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     370     287      35      23     285       1      23       5      11
gene2     712      80       2       1      16      14       7      32      80
gene3      27      97      41     205       6      25       1      12      10
gene4     204       5      45       1      73     150       3      50     212
gene5      24      34       1      92     139      92       4     393       4
gene6       5     130      36     208      62      63       5     426       1
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       90       48      166      120      280        2       33      204
gene2      106       49        1        1        4       17        2      292
gene3      240      104       25      317      100       21       12        4
gene4      170        7       15        1        2       10       14       39
gene5      185       59      128        6       67        1       31      281
gene6       56       41        1       42       24        7      260       68
      sample18 sample19 sample20
gene1        1      311        5
gene2       24       51       17
gene3       31      125        2
gene4        1      308      300
gene5      195      228        7
gene6       23       46      331

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 69.35597  0.56802456 -1.46753545 -0.089513655    2
sample2 50.38482  0.22815864 -1.01807551 -0.515074329    1
sample3 34.82989  0.54694640  1.01723857 -1.014899009    1
sample4 58.56710 -1.05534149  1.78144407 -0.005354572    2
sample5 28.47121 -1.22031511 -0.07678577 -0.565775107    0
sample6 71.49422 -0.08771177 -1.82814438  1.482500718    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   94.5310   1.00004 0.3618333  0.547534  0.823121   236.122   243.092
gene2   82.4607   1.00008 1.4372652  0.230628  0.576570   204.474   211.445
gene3   51.9236   1.00005 2.2475776  0.133827  0.445625   210.933   217.903
gene4   71.5804   1.00020 0.6038443  0.437172  0.780663   217.350   224.320
gene5   76.0829   1.00038 2.3386167  0.126341  0.445625   229.154   236.124
gene6   66.7352   1.00004 0.0260124  0.871993  0.944751   221.828   228.798

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   94.5310 -0.323282  0.421095 -0.767718 0.4426547  0.812868   236.122
gene2   82.4607  0.695544  0.420415  1.654425 0.0980412  0.412828   204.474
gene3   51.9236 -0.430925  0.346482 -1.243714 0.2136047  0.485465   210.933
gene4   71.5804  0.217261  0.430220  0.504999 0.6135595  0.841110   217.350
gene5   76.0829 -0.295385  0.384230 -0.768770 0.4420298  0.812868   229.154
gene6   66.7352 -0.626479  0.354343 -1.767998 0.0770612  0.412828   221.828
            BIC
      <numeric>
gene1   243.092
gene2   211.445
gene3   217.903
gene4   224.320
gene5   236.124
gene6   228.798

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   94.5310 -0.551155   1.53836 -0.358273  0.720139  0.951708   236.122
gene2   82.4607 -0.308438   1.54712 -0.199362  0.841979  0.951708   204.474
gene3   51.9236 -0.137768   1.26550 -0.108864  0.913310  0.951708   210.933
gene4   71.5804  1.375868   1.58442  0.868370  0.385192  0.945544   217.350
gene5   76.0829 -0.570189   1.40461 -0.405941  0.684786  0.951708   229.154
gene6   66.7352  1.645176   1.29495  1.270452  0.203924  0.731182   221.828
            BIC
      <numeric>
gene1   243.092
gene2   211.445
gene3   217.903
gene4   224.320
gene5   236.124
gene6   228.798

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>
gene19   92.8030   2.25231  25.05292 0.000111098 0.00555492   186.256   194.473
gene33   78.5584   1.00009   9.65220 0.001891731 0.04729328   204.895   211.865
gene23   57.7717   1.00008   8.57337 0.003412229 0.05687049   209.513   216.483
gene36  103.9406   1.00004   7.32616 0.006797333 0.08496666   205.171   212.141
gene34   34.0246   1.00007   6.33343 0.011853821 0.11853821   193.753   200.723
gene9    42.9550   1.00013   4.88027 0.027183675 0.22653063   204.756   211.726

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 4.5.1 Patched (2025-09-10 r88807)
Platform: aarch64-apple-darwin20
Running under: macOS Ventura 13.7.7

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/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_4.0.0               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): 2672–78.