NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data

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 NBAMSeq function;

• Step 3: Pulling out DE results using results function.

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       5      77       8       4     293     110     269     213
gene2       1     261      91       2       1      67       5     141       3
gene3      41      19     847      41      56       8     233      50       1
gene4       1     191     201     401       2       2      66     365       1
gene5      75       2     172     450      18      88     315      19       4
gene6       9     433       1      22      13      58     212     105       2
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        4       19        4        1        1       95        3       72
gene2       59        5      353        1        6      180       26       85
gene3        1      201       63      124       38       23        5      104
gene4     1031        6        1       14      555        1        2        5
gene5       21      147        1        1        8       14      133        2
gene6        2        3       98      669       14       36       51       41
      sample18 sample19 sample20
gene1      221        1       38
gene2       20        1        4
gene3       47       53      189
gene4        9        2       41
gene5      386       60        1
gene6        1        1       23

colData 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 43.99816  0.27681741  0.46364183 -0.3164130    2
sample2 68.12538  0.54015001  0.96497549 -0.3988704    0
sample3 47.49410 -0.97645940 -0.01236905 -1.9060785    0
sample4 30.32145  1.56356310  2.44638124 -1.3673932    0
sample5 72.40714  0.81599762  0.61029604  1.0041492    0
sample6 67.71373 -0.01671502 -0.47736963  0.9982541    2

design is a formula which specifies how to model the samples. Compared with other packages performing DE analysis including DESeq2 (Love et al. 2014), edgeR (Robinson et al. 2010), NBPSeq (Di et al. 2015) and BBSeq (Zhou et al. 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 + var4

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) as var4 is 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 et al. 2014), edgeR (Robinson et al. 2010), NBPSeq (Di et al. 2015) or BBSeq (Zhou et al. 2011) instead. e.g.  design = ~ pheno + var1 + var2 + var3 + var4 is 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)
gsd

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 var4

Differential 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.

• gamma argument can be used to control the smoothness of the nonlinear function. Higher gamma means the nonlinear function will be more smooth. See the gamma argument of gam function in mgcv (Wood and Wood 2015) for details. Default gamma is 2.5;

• fitlin is either TRUE or FALSE indicating whether linear model should be fitted after fitting the nonlinear model;

• parallel is either TRUE or FALSE indicating whether parallel should be used. e.g. Run NBAMSeq with parallel = 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   60.8363   1.00010 1.99662095  0.157724  0.413340   205.520   212.490
gene2   65.7910   1.00044 0.42005689  0.517395  0.834508   210.241   217.212
gene3   90.3091   1.00009 0.26496471  0.606854  0.866934   232.751   239.721
gene4  130.0607   1.48705 3.34356610  0.221992  0.432606   208.088   215.544
gene5   80.3782   1.00008 0.00371669  0.951907  0.975026   217.189   224.159
gene6  116.1748   1.00040 0.13846014  0.710086  0.934324   218.817   225.787

For 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   60.8363 -0.22834062  0.546415 -0.4178883 0.6760288  0.868139   205.520
gene2   65.7910 -0.23310058  0.644146 -0.3618755 0.7174451  0.874933   210.241
gene3   90.3091 -0.05426467  0.516746 -0.1050122 0.9163661  0.953275   232.751
gene4  130.0607  0.00651005  0.611296  0.0106496 0.9915030  0.991503   208.088
gene5   80.3782  1.12684260  0.557867  2.0199139 0.0433923  0.216962   217.189
gene6  116.1748  0.13574538  0.634226  0.2140331 0.8305213  0.953275   218.817
            BIC
      <numeric>
gene1   212.490
gene2   217.212
gene3   239.721
gene4   215.544
gene5   224.159
gene6   225.787

For 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   60.8363  2.297231  0.833980  2.754540 0.00587747 0.0587747   205.520
gene2   65.7910  0.722068  0.982709  0.734772 0.46247809 0.7882915   210.241
gene3   90.3091 -1.030550  0.787668 -1.308356 0.19075244 0.5896737   232.751
gene4  130.0607 -2.923495  0.937639 -3.117932 0.00182125 0.0227656   208.088
gene5   80.3782  1.395310  0.851516  1.638618 0.10129279 0.3376426   217.189
gene6  116.1748 -0.237280  0.965315 -0.245806 0.80583269 0.8875836   218.817
            BIC
      <numeric>
gene1   212.490
gene2   217.212
gene3   239.721
gene4   215.544
gene5   224.159
gene6   225.787

Visualization

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
       <numeric> <numeric> <numeric>   <numeric>   <numeric> <numeric>
gene25   90.7122   1.00005  19.25567 1.10139e-05 0.000550693   198.452
gene32  145.2431   1.00010  11.11687 8.56270e-04 0.021406739   223.104
gene30  177.9781   1.00057   8.23442 4.11502e-03 0.068583697   238.923
gene47  164.5586   1.00007   6.68246 9.73777e-03 0.121722074   235.609
gene24  117.7485   1.00007   6.01671 1.41775e-02 0.132712497   224.362
gene7    58.3710   1.00025   5.67368 1.72254e-02 0.132712497   185.826
             BIC
       <numeric>
gene25   205.422
gene32   230.074
gene30   245.894
gene47   242.579
gene24   231.332
gene7    192.796

library(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 version 4.6.0 Patched (2026-05-01 r89994)
Platform: aarch64-apple-darwin23
Running under: macOS Tahoe 26.3.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

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_2.73.1              GenomicRanges_1.65.0       
 [7] Seqinfo_1.3.0               IRanges_2.47.1             
 [9] S4Vectors_0.51.2            BiocGenerics_0.59.2        
[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_0.11.0         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_3.52.0       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_2.81.1    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_0.39.2  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_1.13.2   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): 2672–78.