NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2025-10-07
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 37 3 233 91 47 98 1 31 233
gene2 173 1 4 4 145 1 5 36 22
gene3 13 35 280 1 5 397 2 22 1
gene4 51 36 3 1 3 230 259 3 54
gene5 1 25 1 43 289 7 36 32 309
gene6 6 54 95 41 4 18 97 64 64
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 113 9 9 1 169 29 301 9
gene2 126 62 3 186 31 237 47 1
gene3 91 5 48 30 490 120 72 2
gene4 55 5 62 15 21 379 6 618
gene5 34 17 19 1305 122 9 2 138
gene6 1 21 2 1 2 34 44 354
sample18 sample19 sample20
gene1 145 3 623
gene2 1 10 13
gene3 146 12 8
gene4 1 402 2
gene5 11 224 1
gene6 558 10 835colData 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 59.78855 -0.1130351 -1.1258588 -2.0543204 1
sample2 40.58325 0.8857501 -1.0906763 0.4939448 0
sample3 30.10439 0.1833921 0.6427279 -0.1855790 0
sample4 41.14597 0.9050350 0.8845010 0.6910609 0
sample5 65.49492 0.4860724 1.4264302 1.0496904 2
sample6 61.12732 1.1176470 2.2566607 1.8188325 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 80.7274 1.00010 0.00226462 0.96291502 0.9825663 226.622 233.592
gene2 46.7694 1.00008 0.36676897 0.54486492 0.8681620 190.081 197.052
gene3 76.8399 1.00008 3.34815959 0.06728932 0.3364466 211.791 218.761
gene4 128.9087 1.13274 0.30151277 0.79628358 0.8684552 228.077 235.179
gene5 130.7393 1.00007 6.69544902 0.00966671 0.0690479 222.431 229.401
gene6 96.1041 1.00009 0.25337427 0.61473965 0.8681620 221.068 228.038For 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 80.7274 -0.592137 0.634486 -0.933254 0.350689 0.892943 226.622
gene2 46.7694 -0.313193 0.596043 -0.525453 0.599268 0.907982 190.081
gene3 76.8399 -0.396409 0.645605 -0.614012 0.539208 0.892943 211.791
gene4 128.9087 -1.081177 0.809460 -1.335677 0.181655 0.684800 228.077
gene5 130.7393 0.220314 0.705447 0.312305 0.754809 0.916654 222.431
gene6 96.1041 -0.909008 0.687483 -1.322226 0.186093 0.684800 221.068
BIC
<numeric>
gene1 233.592
gene2 197.052
gene3 218.761
gene4 235.179
gene5 229.401
gene6 228.038For 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 80.7274 0.289920 1.24261 0.233317 0.8155156 0.855558 226.622
gene2 46.7694 2.462774 1.16967 2.105526 0.0352455 0.440569 190.081
gene3 76.8399 -2.334418 1.27263 -1.834325 0.0666057 0.555048 211.791
gene4 128.9087 -0.913329 1.57375 -0.580352 0.5616772 0.855558 228.077
gene5 130.7393 0.886640 1.37853 0.643176 0.5201096 0.855558 222.431
gene6 96.1041 -0.348018 1.34582 -0.258591 0.7959509 0.855558 221.068
BIC
<numeric>
gene1 233.592
gene2 197.052
gene3 218.761
gene4 235.179
gene5 229.401
gene6 228.038Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene11 119.6635 1.00006 12.71149 0.000363407 0.0181704 225.345 232.315
gene31 96.6180 1.00016 8.95796 0.002764802 0.0429987 223.666 230.637
gene8 85.2700 1.00010 8.65755 0.003258310 0.0429987 215.366 222.336
gene29 125.8419 1.00009 8.55863 0.003439892 0.0429987 225.853 232.823
gene10 114.2460 1.00007 7.84439 0.005098682 0.0467697 235.984 242.954
gene26 94.0304 1.00008 7.67128 0.005612363 0.0467697 225.340 232.311library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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_1.43.4
[3] NBAMSeq_1.25.0 SummarizedExperiment_1.39.2
[5] Biobase_2.69.1 GenomicRanges_1.61.5
[7] Seqinfo_0.99.2 IRanges_2.43.5
[9] S4Vectors_0.47.4 BiocGenerics_0.55.1
[11] generics_0.1.4 MatrixGenerics_1.21.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.49.1 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_1.71.1 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_2.77.2 DESeq2_1.49.4
[22] codetools_0.2-20 htmltools_0.5.8.1 sass_0.4.10
[25] yaml_2.3.10 pillar_1.11.1 crayon_1.5.3
[28] jquerylib_0.1.4 DelayedArray_0.35.3 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-168 genefilter_1.91.0
[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_1.9.1 magrittr_2.0.4 S4Arrays_1.9.1
[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_0.49.1 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_1.87.0
[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.