NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2026-04-28
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 123 2 236 2 1 99 22 161 163
gene2 354 624 149 40 1 33 167 1 4
gene3 3 1 93 7 18 29 16 172 1
gene4 1 80 2 875 9 1 241 27 89
gene5 74 26 12 1 21 96 43 13 2
gene6 23 1 39 60 24 1384 12 193 72
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 67 15 65 158 28 35 27
gene2 2 1 162 5 623 5 4 57
gene3 2 11 63 13 86 18 411 1
gene4 71 1 25 116 1 100 716 31
gene5 235 227 3 38 4 34 12 78
gene6 31 52 73 43 28 29 2 2
sample18 sample19 sample20
gene1 150 57 1
gene2 1 42 1
gene3 6 140 105
gene4 6 448 40
gene5 87 36 30
gene6 5 363 7colData 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 53.81336 -0.4770509 -0.98788768 -0.7714960 0
sample2 73.68071 1.2712794 0.67611258 0.9138409 1
sample3 42.47431 1.2173849 -0.44440377 1.1367614 1
sample4 25.84396 -0.7299088 -0.00725924 -0.4265589 0
sample5 47.95385 -1.0185717 -0.85649827 1.1020512 0
sample6 41.15608 -0.3161889 2.57930047 0.6528291 1design 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 64.9990 1.00015 0.5924989 0.441504968 0.6553397 224.906 231.876
gene2 94.1406 1.00008 0.0330549 0.855939402 0.9169568 218.582 225.552
gene3 58.2458 1.00013 13.1724492 0.000284349 0.0142174 195.771 202.741
gene4 120.4412 1.00005 5.9450122 0.014761899 0.1034176 223.342 230.313
gene5 48.7193 1.00004 1.5112270 0.218955373 0.4878139 201.062 208.033
gene6 93.5872 1.09292 7.2249822 0.015578291 0.1034176 222.053 229.115For 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 64.9990 0.0859825 0.393663 0.218416 0.827104895 0.8439846 224.906
gene2 94.1406 0.1529427 0.462348 0.330796 0.740798739 0.8277851 218.582
gene3 58.2458 1.2746771 0.344625 3.698736 0.000216676 0.0108338 195.771
gene4 120.4412 -0.1501855 0.381505 -0.393666 0.693827566 0.8277851 223.342
gene5 48.7193 0.0850536 0.300147 0.283373 0.776891074 0.8277851 201.062
gene6 93.5872 0.2787329 0.372776 0.747723 0.454627439 0.7889796 222.053
BIC
<numeric>
gene1 231.876
gene2 225.552
gene3 202.741
gene4 230.313
gene5 208.033
gene6 229.115For 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 64.9990 0.915450 1.32121 0.692886 0.4883812 0.652613 224.906
gene2 94.1406 -0.812237 1.55263 -0.523137 0.6008792 0.698697 218.582
gene3 58.2458 -1.553265 1.16175 -1.337007 0.1812205 0.396201 195.771
gene4 120.4412 -0.869939 1.27778 -0.680819 0.4959860 0.652613 223.342
gene5 48.7193 -2.402295 1.02748 -2.338040 0.0193852 0.161543 201.062
gene6 93.5872 -1.279696 1.23851 -1.033251 0.3014862 0.486268 222.053
BIC
<numeric>
gene1 231.876
gene2 225.552
gene3 202.741
gene4 230.313
gene5 208.033
gene6 229.115Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene3 58.2458 1.00013 13.17245 0.000284349 0.0142174 195.771 202.741
gene33 94.2656 1.00013 8.80384 0.003007112 0.0568303 231.376 238.346
gene10 53.6530 1.00012 8.57587 0.003409821 0.0568303 205.095 212.065
gene21 59.8853 1.00033 7.95061 0.004820049 0.0602506 201.905 208.876
gene24 71.5148 1.00006 6.08529 0.013637091 0.1034176 213.243 220.213
gene4 120.4412 1.00005 5.94501 0.014761899 0.1034176 223.342 230.313library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.6.0 RC (2026-04-17 r89917)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.4 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.24-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_4.0.3 BiocParallel_1.47.0
[3] NBAMSeq_1.29.0 SummarizedExperiment_1.43.0
[5] Biobase_2.73.0 GenomicRanges_1.65.0
[7] Seqinfo_1.3.0 IRanges_2.47.0
[9] S4Vectors_0.51.0 BiocGenerics_0.59.0
[11] generics_0.1.4 MatrixGenerics_1.25.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.53.0 gtable_0.3.6 xfun_0.57
[4] bslib_0.10.0 lattice_0.22-9 vctrs_0.7.3
[7] tools_4.6.0 parallel_4.6.0 tibble_3.3.1
[10] AnnotationDbi_1.75.0 RSQLite_2.4.6 blob_1.3.0
[13] pkgconfig_2.0.3 Matrix_1.7-5 RColorBrewer_1.1-3
[16] S7_0.2.2 lifecycle_1.0.5 compiler_4.6.0
[19] farver_2.1.2 Biostrings_2.81.0 DESeq2_1.53.0
[22] codetools_0.2-20 htmltools_0.5.9 sass_0.4.10
[25] yaml_2.3.12 crayon_1.5.3 pillar_1.11.1
[28] jquerylib_0.1.4 DelayedArray_0.39.0 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-169 genefilter_1.95.0
[34] tidyselect_1.2.1 locfit_1.5-9.12 digest_0.6.39
[37] dplyr_1.2.1 labeling_0.4.3 splines_4.6.0
[40] fastmap_1.2.0 grid_4.6.0 cli_3.6.6
[43] SparseArray_1.13.0 magrittr_2.0.5 S4Arrays_1.13.0
[46] survival_3.8-6 dichromat_2.0-0.1 XML_3.99-0.23
[49] withr_3.0.2 scales_1.4.0 bit64_4.8.0
[52] rmarkdown_2.31 XVector_0.53.0 httr_1.4.8
[55] bit_4.6.0 otel_0.2.0 png_0.1-9
[58] memoise_2.0.1 evaluate_1.0.5 knitr_1.51
[61] mgcv_1.9-4 rlang_1.2.0 Rcpp_1.1.1-1.1
[64] xtable_1.8-8 glue_1.8.1 DBI_1.3.0
[67] annotate_1.91.0 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.