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       3       3       5       1       3       5     360       7      51
gene2       1     472     298       3       2     345       3     322      56
gene3       2       4       7       3      55     192       1       3      49
gene4       2     157       9       2       3     598      38       1      15
gene5      58       1    1402       1       4     179       2     291       7
gene6      48       2     392     722      59      25       2      80      30
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      185        8       59        1        3       12       98       14
gene2      112        4      110      250      475       50        2       83
gene3       28       51      708       56       69       26        7        8
gene4       39       68      290       39        1        1      135        1
gene5      164       54       63      409       52       37        7      159
gene6        2        1      165        8       91        3        7        1
      sample18 sample19 sample20
gene1        1      284       97
gene2       11        7       78
gene3       31      373       51
gene4        3      195       14
gene5        1        1        1
gene6        2       21      607

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 45.95569  0.8605322 -0.07537501  0.7998795    0
sample2 76.57352  0.3216642  1.22503599 -1.5682601    1
sample3 68.17386  0.7630422  0.19026692 -0.9469453    2
sample4 67.58064 -1.7951475 -0.87237910  0.1558409    0
sample5 59.68017  0.7823192  0.79753803 -0.6131603    2
sample6 64.12638  0.5452854 -1.01082960 -0.6096498    2

design 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:

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, 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 + 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   43.2998   1.00007  1.593277 0.2068561  0.737399   197.324   204.295
gene2  141.5531   1.00008  2.913397 0.0878597  0.488109   236.791   243.761
gene3   57.3542   1.00009  0.135897 0.7125162  0.876844   216.081   223.051
gene4   69.7815   1.00010  1.250297 0.2635504  0.742491   205.427   212.397
gene5   90.8988   1.00004  0.929780 0.3349417  0.742491   220.041   227.011
gene6   86.9726   1.00008  0.726844 0.3939199  0.742491   211.963   218.933

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   43.2998  0.4524963  0.540812  0.8366978 0.4027624  0.652739   197.324
gene2  141.5531 -0.3849312  0.551171 -0.6983875 0.4849349  0.713140   236.791
gene3   57.3542  0.0507267  0.523442  0.0969099 0.9227979  0.943190   216.081
gene4   69.7815  0.5691722  0.575478  0.9890426 0.3226423  0.597486   205.427
gene5   90.8988  1.3885037  0.592285  2.3443180 0.0190619  0.111337   220.041
gene6   86.9726 -1.1999353  0.548368 -2.1881927 0.0286556  0.130253   211.963
            BIC
      <numeric>
gene1   204.295
gene2   243.761
gene3   223.051
gene4   212.397
gene5   227.011
gene6   218.933

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   43.2998  0.83445758  0.895014  0.93234006  0.351161  0.605450   197.324
gene2  141.5531 -0.00120466  0.913607 -0.00131858  0.998948  0.998948   236.791
gene3   57.3542  0.86476573  0.865105  0.99960726  0.317501  0.587964   216.081
gene4   69.7815  1.54061473  0.948034  1.62506339  0.104149  0.325466   205.427
gene5   90.8988 -1.16152166  0.973004 -1.19374860  0.232576  0.531972   220.041
gene6   86.9726  0.17579468  0.910090  0.19316195  0.846832  0.901437   211.963
            BIC
      <numeric>
gene1   204.295
gene2   243.761
gene3   223.051
gene4   212.397
gene5   227.011
gene6   218.933

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       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene31   54.0188   1.00005  14.74381 0.000123048 0.00615238   206.944   213.915
gene9    89.4493   1.00005  10.88490 0.000969998 0.02424995   217.625   224.595
gene22   53.9364   1.00008   7.98217 0.004724271 0.07873785   202.806   209.776
gene42   71.6606   1.00011   7.10536 0.007693722 0.09617152   206.771   213.741
gene24  113.0432   1.00004   5.82089 0.015841448 0.15841448   232.232   239.202
gene8    37.8614   1.00005   5.39638 0.020183743 0.16409659   175.607   182.578

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 (2026-04-24 r89963)
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_1.46.0        
 [3] NBAMSeq_1.28.0              SummarizedExperiment_1.42.0
 [5] Biobase_2.72.0              GenomicRanges_1.64.0       
 [7] Seqinfo_1.2.0               IRanges_2.46.0             
 [9] S4Vectors_0.50.0            BiocGenerics_0.58.0        
[11] generics_0.1.4              MatrixGenerics_1.24.0      
[13] matrixStats_1.5.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.52.0      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_1.74.0 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_2.80.0    DESeq2_1.52.0       
[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_0.38.0  cachem_1.1.0        
[31] abind_1.4-8          nlme_3.1-169         genefilter_1.94.0   
[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_1.12.0   magrittr_2.0.5       S4Arrays_1.12.0     
[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_0.52.0       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_1.90.0      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.