NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2025-10-30
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 1 1 58 6 1 13 19 24 119
gene2 2 11 340 1 9 5 38 1 1
gene3 12 468 87 131 1 117 1 35 143
gene4 94 92 360 26 211 8 86 103 96
gene5 17 6 56 64 2 149 20 52 44
gene6 270 12 568 3 67 355 1 638 14
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 28 26 23 2 349 715 39 10
gene2 96 4 1 15 2044 12 12 11
gene3 82 27 197 20 92 232 1 2
gene4 71 1 1 14 188 61 2 6
gene5 1 72 16 1 320 44 328 27
gene6 45 144 48 12 54 311 10 340
sample18 sample19 sample20
gene1 31 106 1
gene2 605 103 1
gene3 114 504 211
gene4 17 72 35
gene5 236 270 80
gene6 5 39 48colData 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 62.82958 -0.002689273 1.1028230 -0.5829673 2
sample2 31.49372 0.720175326 -1.2430242 1.4324246 1
sample3 67.70154 -1.567042786 -1.1320492 2.1795871 1
sample4 41.96112 0.228503135 0.6246155 1.7791785 2
sample5 70.28506 0.263011699 -0.2869808 -0.5193010 1
sample6 67.82051 0.468280501 -1.1003113 1.2394489 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 63.9746 1.00010 0.01399226 0.9062297 0.999542 204.059 211.029
gene2 108.9646 1.92708 7.31311011 0.0641778 0.299406 204.930 212.823
gene3 103.7318 1.00006 1.57761563 0.2091141 0.522785 238.768 245.739
gene4 54.6856 1.00005 0.00583657 0.9393898 0.999542 217.921 224.891
gene5 72.9503 1.00013 0.86075784 0.3536502 0.631518 229.346 236.317
gene6 97.3324 1.00006 4.44178133 0.0350795 0.219247 234.244 241.215For 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 63.9746 -1.937815 0.624070 -3.105123 0.001902 0.047550 204.059
gene2 108.9646 -0.425864 0.732087 -0.581712 0.560760 0.728552 204.930
gene3 103.7318 -0.455470 0.614833 -0.740803 0.458813 0.674724 238.768
gene4 54.6856 -0.529048 0.534135 -0.990476 0.321942 0.643883 217.921
gene5 72.9503 0.385699 0.601583 0.641141 0.521431 0.722594 229.346
gene6 97.3324 -0.448010 0.539852 -0.829876 0.406609 0.655821 234.244
BIC
<numeric>
gene1 211.029
gene2 212.823
gene3 245.739
gene4 224.891
gene5 236.317
gene6 241.215For 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 63.9746 1.674764 1.076788 1.555333 0.119867 0.428095 204.059
gene2 108.9646 -0.297797 1.296448 -0.229702 0.818323 0.888279 204.930
gene3 103.7318 -0.772162 1.052827 -0.733417 0.463304 0.827329 238.768
gene4 54.6856 -0.226854 0.922367 -0.245948 0.805723 0.888279 217.921
gene5 72.9503 -0.166247 1.030680 -0.161298 0.871858 0.889652 229.346
gene6 97.3324 0.941004 0.928985 1.012938 0.311090 0.723309 234.244
BIC
<numeric>
gene1 211.029
gene2 212.823
gene3 245.739
gene4 224.891
gene5 236.317
gene6 241.215Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene37 130.4533 1.00011 12.65184 0.000375455 0.0187727 210.763 217.734
gene47 62.5616 1.00008 9.30229 0.002289977 0.0572494 205.593 212.564
gene19 26.9169 1.00007 7.19651 0.007308364 0.1123068 164.448 171.418
gene14 183.2612 1.00018 6.48856 0.010863211 0.1123068 243.540 250.510
gene39 139.8912 1.00006 6.39845 0.011426225 0.1123068 231.067 238.038
gene48 59.3266 1.00012 6.10646 0.013476818 0.1123068 201.557 208.527library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.5.1 Patched (2025-08-23 r88802)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.22-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_1.44.0
[3] NBAMSeq_1.26.0 SummarizedExperiment_1.40.0
[5] Biobase_2.70.0 GenomicRanges_1.62.0
[7] Seqinfo_1.0.0 IRanges_2.44.0
[9] S4Vectors_0.48.0 BiocGenerics_0.56.0
[11] generics_0.1.4 MatrixGenerics_1.22.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.50.0 gtable_0.3.6 xfun_0.53
[4] bslib_0.9.0 lattice_0.22-7 vctrs_0.6.5
[7] tools_4.5.1 parallel_4.5.1 tibble_3.3.0
[10] AnnotationDbi_1.72.0 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_4.5.1
[19] farver_2.1.2 Biostrings_2.78.0 DESeq2_1.50.0
[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_0.36.0 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-168 genefilter_1.92.0
[34] tidyselect_1.2.1 locfit_1.5-9.12 digest_0.6.37
[37] dplyr_1.1.4 labeling_0.4.3 splines_4.5.1
[40] fastmap_1.2.0 grid_4.5.1 cli_3.6.5
[43] SparseArray_1.10.0 magrittr_2.0.4 S4Arrays_1.10.0
[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_0.50.0 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_1.88.0
[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.