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     115      12      11       3      38     251     152      29
gene2      59       1     426     146     149      11       2       2      53
gene3     229      19       7      45       2      49     168       2     238
gene4     107     202     175     164     180      30      24       1      57
gene5       1       9      74       1      52       1      71      93       3
gene6      15       1     258     158     641     546      28       1      79
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        2       50       89        1        9      195      868        1
gene2       18      107        1        4      311       54       48       21
gene3       64      400        2        1      154       34        2      149
gene4       55       33        5       37        6       54        3        1
gene5       19      172        1      231       82        1       16        4
gene6      131       13        1       74       24      318      137        1
      sample18 sample19 sample20
gene1        1      223       13
gene2       72       76        5
gene3      123       26      345
gene4        1       57       10
gene5       22      158        9
gene6      184       15        3

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 28.39888 -1.6106449  0.2443170 -0.5759374    0
sample2 79.81509  0.5498255 -0.4128137  0.6991743    0
sample3 62.28843  1.0343489 -0.6954318 -1.2310704    2
sample4 28.97321  0.0309453  0.3888532  0.4492495    2
sample5 35.82154  1.7102626 -0.1733975 -0.9668859    2
sample6 72.61076 -0.9727160 -1.3187190  0.7868464    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   92.4920   1.00006 10.25188401 0.00136613 0.0170766   206.738   213.708
gene2   79.5869   1.00010  1.20410221 0.27256482 0.6344286   218.035   225.005
gene3   86.5747   1.00009  0.39571559 0.52936692 0.8881424   227.677   234.647
gene4   60.5333   1.00009  0.00826058 0.92790772 0.9953966   212.979   219.949
gene5   45.3715   1.00004  1.34049508 0.24697495 0.6344286   194.630   201.600
gene6  105.1258   1.00018  0.01158613 0.91494663 0.9953966   231.648   238.619

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   92.4920  0.9009801  0.334242  2.695590 0.00702641  0.175660   206.738
gene2   79.5869  0.3269240  0.357601  0.914215 0.36060412  0.593489   218.035
gene3   86.5747 -0.8053223  0.351625 -2.290290 0.02200452  0.203750   227.677
gene4   60.5333  0.3229310  0.349738  0.923351 0.35582454  0.593489   212.979
gene5   45.3715  1.0794116  0.354387  3.045851 0.00232022  0.116011   194.630
gene6  105.1258 -0.0558527  0.379107 -0.147327 0.88287400  0.911519   231.648
            BIC
      <numeric>
gene1   213.708
gene2   225.005
gene3   234.647
gene4   219.949
gene5   201.600
gene6   238.619

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   92.4920  0.5411526  0.887028  0.6100740 0.5418128  0.774018   206.738
gene2   79.5869  1.0834430  0.939071  1.1537397 0.2486069  0.540450   218.035
gene3   86.5747  0.0299274  0.919879  0.0325340 0.9740462  0.974046   227.677
gene4   60.5333 -1.5189900  0.913979 -1.6619522 0.0965224  0.523307   212.979
gene5   45.3715  0.0481165  0.935906  0.0514116 0.9589975  0.974046   194.630
gene6  105.1258  0.9730234  0.990318  0.9825364 0.3258357  0.581849   231.648
            BIC
      <numeric>
gene1   213.708
gene2   225.005
gene3   234.647
gene4   219.949
gene5   201.600
gene6   238.619

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>
gene10  115.7011   1.00017  15.57843 7.99153e-05 0.00399577   218.740   225.710
gene8    57.1378   1.00008  10.71468 1.06346e-03 0.01707657   202.394   209.364
gene31  165.5349   1.00011  10.44319 1.23227e-03 0.01707657   232.138   239.108
gene1    92.4920   1.00006  10.25188 1.36613e-03 0.01707657   206.738   213.708
gene36   75.6337   1.00005   6.36120 1.16664e-02 0.11666424   206.256   213.226
gene17  155.4186   1.00009   3.84429 4.99324e-02 0.38639093   242.841   249.811

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 4.6.1 (2026-06-24)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 26.04 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-r0.3.32.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=en_US.UTF-8    
 [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_4.0.3               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_2.47.2             
 [9] S4Vectors_0.51.5            BiocGenerics_0.59.9        
[11] generics_0.1.4              MatrixGenerics_1.25.0      
[13] matrixStats_1.5.0           rmarkdown_2.31             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.53.4      gtable_0.3.6         xfun_0.59           
 [4] bslib_0.11.0         lattice_0.22-9       vctrs_0.7.3         
 [7] tools_4.6.1          parallel_4.6.1       AnnotationDbi_1.75.0
[10] RSQLite_3.53.3       blob_1.3.0           Matrix_1.7-5        
[13] RColorBrewer_1.1-3   S7_0.2.2             lifecycle_1.0.5     
[16] compiler_4.6.1       farver_2.1.2         Biostrings_2.81.3   
[19] DESeq2_1.53.0        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_0.39.3  cachem_1.1.0         abind_1.4-8         
[31] nlme_3.1-169         genefilter_1.95.0    locfit_1.5-9.12     
[34] digest_0.6.39        labeling_0.4.3       splines_4.6.1       
[37] maketools_1.3.2      fastmap_1.2.0        grid_4.6.1          
[40] cli_3.6.6            SparseArray_1.13.2   S4Arrays_1.13.0     
[43] survival_3.8-6       XML_3.99-0.23        withr_3.0.3         
[46] scales_1.4.0         bit64_4.8.2          XVector_0.53.0      
[49] httr_1.4.8           bit_4.6.0            otel_0.2.0          
[52] png_0.1-9            memoise_2.0.1        evaluate_1.0.5      
[55] knitr_1.51           mgcv_1.9-4           rlang_1.2.0         
[58] Rcpp_1.1.1-1.1       xtable_1.8-8         glue_1.8.1          
[61] DBI_1.3.0            annotate_1.91.0      jsonlite_2.0.0      
[64] R6_2.6.1