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      19      15      32       5       3     256     206      73     152
gene2       1      29      29       5       1     710     244       5      19
gene3     106     126       1      72      56      48     127       1       3
gene4      27      13    1124     226       2       5     310       1     296
gene5     373      34       1       1      57       4      12       1       1
gene6       5      58       1       1     183     107      81    1268     228
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        2        1       27       62      309       83       21       85
gene2      113        1       52        2        9        1       12       13
gene3       41       50      560       56       44        1       15        5
gene4      303        8      210        3        3      238        1        8
gene5        8        2       18       13       34       11      473       14
gene6       67      273      128      110       79      135      346      245
      sample18 sample19 sample20
gene1      634       47        6
gene2      192       11        1
gene3        2       10       42
gene4      791      162        1
gene5      316       65      457
gene6       33       16        8

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 27.72766  1.5486634  0.1701477 -1.1598660    0
sample2 55.32085  0.1250517  2.3123090  0.1174632    2
sample3 57.62663  0.3538677  0.4820402  0.5747464    2
sample4 28.95509 -0.2606925  1.2875045  0.4958720    1
sample5 58.89602 -1.9020619 -0.1418307 -0.7944310    2
sample6 47.17494  0.9479394  0.2035777 -0.2471525    1

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   92.6186   1.00016 1.1866979  0.276048  0.761134   232.136   239.106
gene2   89.9338   1.00010 0.0863429  0.769049  0.967222   199.202   206.172
gene3   62.5782   1.00014 0.2371985  0.626346  0.967222   216.614   223.584
gene4  172.5156   1.00038 0.0528435  0.818361  0.967222   239.867   246.837
gene5   92.2048   1.00011 0.0480500  0.826715  0.967222   214.935   221.905
gene6  114.1850   1.00023 0.7144809  0.398002  0.904550   250.043   257.013

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   92.6186  0.5756334  0.535281  1.0753863 0.28220182 0.6413678   232.136
gene2   89.9338  1.5076918  0.600984  2.5087051 0.01211746 0.0865533   199.202
gene3   62.5782 -0.2331701  0.546836 -0.4263985 0.66981748 0.9089865   216.614
gene4  172.5156  1.8076984  0.666389  2.7126760 0.00667423 0.0777521   239.867
gene5   92.2048  0.5816079  0.605222  0.9609821 0.33656118 0.6731224   214.935
gene6  114.1850  0.0291906  0.505099  0.0577918 0.95391447 0.9671968   250.043
            BIC
      <numeric>
gene1   239.106
gene2   206.172
gene3   223.584
gene4   246.837
gene5   221.905
gene6   257.013

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   92.6186  0.773449   1.06342  0.727320  0.467030  0.686809   232.136
gene2   89.9338  3.090815   1.20817  2.558252  0.010520  0.131500   199.202
gene3   62.5782 -1.503919   1.08568 -1.385238  0.165980  0.593131   216.614
gene4  172.5156  1.450402   1.31918  1.099469  0.271563  0.686236   239.867
gene5   92.2048  0.361470   1.20275  0.300536  0.763768  0.844027   214.935
gene6  114.1850 -0.394863   1.00374 -0.393392  0.694030  0.835123   250.043
            BIC
      <numeric>
gene1   239.106
gene2   206.172
gene3   223.584
gene4   246.837
gene5   221.905
gene6   257.013

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>
gene17   61.0425   1.00003  14.56663 0.000135698 0.00678491   172.904   179.874
gene8   100.5595   1.00014  10.06430 0.001513774 0.03784435   216.902   223.872
gene9   116.1673   1.00005   6.18501 0.012887067 0.21478446   227.740   234.711
gene23  136.1298   1.00007   5.61030 0.017858099 0.22322623   205.764   212.734
gene40  111.8965   1.00013   5.12068 0.023663514 0.23663514   241.243   248.213
gene42   48.7367   1.00010   3.91510 0.047873535 0.31673854   198.574   205.544

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 4.5.2 (2025-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        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: Etc/UTC
tzcode source: system (glibc)

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] ggplot2_4.0.1               BiocParallel_1.44.0        
 [3] NBAMSeq_1.26.0              SummarizedExperiment_1.40.0
 [5] Biobase_2.70.0              GenomicRanges_1.62.1       
 [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           rmarkdown_2.30             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.50.0      gtable_0.3.6         xfun_0.56           
 [4] bslib_0.10.0         lattice_0.22-7       vctrs_0.7.1         
 [7] tools_4.5.2          parallel_4.5.2       AnnotationDbi_1.72.0
[10] RSQLite_2.4.5        blob_1.3.0           Matrix_1.7-4        
[13] RColorBrewer_1.1-3   S7_0.2.1             lifecycle_1.0.5     
[16] compiler_4.5.2       farver_2.1.2         Biostrings_2.78.0   
[19] DESeq2_1.50.2        codetools_0.2-20     htmltools_0.5.9     
[22] sys_3.4.3            buildtools_1.0.0     sass_0.4.10         
[25] yaml_2.3.12          crayon_1.5.3         jquerylib_0.1.4     
[28] DelayedArray_0.36.0  cachem_1.1.0         abind_1.4-8         
[31] nlme_3.1-168         genefilter_1.92.0    locfit_1.5-9.12     
[34] digest_0.6.39        labeling_0.4.3       splines_4.5.2       
[37] maketools_1.3.2      fastmap_1.2.0        grid_4.5.2          
[40] cli_3.6.5            SparseArray_1.10.8   S4Arrays_1.10.1     
[43] survival_3.8-6       XML_3.99-0.20        withr_3.0.2         
[46] scales_1.4.0         bit64_4.6.0-1        XVector_0.50.0      
[49] httr_1.4.7           bit_4.6.0            png_0.1-8           
[52] memoise_2.0.1        evaluate_1.0.5       knitr_1.51          
[55] mgcv_1.9-4           rlang_1.1.7          Rcpp_1.1.1          
[58] xtable_1.8-4         glue_1.8.0           DBI_1.2.3           
[61] annotate_1.88.0      jsonlite_2.0.0       R6_2.6.1