NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2022-11-01
Installation
To install and load NBAMSeq
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("NBAMSeq")library(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 11 311 213 27 5 374 81 6 17
gene2 1 8 124 64 1 1 95 280 100
gene3 66 16 125 50 2 96 68 171 13
gene4 6 1 1 76 28 291 1 30 166
gene5 6 7 1 1 9 41 1 238 17
gene6 41 148 8 29 8 160 82 2 302
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 98 101 22 126 4 1 108 77
gene2 158 1 206 184 16 3 5 2
gene3 10 1 183 4 1 35 9 61
gene4 106 676 247 8 1 1 6 93
gene5 91 22 70 5 1 35 288 237
gene6 17 159 254 170 6 85 46 208
sample18 sample19 sample20
gene1 18 3 65
gene2 189 50 18
gene3 142 83 103
gene4 37 3 155
gene5 4 30 465
gene6 10 69 2colData 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 22.20976 -0.6861990 -0.46831152 -1.13695678 1
sample2 51.48763 -0.2329253 1.38927429 -0.09283967 1
sample3 41.91769 -0.4907470 1.68299231 -0.45066115 1
sample4 57.49310 0.7780957 -0.41440236 0.64666067 0
sample5 34.94452 -0.4807003 -1.86523946 0.11369116 0
sample6 36.39463 -0.4595581 -0.05138813 0.12378722 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:
design = ~ s(pheno) + var1 + var2 + var3 + var4Several 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:
gsd = NBAMSeqDataSet(countData = countData, colData = colData, design = design)
gsdclass: 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:
gsd = NBAMSeq(gsd)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:
library(BiocParallel)
gsd = NBAMSeq(gsd, parallel = 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.
res1 = results(gsd, name = "pheno")
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 60.4409 1.00008 1.355475 0.244330151 0.4072169 217.769 224.739
gene2 68.0942 1.00004 12.133842 0.000495205 0.0125431 209.872 216.842
gene3 50.1512 1.00007 0.060392 0.806021162 0.8976087 216.196 223.167
gene4 70.7558 1.78759 3.843925 0.201767279 0.3602987 216.246 224.001
gene5 59.1123 1.54425 1.674631 0.325896316 0.4792593 205.701 213.213
gene6 72.2962 1.00005 1.022798 0.311882309 0.4725490 231.047 238.017For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.
res2 = results(gsd, name = "var1")
head(res2)DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 60.4409 -0.606706 0.472863 -1.283049 0.1994750 0.4533523 217.769
gene2 68.0942 1.380261 0.549856 2.510223 0.0120655 0.0861821 209.872
gene3 50.1512 0.172402 0.503254 0.342575 0.7319181 0.8827780 216.196
gene4 70.7558 -0.554656 0.618544 -0.896712 0.3698727 0.6776470 216.246
gene5 59.1123 0.251822 0.556411 0.452583 0.6508489 0.8452655 205.701
gene6 72.2962 -0.727265 0.511348 -1.422252 0.1549531 0.3873828 231.047
BIC
<numeric>
gene1 224.739
gene2 216.842
gene3 223.167
gene4 224.001
gene5 213.213
gene6 238.017For discrete covariates, the contrast argument should be specified. e.g. contrast = c("var4", "2", "0") means comparing level 2 vs. level 0 in var4.
res3 = results(gsd, contrast = c("var4", "2", "0"))
head(res3)DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 60.4409 0.652802 0.819469 0.7966165 0.425674 0.625991 217.769
gene2 68.0942 0.857123 0.950514 0.9017469 0.367191 0.583869 209.872
gene3 50.1512 1.194465 0.871285 1.3709239 0.170399 0.405711 216.196
gene4 70.7558 0.061954 1.050754 0.0589615 0.952983 0.952983 216.246
gene5 59.1123 0.817297 0.949819 0.8604766 0.389526 0.590191 205.701
gene6 72.2962 -0.432981 0.874472 -0.4951342 0.620505 0.738697 231.047
BIC
<numeric>
gene1 224.739
gene2 216.842
gene3 223.167
gene4 224.001
gene5 213.213
gene6 238.017Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene2 68.0942 1.00004 12.13384 0.000495205 0.0125431 209.872 216.842
gene43 66.7524 1.00006 12.10937 0.000501724 0.0125431 199.390 206.360
gene17 87.0458 1.00005 9.37105 0.002204833 0.0344369 219.077 226.047
gene27 129.5501 1.00005 8.96357 0.002754954 0.0344369 242.456 249.426
gene25 53.9172 1.00004 8.45000 0.003651689 0.0365169 193.746 200.716
gene13 29.8594 1.00012 7.45604 0.006324872 0.0527073 179.124 186.094library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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
sessionInfo()R Under development (unstable) (2022-10-25 r83175)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.1 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.17-bioc/R/lib/libRblas.so
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_GB 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] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.3.6 BiocParallel_1.33.0
[3] NBAMSeq_1.15.0 SummarizedExperiment_1.29.0
[5] Biobase_2.59.0 GenomicRanges_1.51.0
[7] GenomeInfoDb_1.35.0 IRanges_2.33.0
[9] S4Vectors_0.37.0 BiocGenerics_0.45.0
[11] MatrixGenerics_1.11.0 matrixStats_0.62.0
loaded via a namespace (and not attached):
[1] tidyselect_1.2.0 farver_2.1.1 dplyr_1.0.10
[4] blob_1.2.3 Biostrings_2.67.0 bitops_1.0-7
[7] fastmap_1.1.0 RCurl_1.98-1.9 XML_3.99-0.12
[10] digest_0.6.30 lifecycle_1.0.3 survival_3.4-0
[13] KEGGREST_1.39.0 RSQLite_2.2.18 magrittr_2.0.3
[16] genefilter_1.81.0 compiler_4.3.0 rlang_1.0.6
[19] sass_0.4.2 tools_4.3.0 utf8_1.2.2
[22] yaml_2.3.6 knitr_1.40 labeling_0.4.2
[25] bit_4.0.4 DelayedArray_0.25.0 RColorBrewer_1.1-3
[28] withr_2.5.0 grid_4.3.0 fansi_1.0.3
[31] xtable_1.8-4 colorspace_2.0-3 scales_1.2.1
[34] cli_3.4.1 rmarkdown_2.17 crayon_1.5.2
[37] generics_0.1.3 httr_1.4.4 DBI_1.1.3
[40] cachem_1.0.6 stringr_1.4.1 zlibbioc_1.45.0
[43] splines_4.3.0 assertthat_0.2.1 parallel_4.3.0
[46] AnnotationDbi_1.61.0 XVector_0.39.0 vctrs_0.5.0
[49] Matrix_1.5-1 jsonlite_1.8.3 geneplotter_1.77.0
[52] bit64_4.0.5 locfit_1.5-9.6 jquerylib_0.1.4
[55] annotate_1.77.0 glue_1.6.2 codetools_0.2-18
[58] stringi_1.7.8 gtable_0.3.1 munsell_0.5.0
[61] tibble_3.1.8 pillar_1.8.1 htmltools_0.5.3
[64] GenomeInfoDbData_1.2.9 R6_2.5.1 evaluate_0.17
[67] lattice_0.20-45 highr_0.9 png_0.1-7
[70] memoise_2.0.1 bslib_0.4.0 Rcpp_1.0.9
[73] nlme_3.1-160 mgcv_1.8-41 DESeq2_1.39.0
[76] xfun_0.34 pkgconfig_2.0.3 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.