NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2025-10-31
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 9 105 174 82 5 75 3 48 1
gene2 2 71 1 1 118 55 365 104 94
gene3 39 3 22 1 152 76 52 376 2
gene4 175 26 1 335 6 26 22 333 7
gene5 116 518 25 8 108 15 18 55 5
gene6 1 4 113 2 82 11 19 5 9
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 85 13 39 496 2 1 1 127
gene2 7 8 6 1 65 1 62 49
gene3 143 11 153 1 275 59 5 78
gene4 61 18 274 550 1 245 3 44
gene5 71 9 1 79 4 26 306 235
gene6 36 95 233 9 1 43 17 1
sample18 sample19 sample20
gene1 6 1 337
gene2 1 13 1
gene3 214 1 349
gene4 148 248 9
gene5 3 5 99
gene6 47 20 33colData 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 27.19290 -0.5861555 1.7585950 -0.9905229 0
sample2 29.05819 0.1147545 0.8510832 -0.5310150 0
sample3 72.55932 0.2655290 0.6709331 1.1109882 2
sample4 45.80138 -0.3306476 -1.2182899 -0.5207085 2
sample5 21.57738 1.2043281 -1.6277578 -0.3555773 1
sample6 30.49804 0.5029970 1.0251392 -1.7668132 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 54.3424 1.00012 1.648106 0.1992389 0.622761 205.453 212.423
gene2 43.3224 1.00013 2.600316 0.1068709 0.534355 195.032 202.002
gene3 80.1094 1.00008 0.508392 0.4759182 0.699880 229.597 236.567
gene4 94.2934 1.00010 3.356670 0.0669421 0.478158 233.426 240.396
gene5 65.3469 1.00045 0.103066 0.7483486 0.872978 215.109 222.079
gene6 33.8218 1.00005 3.111227 0.0777717 0.486073 185.647 192.617For 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 54.3424 -0.477274 0.600484 -0.794816 0.426721 0.677558 205.453
gene2 43.3224 0.184703 0.625577 0.295252 0.767802 0.871944 195.032
gene3 80.1094 0.122362 0.639071 0.191468 0.848159 0.883499 229.597
gene4 94.2934 -0.204624 0.592645 -0.345272 0.729890 0.871944 233.426
gene5 65.3469 0.559950 0.536059 1.044567 0.296223 0.643963 215.109
gene6 33.8218 0.402422 0.494180 0.814323 0.415460 0.677558 185.647
BIC
<numeric>
gene1 212.423
gene2 202.002
gene3 236.567
gene4 240.396
gene5 222.079
gene6 192.617For 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 54.3424 -0.2673007 0.948476 -0.2818212 0.7780806 0.884182 205.453
gene2 43.3224 0.0958975 1.012920 0.0946742 0.9245736 0.983589 195.032
gene3 80.1094 -0.4629410 1.029157 -0.4498257 0.6528362 0.796142 229.597
gene4 94.2934 -1.6747475 0.951779 -1.7595962 0.0784763 0.392381 233.426
gene5 65.3469 -1.3003584 0.858959 -1.5138774 0.1300569 0.464489 215.109
gene6 33.8218 -0.8194133 0.805575 -1.0171786 0.3090685 0.669371 185.647
BIC
<numeric>
gene1 212.423
gene2 202.002
gene3 236.567
gene4 240.396
gene5 222.079
gene6 192.617Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene26 55.0138 1.00016 11.05631 0.000884561 0.044228 208.014 214.985
gene22 84.8739 1.00045 7.44304 0.006375755 0.110306 221.960 228.930
gene29 90.8773 1.00015 7.37682 0.006618348 0.110306 223.067 230.037
gene16 55.9561 1.00007 5.54155 0.018576126 0.232202 203.767 210.738
gene48 62.8462 1.00003 4.40382 0.035865656 0.358657 210.116 217.086
gene40 110.5123 1.00009 3.45636 0.063027811 0.478158 218.549 225.519library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 Under development (unstable) (2025-10-20 r88955)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.23-bioc/R/lib/libRblas.so
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
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
time zone: America/New_York
tzcode source: system (glibc)
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_4.0.0 BiocParallel_1.45.0
[3] NBAMSeq_1.27.0 SummarizedExperiment_1.41.0
[5] Biobase_2.71.0 GenomicRanges_1.63.0
[7] Seqinfo_1.1.0 IRanges_2.45.0
[9] S4Vectors_0.49.0 BiocGenerics_0.57.0
[11] generics_0.1.4 MatrixGenerics_1.23.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.51.0 gtable_0.3.6 xfun_0.54
[4] bslib_0.9.0 lattice_0.22-7 vctrs_0.6.5
[7] tools_4.6.0 parallel_4.6.0 tibble_3.3.0
[10] AnnotationDbi_1.73.0 RSQLite_2.4.3 blob_1.2.4
[13] pkgconfig_2.0.3 Matrix_1.7-4 RColorBrewer_1.1-3
[16] S7_0.2.0 lifecycle_1.0.4 compiler_4.6.0
[19] farver_2.1.2 Biostrings_2.79.1 DESeq2_1.51.0
[22] codetools_0.2-20 htmltools_0.5.8.1 sass_0.4.10
[25] yaml_2.3.10 crayon_1.5.3 pillar_1.11.1
[28] jquerylib_0.1.4 DelayedArray_0.37.0 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-168 genefilter_1.93.0
[34] tidyselect_1.2.1 locfit_1.5-9.12 digest_0.6.37
[37] dplyr_1.1.4 labeling_0.4.3 splines_4.6.0
[40] fastmap_1.2.0 grid_4.6.0 cli_3.6.5
[43] SparseArray_1.11.1 magrittr_2.0.4 S4Arrays_1.11.0
[46] survival_3.8-3 dichromat_2.0-0.1 XML_3.99-0.19
[49] withr_3.0.2 scales_1.4.0 bit64_4.6.0-1
[52] rmarkdown_2.30 XVector_0.51.0 httr_1.4.7
[55] bit_4.6.0 png_0.1-8 memoise_2.0.1
[58] evaluate_1.0.5 knitr_1.50 mgcv_1.9-3
[61] rlang_1.1.6 Rcpp_1.1.0 xtable_1.8-4
[64] glue_1.8.0 DBI_1.2.3 annotate_1.89.0
[67] jsonlite_2.0.0 R6_2.6.1 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.