NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2020-10-29
Installation
To install and load NBAMSeq
Introduction
High-throughput sequencing experiments followed by differential expression analysis is a widely used approach to detect genomic biomarkers. A fundamental step in differential expression analysis is to model the association between gene counts and covariates of interest. NBAMSeq is a flexible statistical model based on the generalized additive model and allows for information sharing across genes in variance estimation. Specifically, we model the logarithm of mean gene counts as sums of smooth functions with the smoothing parameters and coefficients estimated simultaneously by a nested iteration. The variance is estimated by the Bayesian shrinkage approach to fully exploit the information across all genes.
The workflow of NBAMSeq contains three main steps:
Step 1: Data input using
NBAMSeqDataSet;Step 2: Differential expression (DE) analysis using
NBAMSeqfunction;Step 3: Pulling out DE results using
resultsfunction.
Here we illustrate each of these steps respectively.
Data input
Users are expected to provide three parts of input, i.e. countData, colData, and design.
countData is a matrix of gene counts generated by RNASeq experiments.
## An example of countData
n = 50 ## n stands for number of genes
m = 20 ## m stands for sample size
countData = matrix(rnbinom(n*m, mu=100, size=1/3), ncol = m) + 1
mode(countData) = "integer"
colnames(countData) = paste0("sample", 1:m)
rownames(countData) = paste0("gene", 1:n)
head(countData) sample1 sample2 sample3 sample4 sample5 sample6 sample7 sample8 sample9
gene1 42 12 64 276 6 299 1 9 86
gene2 610 1 99 806 138 54 6 6 3
gene3 214 16 9 235 19 1 12 6 32
gene4 85 289 9 422 2 133 221 2 2
gene5 505 140 11 1 23 21 6 14 65
gene6 3 15 254 58 12 347 85 4 13
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 72 83 1 13 1 1 142 20
gene2 554 8 420 13 6 1 1 1
gene3 1 116 17 546 105 3 12 1063
gene4 106 29 1 471 11 1 49 60
gene5 938 41 88 1 218 8 301 16
gene6 108 7 35 281 1316 40 9 29
sample18 sample19 sample20
gene1 2 122 2
gene2 90 7 1
gene3 36 47 21
gene4 68 657 1
gene5 235 5 1
gene6 2 8 19colData is a data frame which contains the covariates of samples. The sample order in colData should match the sample order in countData.
## An example of colData
pheno = runif(m, 20, 80)
var1 = rnorm(m)
var2 = rnorm(m)
var3 = rnorm(m)
var4 = as.factor(sample(c(0,1,2), m, replace = TRUE))
colData = data.frame(pheno = pheno, var1 = var1, var2 = var2,
var3 = var3, var4 = var4)
rownames(colData) = paste0("sample", 1:m)
head(colData) pheno var1 var2 var3 var4
sample1 79.79865 -0.06153226 0.9076525 -0.5013926 2
sample2 65.33880 0.98638962 -0.7226681 2.1574485 0
sample3 46.79358 0.47751731 -0.5039563 -1.3706989 2
sample4 52.01470 -0.13822694 0.6972845 1.5473712 2
sample5 35.14663 0.82205264 1.2476779 1.2422261 1
sample6 66.79806 -0.65425491 -0.5837493 -0.2428002 2design is a formula which specifies how to model the samples. Compared with other packages performing DE analysis including DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2010), NBPSeq (Di et al. 2015) and BBSeq (Zhou, Xia, and Wright 2011), NBAMSeq supports the nonlinear model of covariates via mgcv (Wood and Wood 2015). To indicate the nonlinear covariate in the model, users are expected to use s(variable_name) in the design formula. In our example, if we would like to model pheno as a nonlinear covariate, the design formula should be:
Several notes should be made regarding the design formula:
multiple nonlinear covariates are supported, e.g.
design = ~ s(pheno) + s(var1) + var2 + var3 + var4;the nonlinear covariate cannot be a discrete variable, e.g.
design = ~ s(pheno) + var1 + var2 + var3 + s(var4)asvar4is a factor, and it makes no sense to model a factor as nonlinear;at least one nonlinear covariate should be provided in
design. If all covariates are assumed to have linear effect on gene count, use DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2010), NBPSeq (Di et al. 2015) or BBSeq (Zhou, Xia, and Wright 2011) instead. e.g.design = ~ pheno + var1 + var2 + var3 + var4is not supported in NBAMSeq;design matrix is not supported.
We then construct the NBAMSeqDataSet using countData, colData, and design:
class: NBAMSeqDataSet
dim: 50 20
metadata(1): fitted
assays(1): counts
rownames(50): gene1 gene2 ... gene49 gene50
rowData names(0):
colnames(20): sample1 sample2 ... sample19 sample20
colData names(5): pheno var1 var2 var3 var4Differential expression analysis
Differential expression analysis can be performed by NBAMSeq function:
Several other arguments in NBAMSeq function are available for users to customize the analysis.
gammaargument can be used to control the smoothness of the nonlinear function. Highergammameans the nonlinear function will be more smooth. See thegammaargument of gam function in mgcv (Wood and Wood 2015) for details. Defaultgammais 2.5;fitlinis eitherTRUEorFALSEindicating whether linear model should be fitted after fitting the nonlinear model;parallelis eitherTRUEorFALSEindicating whether parallel should be used. e.g. RunNBAMSeqwithparallel = TRUE:
Pulling out DE results
Results of DE analysis can be pulled out by results function. For continuous covariates, the name argument should be specified indicating the covariate of interest. For nonlinear continuous covariates, base mean, effective degrees of freedom (edf), test statistics, p-value, and adjusted p-value will be returned.
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 50.6332 1.00003 8.0173123 0.00463400 0.0579250 197.202 204.172
gene2 137.0070 1.00005 0.0176062 0.89462202 0.9502937 215.172 222.143
gene3 88.0940 1.00006 0.1540755 0.69473999 0.8892969 218.179 225.149
gene4 99.0527 1.00004 2.6706575 0.10222217 0.3006534 226.258 233.228
gene5 120.0785 1.00004 6.8599270 0.00881689 0.0734741 229.064 236.034
gene6 96.9594 1.00002 3.5402373 0.05990633 0.1953475 228.219 235.189For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 50.6332 -0.642995 0.382280 -1.681999 0.09256908 0.2892784 197.202
gene2 137.0070 -0.740851 0.464692 -1.594285 0.11087232 0.3260951 215.172
gene3 88.0940 -0.394955 0.376514 -1.048979 0.29418783 0.5883757 218.179
gene4 99.0527 -1.384980 0.431403 -3.210408 0.00132547 0.0331367 226.258
gene5 120.0785 -0.129879 0.429034 -0.302725 0.76209913 0.9406000 229.064
gene6 96.9594 -0.283982 0.406718 -0.698227 0.48503506 0.6978130 228.219
BIC
<numeric>
gene1 204.172
gene2 222.143
gene3 225.149
gene4 233.228
gene5 236.034
gene6 235.189For discrete covariates, the contrast argument should be specified. e.g. contrast = c("var4", "2", "0") means comparing level 2 vs. level 0 in var4.
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 50.6332 2.924086 1.12270 2.604501 0.009200810 0.115010 197.202
gene2 137.0070 4.606767 1.37670 3.346248 0.000819132 0.019993 215.172
gene3 88.0940 -1.633997 1.09340 -1.494412 0.135067947 0.350687 218.179
gene4 99.0527 -0.583349 1.21398 -0.480526 0.630853432 0.789194 226.258
gene5 120.0785 0.489929 1.24737 0.392769 0.694490329 0.789194 229.064
gene6 96.9594 -0.642245 1.18273 -0.543020 0.587116334 0.789194 228.219
BIC
<numeric>
gene1 204.172
gene2 222.143
gene3 225.149
gene4 233.228
gene5 236.034
gene6 235.189Visualization
We suggest two approaches to visualize the nonlinear associations. The first approach is to plot the smooth components of a fitted negative binomial additive model by plot.gam function in mgcv (Wood and Wood 2015). This can be done by calling makeplot function and passing in NBAMSeqDataSet object. Users are expected to provide the phenotype of interest in phenoname argument and gene of interest in genename argument.
## assuming we are interested in the nonlinear relationship between gene10's
## expression and "pheno"
makeplot(gsd, phenoname = "pheno", genename = "gene10", main = "gene10")
In addition, to explore the nonlinear association of covariates, it is also instructive to look at log normalized counts vs. variable scatter plot. Below we show how to produce such plot.
## here we explore the most significant nonlinear association
res1 = res1[order(res1$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene31 84.9508 1.00008 17.89424 2.37181e-05 0.0011859 209.366 216.336
gene37 94.5447 1.00008 8.07125 4.49956e-03 0.0579250 212.226 219.197
gene13 84.4954 1.00011 8.06034 4.52787e-03 0.0579250 212.581 219.551
gene1 50.6332 1.00003 8.01731 4.63400e-03 0.0579250 197.202 204.172
gene15 98.4627 1.00003 7.46910 6.27837e-03 0.0627837 220.124 227.094
gene5 120.0785 1.00004 6.85993 8.81689e-03 0.0734741 229.064 236.034library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$pheno)-5, y = max(df$logcount)-1,
label = paste0("edf: ", signif(res1[topgene,"edf"],digits = 4)))+
ggtitle(setTitle)+
theme(text = element_text(size=10), plot.title = element_text(hjust = 0.5))
Session info
R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.5 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.12-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] parallel stats4 stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] ggplot2_3.3.2 BiocParallel_1.24.0
[3] NBAMSeq_1.6.1 SummarizedExperiment_1.20.0
[5] Biobase_2.50.0 GenomicRanges_1.42.0
[7] GenomeInfoDb_1.26.0 IRanges_2.24.0
[9] S4Vectors_0.28.0 BiocGenerics_0.36.0
[11] MatrixGenerics_1.2.0 matrixStats_0.57.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.5 locfit_1.5-9.4 lattice_0.20-41
[4] digest_0.6.27 R6_2.5.0 RSQLite_2.2.1
[7] evaluate_0.14 httr_1.4.2 pillar_1.4.6
[10] zlibbioc_1.36.0 rlang_0.4.8 annotate_1.68.0
[13] blob_1.2.1 Matrix_1.2-18 rmarkdown_2.5
[16] labeling_0.4.2 splines_4.0.3 geneplotter_1.68.0
[19] stringr_1.4.0 RCurl_1.98-1.2 bit_4.0.4
[22] munsell_0.5.0 DelayedArray_0.16.0 compiler_4.0.3
[25] xfun_0.18 pkgconfig_2.0.3 mgcv_1.8-33
[28] htmltools_0.5.0 tidyselect_1.1.0 tibble_3.0.4
[31] GenomeInfoDbData_1.2.4 XML_3.99-0.5 withr_2.3.0
[34] crayon_1.3.4 dplyr_1.0.2 bitops_1.0-6
[37] grid_4.0.3 nlme_3.1-150 xtable_1.8-4
[40] gtable_0.3.0 lifecycle_0.2.0 DBI_1.1.0
[43] magrittr_1.5 scales_1.1.1 stringi_1.5.3
[46] farver_2.0.3 XVector_0.30.0 genefilter_1.72.0
[49] ellipsis_0.3.1 vctrs_0.3.4 generics_0.0.2
[52] RColorBrewer_1.1-2 tools_4.0.3 bit64_4.0.5
[55] glue_1.4.2 DESeq2_1.30.0 purrr_0.3.4
[58] survival_3.2-7 yaml_2.2.1 AnnotationDbi_1.52.0
[61] colorspace_1.4-1 memoise_1.1.0 knitr_1.30 References
Di, Y, DW Schafer, JS Cumbie, and JH Chang. 2015. “NBPSeq: Negative Binomial Models for Rna-Sequencing Data.” R Package Version 0.3. 0, URL Http://CRAN. R-Project. Org/Package= NBPSeq.
Love, Michael I, Wolfgang Huber, and Simon Anders. 2014. “Moderated Estimation of Fold Change and Dispersion for Rna-Seq Data with Deseq2.” Genome Biology 15 (12): 550.
Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “EdgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.
Wood, Simon, and Maintainer Simon Wood. 2015. “Package ’Mgcv’.” R Package Version 1: 29.
Zhou, Yi-Hui, Kai Xia, and Fred A Wright. 2011. “A Powerful and Flexible Approach to the Analysis of Rna Sequence Count Data.” Bioinformatics 27 (19): 2672–8.