 2.3 Multifactor experiment . . . . . . . . . . . . . . . . . . . . . . 6 Using DSS for differential methylation analysis . . . . . . . . . . . 7 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Input data preparation . . . . . . . . . . . . . . . . . . . . . . 8 3.3 DML/DMR detection from two-group comparison . . . . . . . . . 9 3.4 DML/DMR detection from general experimental design . . . . . . 14 3.4.1 Hypothesis testing in general experimental design . . . . . . . 14 3.4.2 Example analysis for data from general experimental design . . . 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Session Info . Abstract This vignette introduces the use of the Bioconductor package DSS (Dispersion Shrinkage for Sequencing data), which is designed for differential analysis based on high-throughput sequencing data. It performs differential expression analyses for RNA-seq, and differential Differential analyses with DSS methylation analyses for bisulfite sequencing (BS-seq) data. The core of DSS is a procedure based on Bayesian hierarchical model to estimate and shrink gene- or CpG site-specific dispersions, then conduct Wald tests for detecting differential expression/methylation. 1 Introduction Recent advances in various high-throughput sequencing technologies have revolutionized genomics research. Among them, RNA-seq is designed to measure the the abundance of RNA products, and Bisulfite sequencing (BS-seq) is for measuring DNA methylation. A fundamental question in functional genomics research is whether gene expression or DNA methylation vary under different biological contexts. Thus, identifying differential expression genes (DEGs) or differential methylation loci/regions (DML/DMRs) are key tasks in RNA-seq or BS-seq data analyses. The differential expression (DE) or differential methylation (DM) analyses are often based on gene- or CpG-specific statistical test. A key limitation in RNA- or BS-seq experiments is that the number of biological replicates is usually limited due to cost constraints. This can lead to unstable estimation of within group variance, and subsequently undesirable results from hypothesis testing. Variance shrinkage methods have been widely applied in DE analyses in microarray data to improve the estimation of gene-specific within group variances. These methods are typically based on a Bayesian hierarchical model, with a prior imposed on the gene-specific variances to provide a basis for information sharing across all genes. A distinct feature of RNA-seq or BS-seq data is that the measurements are in the form of counts and have to be modeld by discrete distributions. Unlike continuous distributions (such as Gaussian), the variances depend on means in these discrete distributions. This implies that the sample variances do not account for biological variation, and shrinkage cannot be applied on variances directly. In DSS, we assume that the count data are from the GammaPoisson (for RNA-seq) or Beta-Binomial (for BS-seq) distribution. We then parameterize the distributions by a mean and a dispersion parameters. The dispersion parameters, which represent the biological variation for replicates within a treatment group, play a central role in the differential analyses. DSS implements a series of DE/DM detection algorithms based on the dispersion shrinkage method followed by Wald statistical test to test each gene/CpG site for differential expression/methylation. It provides functions for RNA-seq DE analysis for both two group comparision and multi-factor design, BS-seq DM analysis for two group comparision, multifactor design, and data without biological replicate. Simulation and real data results show that the methods provides excellent performance compared to existing methods, especially when the overall dispersion level is high or the number of replicates is small. 2 Differential analyses with DSS For more details of the data model, the shrinkage method, and test procedures, please read [4] for differential expression from RNA-seq, [1] for differential methylation for two-group comparison from BS-seq, [2] for differential methylation for data without biological replicate, and [3] for differential methylation for general experimental design. 2 Using DSS for differential expression analysis 2.1 Input data preparation DSS requires a count table (a matrix of integers) for gene expression values (rows are for genes and columns are for samples). This is different from the isoform expression based analysis such as in cufflink/cuffdiff, where the gene expressions are represented as non-integers values. There are a number of ways to obtain the count table from raw sequencing data (fastq file), here we provide some example codes using several Bioconductor packages (the codes require installation of GenomicFeatures, Rsamtools, and GenomicRanges packages). 1. Sequence alignment. There are several RNA-seq aligner, for example, Assume the alignment result is saved in a BAM file 2. Choose a gene annotation. GenomicFeatures tophat or STAR. data.bam. package provides a convenient way to access different gene annotations. For example, if one wants to use RefSeq annotation for human genome build hg19, one can use following codes: > library(GenomicFeatures) > txdb = makeTranscriptDbFromUCSC(genom="hg19",tablename="refGene") > genes = genes(txdb) 3. Obtain count table based on the alignment results and gene annotation. This can be done in several steps. First read in the BAM file using the > package: bam=scanBam("data.bam") Next, create > Rsamtools GRanges object for the aligned sequence reads. IRange.reads=GRanges(seqnames=Rle(bam$rname), ranges=IRanges(bam$pos, width=bam$qwidth)) Finally, use the countOverlaps function in GenomicRanges function to obtain the read counts overlap each gene. > counts = countOverlaps(genes, IRange.reads) 3 Differential analyses with DSS There are other ways to obtain the counts, for example, using QuasR or easyRNASeq Biocon- ductor package. Please refer to the package vignettes for more details. 2.2 Single factor experiment In single factor RNA-seq experiment, DSS also requires a vector representing experimental designs. The length of the design vector must match the number of columns of the count table. Optionally, normalization factors or additional annotation for genes can be supplied. The basic data container in the package is from ExpressionSet class defined in SeqCountSet Biobase. class, which is directly inherited An object of the class contains all necessary information for a DE analysis: gene expression values, experimental designs, and additional annotations. A typical DE analysis contains the following simple steps. 1. Create a SeqCountSet object using newSeqCountSet. 2. Estimate normalization factor using estNormFactors. 3. Estimate and shrink gene-wise dispersion using 4. Two-group comparison using estDispersion waldTest. The usage of DSS is demonstrated in the simple simulation below. 1. First load in the library, and make a SeqCountSet object from some counts for 2000 genes and 6 samples. > library(DSS) > counts1=matrix(rnbinom(300, mu=10, size=10), ncol=3) > counts2=matrix(rnbinom(300, mu=50, size=10), ncol=3) > X1=cbind(counts1, counts2) ## these are 100 DE genes > X2=matrix(rnbinom(11400, mu=10, size=10), ncol=6) > X=rbind(X1,X2) > designs=c(0,0,0,1,1,1) > seqData=newSeqCountSet(X, designs) > seqData SeqCountSet (storageMode: lockedEnvironment) assayData: 2000 features, 6 samples element names: exprs protocolData: none phenoData sampleNames: 1 2 ... 6 (6 total) 4 Differential analyses with DSS varLabels: designs varMetadata: labelDescription featureData: none experimentData: use 'experimentData(object)' Annotation: 2. Estimate normalization factor. > seqData=estNormFactors(seqData) 3. Estimate and shrink gene-wise dispersions > seqData=estDispersion(seqData) 4. With the normalization factors and dispersions ready, the two-group comparison can be conducted via a Wald test: > result=waldTest(seqData, 0, 1) > head(result,5) geneIndex muA muB lfc difExpr stats pval 35 35 6.000000 72.79487 -2.422688 -66.79487 -6.106274 1.019840e-09 60 60 4.333333 59.94872 -2.526259 -55.61538 -6.063770 1.329677e-09 12 12 7.666667 74.92308 -2.223052 -67.25641 -5.965320 2.441553e-09 99 99 7.666667 70.97436 -2.169278 -63.30769 -5.885008 3.980348e-09 52 52 7.333333 62.79487 -2.089416 -55.46154 -5.749004 8.977052e-09 local.fdr fdr 35 1.469796e-05 1.469796e-05 60 1.474650e-05 1.469796e-05 12 2.016697e-05 1.704275e-05 99 2.580658e-05 1.994590e-05 52 3.904835e-05 2.802468e-05 A higher level wrapper function DSS.DE is provided for simple RNA-seq DE analysis in a two-group comparison. User only needs to provide a count matrix and a vector of 0’s and 1’s representing the design, and get DE test results in one line. A simple example is listed below: > counts = matrix(rpois(600, 10), ncol=6) > designs = c(0,0,0,1,1,1) > result = DSS.DE(counts, designs) > head(result) 5 Differential analyses with DSS geneIndex muA muB lfc difExpr stats pval 68 68 6.255892 11.963636 -0.6124003 -5.707744 -2.044332 0.04092073 19 19 5.973064 10.403030 -0.5213912 -4.429966 -1.703204 0.08852996 33 33 8.956229 22 22 7.164983 11.860606 -0.4778522 -4.695623 -1.644890 0.09999251 55 55 7.481481 12.218182 -0.4659086 -4.736700 -1.622868 0.10461760 7 5.072727 0.5287891 3.883502 1.651242 0.09868912 7 7.474747 11.796970 -0.4330729 -4.322222 -1.502718 0.13291190 local.fdr fdr 68 0.3178875 0.3178875 19 0.5192850 0.4198830 33 0.7003377 0.4727321 22 0.5619836 0.4443812 55 0.5788054 0.4572273 7 2.3 0.6804533 0.5543755 Multifactor experiment DSS provides functionalities for dispersion shrinkage for multifactor experimental designs. Downstream model fitting (through genearlized linear model) and hypothesis testing can be performed using other packages such as edgeR, with the dispersions estimated from DSS. Below is an example, based a simple simulation, to illustrate the DE analysis of a crossed design. 1. First simulate data for a 2x2 crossed experiments. Note the counts are randomly generated. > library(DSS) > library(edgeR) > counts=matrix(rpois(800, 10), ncol=8) > design=data.frame(gender=c(rep("M",4), rep("F",4)), strain=rep(c("WT", "Mutant"),4)) > X=model.matrix(~gender+strain, data=design) 2. make SeqCountSet, then estimate size factors and dispersion > seqData=newSeqCountSet(counts, as.data.frame(X)) > seqData=estNormFactors(seqData) > seqData=estDispersion(seqData) 3. Using edgeR’s function to do glm model fitting, but plugging in the estimated size factors and dispersion from DSS. 6 Differential analyses with DSS > fit.edgeR <- glmFit(counts, X, lib.size=normalizationFactor(seqData), + dispersion=dispersion(seqData)) 4. Using edgeR’s function to do hypothesis testing on the second parameter of the model (gender). > lrt.edgeR <- glmLRT(glmfit=fit.edgeR, coef=2) > head(lrt.edgeR$table) logFC logCPM LR PValue 1 -0.2062103 21.32223 0.23420850 0.6284207 2 -0.4818837 21.22234 1.32917575 0.2489519 3 -0.2443803 21.17545 0.32698607 0.5674392 4 0.1101438 21.23479 0.06787492 0.7944564 5 -0.0988723 21.28219 0.04780051 0.8269357 6 -0.2587670 20.97309 0.31941263 0.5719608 3 Using DSS for differential methylation analysis 3.1 Overview To detect differential methylation, statistical tests are conducted at each CpG site, and then the differential methylation loci (DML) or differential methylation regions (DMR) are called based on user specified threshold. A rigorous statistical tests should account for biological variations among replicates and the sequencing depth. Most existing methods for DM analysis are based on ad hoc methods. For example, using Fisher’s exact ignores the biological variations, using t-test on estimated methylation levels ignores the sequencing depth. Sometimes arbitrary filtering are implemented: loci with depth lower than an arbitrary threshold are filtered out, which results in information loss The DM detection procedure implemented in DSS is based on a rigorous Wald test for betabinomial distributions. The test statistics depend on the biological variations (characterized by dispersion parameter) as well as the sequencing depth. An important part of the algorithm is the estimation of dispersion parameter, which is achieved through a shrinkage estimator based on a Bayesian hierarchical model [1]. An advantage of DSS is that the test can be performed even when there is no biological replicates. That’s because by smoothing, the neighboring CpG sites can be viewed as “pseudo-replicates", and the dispersion can still be estimated with reasonable precision. 7 Differential analyses with DSS DSS also works for general experimental design, based on a beta-binomial regression model with “arcsine” link function. Model fitting is performed on transformed data with generalized least square method, which achieves much improved computational performance compared with methods based on generalized linear model. DSS depends on bsseq Bioconductor package, which has neat definition of data structures and many useful utility functions. In order to use the DM detection functionalities, bsseq needs to be pre-installed. 3.2 Input data preparation DSS requires data from each BS-seq experiment to be summarized into following information for each CG position: chromosome number, genomic coordinate, total number of reads, and number of reads showing methylation. For a sample, this information are saved in a simple text file, with each row representing a CpG site. Below shows an example of a small part of such a file: chr pos N X chr18 3014904 26 2 chr18 3031032 33 12 chr18 3031044 33 13 chr18 3031065 48 24 One can follow below steps to obtain such data from raw sequence file (fastq file), using bismark (version 0.10.0, commands for newer versions could be different) for BS-seq align- ment and count extraction. These steps require installation of bowtie or bowtie2, bismark, and the fasta file for reference genome. 1. Prepare Bisulfite reference genome. This can be done using the bismark_genome_preparation function (details in bismark manual). Example command is: bismark_genome_preparation -path_to_bowtie /usr/local/bowtie/ -verbose /path/to/refgenomes/ 2. BS-seq alignment. Example command is: bismark -q -n 1 -l 50 -path_to_bowtie /path/bowtie/ BS-refGenome reads.fastq This step will produce two text files reads.fastq_bismark.sam and reads.fastq_bismark_SE_report.txt. 3. Extract methylation counts using bismark_methylation_extractor function: bismark_methylation_extractor -s -bedGraph reads.fastq_bismark.sam. This will create multiple txt files to summarize methylation call and cytosine context, a bedGraph file to display methylation percentage, and a coverage file containing counts information. The count file contain following columns:chr, count methylated, count unmethylated. start, end, methylation%, This file can be modified to make the input file for DSS. 8 Differential analyses with DSS A typical DML detection contains two simple steps. First one conduct DM test at each CpG site, then DML/DMR are called based on the test result and user specified threshold. 3.3 DML/DMR detection from two-group comparison Below are the steps to call DML or DMR for BS-seq data in two-group comparison setting. 1. Load in library. Read in text files and create an object of BSseq class, which is defined in bsseq Bioconductor package. This step requires bsseq Bioconductor package. BSseq class is defined in that package. > library(DSS) > require(bsseq) > path <- file.path(system.file(package="DSS"), "extdata") > dat1.1 <- read.table(file.path(path, "cond1_1.txt"), header=TRUE) > dat1.2 <- read.table(file.path(path, "cond1_2.txt"), header=TRUE) > dat2.1 <- read.table(file.path(path, "cond2_1.txt"), header=TRUE) > dat2.2 <- read.table(file.path(path, "cond2_2.txt"), header=TRUE) > BSobj <- makeBSseqData( list(dat1.1, dat1.2, dat2.1, dat2.2), + c("C1","C2", "N1", "N2") )[1:1000,] > BSobj An object of type 'BSseq' with 1000 methylation loci 4 samples has not been smoothed All assays are in-memory 2. Perform statistical test for DML by calling DMLtest function. This function basically performs following steps: (1) estimate mean methylation levels for all CpG site; (2) estimate dispersions at each CpG sites; (3) conduct Wald test. For the first step, there’s an option for smoothing or not. Because the methylation levels show strong spatial correlations, smoothing can help obtain better estimates of mean methylation when the CpG sites are dense in the data (such as from the whole-genome BS-seq). However for data with sparse CpG, such as from RRBS or hydroxyl-methylation, smoothing is not recommended. To perform DML test without smoothing, do: > dmlTest <- DMLtest(BSobj, group1=c("C1", "C2"), group2=c("N1", "N2")) Estimating dispersion for each CpG site, this will take a while ... 9 Differential analyses with DSS > head(dmlTest) chr pos mu1 mu2 diff diff.se stat 1 chr18 3014904 0.3817233 0.4624549 -0.08073162 0.24997034 -0.3229648 2 chr18 3031032 0.3380579 0.1417008 0.19635711 0.11086362 1.7711592 3 chr18 3031044 0.3432172 0.3298853 0.01333190 0.12203116 0.1092500 4 chr18 3031065 0.4369377 0.3649218 0.07201587 0.10099395 0.7130711 5 chr18 3031069 0.2933572 0.5387464 -0.24538920 0.13178800 -1.8619996 6 chr18 3031082 0.3526311 0.3905718 -0.03794068 0.07847999 -0.4834440 phi1 phi2 pval fdr 1 0.300542998 0.01706260 0.74672190 0.9985094 2 0.008911745 0.04783892 0.07653423 0.6792127 3 0.010409029 0.01994821 0.91300423 0.9985094 4 0.010320888 0.01603200 0.47580174 0.9985094 5 0.012537553 0.02320887 0.06260315 0.6158797 6 0.007665696 0.01145531 0.62878051 0.9985094 To perform statistical test for DML with smoothing, do: > dmlTest.sm <- DMLtest(BSobj, group1=c("C1", "C2"), group2=c("N1", "N2"), smoothing=TRUE) Smoothing ... Estimating dispersion for each CpG site, this will take a while ... User has the option to smooth the methylation levels or not. For WGBS data, smoothing is recommended so that information from nearby CpG sites can be combined to improve the estimation of methylation levels. A simple moving average algorithm is implemented for smoothing. In RRBS since the CpG coverage is sparse, smoothing might not alter the results much. If smoothing is requested, smoothing span is an important parameter which has non-trivial impact on DMR calling. We use 500 bp as default, and think that it performs well in real data tests. 3. With the test results, one can call DML by using callDML function. The results DMLs are sorted by the significance. > dmls <- callDML(dmlTest, p.threshold=0.001) > head(dmls) chr pos mu1 mu2 diff diff.se stat 450 chr18 3976129 0.01027497 0.9390339 -0.9287590 0.06544340 -14.19179 451 chr18 3976138 0.01027497 0.9390339 -0.9287590 0.06544340 -14.19179 638 chr18 4431501 0.01331553 0.9430566 -0.9297411 0.09273779 -10.02548 10 Differential analyses with DSS 639 chr18 4431511 0.01327049 0.9430566 -0.9297862 0.09270080 -10.02997 710 chr18 4564237 0.91454619 0.0119300 0.9026162 0.05260037 17.15988 782 chr18 4657576 0.98257334 0.0678355 0.9147378 0.06815000 13.42242 phi1 phi2 pval fdr postprob.overThreshold 450 0.052591567 0.02428826 0 0 1 451 0.052591567 0.02428826 0 0 1 638 0.053172411 0.07746835 0 0 1 639 0.053121697 0.07746835 0 0 1 710 0.009528898 0.04942849 0 0 1 782 0.010424723 0.06755651 0 0 1 By default, the test is based on the null hypothesis that the difference in methylation levels is 0. Alternatively, users can specify a threshold for difference. For example, to detect loci with difference greater than 0.1, do: > dmls2 <- callDML(dmlTest, delta=0.1, p.threshold=0.001) > head(dmls2) chr pos mu1 mu2 diff diff.se stat 450 chr18 3976129 0.01027497 0.9390339 -0.9287590 0.06544340 -14.19179 451 chr18 3976138 0.01027497 0.9390339 -0.9287590 0.06544340 -14.19179 638 chr18 4431501 0.01331553 0.9430566 -0.9297411 0.09273779 -10.02548 639 chr18 4431511 0.01327049 0.9430566 -0.9297862 0.09270080 -10.02997 710 chr18 4564237 0.91454619 0.0119300 0.9026162 0.05260037 17.15988 782 chr18 4657576 0.98257334 0.0678355 0.9147378 0.06815000 13.42242 phi1 phi2 pval fdr postprob.overThreshold 450 0.052591567 0.02428826 0 0 1 451 0.052591567 0.02428826 0 0 1 638 0.053172411 0.07746835 0 0 1 639 0.053121697 0.07746835 0 0 1 710 0.009528898 0.04942849 0 0 1 782 0.010424723 0.06755651 0 0 1 When delta is specified, the function will compute the posterior probability that the difference of the means is greater than delta. So technically speaking, the threshold for p-value here actually refers to the threshold for 1-posterior probability, or the local FDR. Here we use the same parameter name for the sake of the consistence of function syntax. 11 Differential analyses with DSS 4. DMR detection is also Based on the DML test results, by calling callDMR function. Regions with many statistically significant CpG sites are identified as DMRs. Some restrictions are provided by users, including the minimum length, minimum number of CpG sites, percentage of CpG site being significant in the region, etc. There are some post hoc procedures to merge nearby DMRs into longer ones. > dmrs <- callDMR(dmlTest, p.threshold=0.01) > head(dmrs) chr start end length nCG meanMethy1 meanMethy2 diff.Methy areaStat 27 chr18 4657576 4657639 64 4 0.506453 0.318348 Here the DMRs are sorted by “areaStat", which is defined in bsseq 0.188105 14.34236 as the sum of the test statistics of all CpG sites within the DMR. Similarly, users can specify a threshold for difference. For example, to detect regions with difference greater than 0.1, do: > dmrs2 <- callDMR(dmlTest, delta=0.1, p.threshold=0.05) > head(dmrs2) chr start end length nCG meanMethy1 meanMethy2 diff.Methy areaStat 31 chr18 4657576 4657639 64 4 0.5064530 0.3183480 0.188105 14.34236 19 chr18 4222533 4222608 76 4 0.7880276 0.3614195 0.426608 12.91667 Note that the distribution of test statistics (and p-values) depends on the differences in methylation levels and biological variations, as well as technical factors such as coverage depth. It is very difficulty to select a natural and rigorous threshold for defining DMRs. We recommend users try different thresholds in order to obtain satisfactory results. 5. The DMRs can be visualized using information than the plotRegion showOneDMR function in function, This function provides more bsseq. It plots the methylation percent- ages as well as the coverage depths at each CpG sites, instead of just the smoothed curve. So the coverage depth information will be available in the figure. To use the function, do > showOneDMR(dmrs[1,], BSobj) The result figure looks like the following. Note that the figure below is not generated from the above example. The example data are from RRBS experiment so the DMRs are much shorter. 12 Differential analyses with DSS 0.0 methyl% 0.6 0 10 19 read depth C1 32930000 32931000 chr21 32932000 32933000 32932000 32933000 32932000 32933000 32932000 32933000 32932000 32933000 32932000 32933000 0.0 methyl% 0.6 0 10 19 read depth C2 32930000 32931000 chr21 0.0 methyl% 0.6 0 10 19 read depth C3 32930000 32931000 chr21 0.0 methyl% 0.6 0 10 19 read depth N1 32930000 32931000 chr21 0.0 methyl% 0.6 0 10 19 read depth N2 32930000 32931000 chr21 0.0 methyl% 0.6 0 10 19 read depth N3 32930000 32931000 chr21 13 Differential analyses with DSS 3.4 DML/DMR detection from general experimental design In DSS, BS-seq data from a general experimental design (such as crossed experiment, or experiment with covariates) is modeled through a generalized linear model framework. We use “arcsine” link function instead of the typical logit link for it better deals with data at boundaries (methylation levels close to 0 or 1). Linear model fitting is done through ordinary least square on transformed methylation levels. Variance/covariance matrices for the estimates are derived with consideration of count data distribution and transformation. 3.4.1 Hypothesis testing in general experimental design In a general design, the data are modeled through a multiple regression thus there are multiple regression coefficients. In contrast, there is only one parameter in two-group comparison which is the difference between two groups. Under this type of design, hypothesis testing can be performed for one, multiple, or any linear combination of the parameters. DSS provides flexible functionalities for hypothesis testing. User can test one parameter in the model through a Wald test, or any linear combination of the parameters through an F-test. The DMLtest.multiFactor coef parameter), one term in the model (through term parameter), or linear combinations of the parameters (through function provide interfaces for testing one parameter (through Contrast parameter). We illustrate the usage of these parameters through a simple example below. Assume we have an experiment from three strains (A, B, C) and two sexes (M and F), each has 2 biological replicates (so there are 12 datasets in total). > Strain = rep(c("A", "B", "C"), 4) > Sex = rep(c("M", "F"), each=6) > design = data.frame(Strain,Sex) > design Strain Sex 1 A M 2 B M 3 C M 4 A M 5 B M 6 C M 7 A F 8 B F 14 Differential analyses with DSS 9 C F 10 A F 11 B F 12 C F To test the additive effect of Strain and Sex, a design formula is Strain+Sex, and the corresponding design matrix for the linear model is: > X = model.matrix(~Strain+ Sex, design) > X (Intercept) StrainB StrainC SexM 1 1 0 0 1 2 1 1 0 1 3 1 0 1 1 4 1 0 0 1 5 1 1 0 1 6 1 0 1 1 7 1 0 0 0 8 1 1 0 0 9 1 0 1 0 10 1 0 0 0 11 1 1 0 0 12 1 0 1 0 attr(,"assign") [1] 0 1 1 2 attr(,"contrasts") attr(,"contrasts")$Strain [1] "contr.treatment" attr(,"contrasts")$Sex [1] "contr.treatment" Under this design, we can do different tests using the DMLtest.multiFactor • If we want to test the sex effect, we can either specify term="Sex". function: coef=4, coef="SexM", or Notice that when using character for coef, the character must match the column name of the design matrix, cannot do note that using term="Sex" coef="Sex". It is also important to only tests a single paramter in the model because sex only has two levels. 15 Differential analyses with DSS • If we want to test the effect of Strain B versus Strain A (this is also testing a single parameter), we do coef=2 or coef="StrainB". • If we want to test the whole Strain effect, it becomes a compound test because Strain has three levels. We do term="Strain", which tests StrainB and StrainC simulta- neously. We can also make a Contrast matrix L as following. It’s clear that testing LT β = 0 is equivalent to testing StrainB=0 and StrainC=0. > L = cbind(c(0,1,0,0),c(0,0,1,0)) > L [,1] [,2] [1,] 0 0 [2,] 1 0 [3,] 0 1 [4,] 0 0 • One can perform more general test, for example, to test StrainB=StrainC, or that strains B and C has no difference (but they could be different from Strain A). In this case, we need to make following contrast matrix: > matrix(c(0,1,-1,0), ncol=1) [,1] 3.4.2 [1,] 0 [2,] 1 [3,] -1 [4,] 0 Example analysis for data from general experimental design 1. Load in data distributed with DSS. This is a small portion of a set of RRBS experiments. There are 5000 CpG sites and 16 samples. The experiment is a 2 design (2 cases and 2 cell types). There are 4 replicates in each case:cell combination. > data(RRBS) > RRBS An object of type 'BSseq' with 5000 methylation loci 16 samples has not been smoothed All assays are in-memory 16 Differential analyses with DSS > design case cell 1 HC rN 2 HC rN 3 HC rN 4 SLE aN 5 SLE rN 6 SLE aN 7 SLE rN 8 SLE aN 9 SLE rN 10 SLE aN 11 SLE rN 12 HC aN 13 HC aN 14 HC aN 15 HC aN 16 HC rN 2. Fit a linear model using DMLfit.multiFactor function, include case, cell, and case:cell interaction. > DMLfit = DMLfit.multiFactor(RRBS, design=design, formula=~case+cell+case:cell) Fitting DML model for CpG site: 3. Use the DMLtest.multiFactor coef function to test the cell effect. It is important to note that parameter is the index of the coefficient to be tested for being 0. Because the model (as specified by formula in DMLfit.multiFactor) effect is the 3rd column in the design matrix, so we use include intercept, the cell coef=3 here. > DMLtest.cell = DMLtest.multiFactor(DMLfit, coef=3) Alternatively, one can specify the name of the parameter to be tested. In this case, the input coef is a character, and it must match one of the column names in the design matrix. The column names of the design matrix can be viewed by > colnames(DMLfit$X) [1] "(Intercept)" "caseSLE" "cellrN" "caseSLE:cellrN" 17 Differential analyses with DSS The following line also works. Specifying coef="cellrN" is the same as specifying coef=3. > DMLtest.cell = DMLtest.multiFactor(DMLfit, coef="cellrN") Result from this step is a data frame with chromosome number, CpG site position, test statistics, p-values (from normal distribution), and FDR. Rows are sorted by chromosome/position of the CpG sites. To obtain top ranked CpG sites, one can sort the data frame using following codes: > ix=sort(DMLtest.cell[,"pvals"], index.return=TRUE)$ix > head(DMLtest.cell[ix,]) chr pos stat pvals fdrs 1273 chr1 2930315 5.280301 1.289720e-07 0.0006448599 4706 chr1 3321251 5.037839 4.708164e-07 0.0011770409 3276 chr1 3143987 4.910412 9.088510e-07 0.0015147517 2547 chr1 3069876 4.754812 1.986316e-06 0.0024828953 3061 chr1 3121473 4.675736 2.929010e-06 0.0029290097 527 chr1 2817715 4.441198 8.945925e-06 0.0065858325 Below is a figure showing the distributions of test statistics and p-values from this example dataset > par(mfrow=c(1,2)) > hist(DMLtest.cell$stat, 50, main="test statistics", xlab="") > hist(DMLtest.cell$pvals, 50, main="P values", xlab="") P values 250 0 50 150 Frequency 200 100 0 Frequency 300 350 test statistics −4 −2 0 2 4 4. DMRs for multifactor design can be called using 0.0 0.2 callDMR 0.4 0.6 0.8 1.0 function: 18 Differential analyses with DSS > callDMR(DMLtest.cell, p.threshold=0.05) chr 33 start end length nCG areaStat chr1 2793724 2793907 184 5 12.619968 413 chr1 3309867 3310133 267 7 -12.093850 250 chr1 3094266 3094486 221 4 11.691413 262 chr1 3110129 3110394 266 5 11.682579 180 chr1 2999977 3000206 230 4 11.508302 121 chr1 2919111 2919273 163 4 9.421873 298 chr1 3146978 3147236 259 5 8.003469 248 chr1 3090627 3091585 959 5 -7.963547 346 chr1 3200758 3201006 249 4 -4.451691 213 chr1 3042371 3042459 89 5 4.115296 169 chr1 2995532 2996558 1027 4 -2.988665 Note that for results from for multifactor design, delta is NOT supported. This is because in multifactor design, the estimated coefficients in the regression are based on a GLM framework (loosely speaking), thus they don’t have clear meaning of methylation level differences. So when the input DMLresult is from DMLtest.multiFactor, delta cannot be specified. 5. More flexible way to specify a hypothesis test. Following 4 tests should produce the same results, since ’case’ only has two levels. However the p-values from F-tests (using term or Contrast) are slightly different, due to normal approximation in Wald test. > ## fit a model with additive effect only > DMLfit = DMLfit.multiFactor(RRBS, design, ~case+cell) Fitting DML model for CpG site: > ## test case effect > test1 = DMLtest.multiFactor(DMLfit, coef=2) > test2 = DMLtest.multiFactor(DMLfit, coef="caseSLE") > test3 = DMLtest.multiFactor(DMLfit, term="case") > Contrast = matrix(c(0,1,0), ncol=1) > test4 = DMLtest.multiFactor(DMLfit, Contrast=Contrast) > cor(cbind(test1$pval, test2$pval, test3$pval, test4$pval)) [,1] [,2] [,3] [,4] [1,] 1 1 1 1 [2,] 1 1 1 1 [3,] 1 1 1 1 [4,] 1 1 1 1 19 Differential analyses with DSS The model fitting and hypothesis test procedures are computationally very efficient. For a typical RRBS dataset with 4 million CpG sites, it usually takes less than half hour. In comparison, other similar software such as RADMeth or BiSeq takes at least 10 times longer. 20 Differential analyses with DSS 4 Session Info > sessionInfo() R version 3.4.2 (2017-09-28) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 16.04.3 LTS Matrix products: default BLAS: /home/biocbuild/bbs-3.6-bioc/R/lib/libRblas.so LAPACK: /home/biocbuild/bbs-3.6-bioc/R/lib/libRlapack.so locale: [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 [7] LC_PAPER=en_US.UTF-8 LC_NAME=C [9] LC_ADDRESS=C LC_TELEPHONE=C [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] splines stats4 parallel [8] datasets methods base stats graphics grDevices utils other attached packages: [1] edgeR_3.20.0 limma_3.34.0 [3] DSS_2.26.0 bsseq_1.14.0 [5] SummarizedExperiment_1.8.0 DelayedArray_0.4.0 [7] matrixStats_0.52.2 GenomicRanges_1.30.0 [9] GenomeInfoDb_1.14.0 IRanges_2.12.0 [11] S4Vectors_0.16.0 Biobase_2.38.0 [13] BiocGenerics_0.24.0 loaded via a namespace (and not attached): [1] Rcpp_0.12.13 compiler_3.4.2 plyr_1.8.4 [4] XVector_0.18.0 R.methodsS3_1.7.1 bitops_1.0-6 [7] R.utils_2.5.0 tools_3.4.2 zlibbioc_1.24.0 [10] digest_0.6.12 evaluate_0.10.1 lattice_0.20-35 [13] Matrix_1.2-11 yaml_2.1.14 GenomeInfoDbData_0.99.1 21 Differential analyses with DSS [16] stringr_1.2.0 knitr_1.17 gtools_3.5.0 [19] locfit_1.5-9.1 rprojroot_1.2 grid_3.4.2 [22] data.table_1.10.4-3 rmarkdown_1.6 magrittr_1.5 [25] backports_1.1.1 scales_0.5.0 htmltools_0.3.6 [28] permute_0.9-4 BiocStyle_2.6.0 colorspace_1.3-2 [31] stringi_1.1.5 RCurl_1.95-4.8 munsell_0.4.3 [34] R.oo_1.21.0 References [1] Hao Feng, Karen Conneely and Hao Wu. (2014). A bayesian hierarchical model to detect differentially methylated loci from single nucleotide resolution sequencing data. Nucleic Acids Research. 42(8), e69–e69. [2] Hao Wu, Tianlei Xu, Hao Feng, Li Chen, Ben Li, Bing Yao, Zhaohui Qin, Peng Jin and Karen N. Conneely. (2015). Detection of differentially methylated regions from whole-genome bisulfite sequencing data without replicates. Nucleic Acids Research. doi: 10.1093/nar/gkv715. [3] Yongseok Park, Hao Wu. (2016). Differential methylation analysis for BS-seq data under general experimental design. Bioinformatics. doi:10.1093/bioinformatics/btw026. [4] Hao Wu, Chi Wang and Zhijing Wu. (2013). A new shrinkage estimator for dispersion improves differential expression detection in RNA-seq data. Biostatistics. 14(2), 232–243. 22
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