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      78       1     534       1       1       5     158       3      12
gene2      14     375      23       1     106       1       7      80     355
gene3     808       1      61      49     440     518      29     587     177
gene4     124      13       2      22     239     122       8       8      95
gene5      51      92       1     189      58     246     108      16       5
gene6      55       1      25       1      20      17     510      70     203
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      238       58        2        4       71       38        7        1
gene2       31        1       69        1        4       73        2       18
gene3      349       36      258        3        1        1      280       16
gene4       15        2       49        5        1       10       42        1
gene5       63       21        2       57        1       16      251       52
gene6       31       61        3      336        4        1       75       59
      sample18 sample19 sample20
gene1       48      203        2
gene2       13      136        6
gene3        1        3      177
gene4     1467      297        1
gene5      181      355        2
gene6       61       43       37

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 56.26184  0.4651506 -0.38889571  0.74250174    0
sample2 60.19626  1.4625902 -0.07242863  0.04894054    0
sample3 79.84873  1.1603969 -0.10579025 -1.19299103    2
sample4 21.11003 -1.0029060 -0.84281128  0.91089799    2
sample5 22.39980  0.9917519  1.02071391 -0.17346598    0
sample6 25.89588 -0.1541380 -0.29073336  0.08104339    1

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   62.5795   1.00030 0.08912393  0.765908  0.870350   200.844   207.815
gene2   49.2855   1.00009 0.00754922  0.931163  0.977512   209.057   216.027
gene3  147.6528   1.00006 0.84222951  0.358801  0.578711   244.713   251.683
gene4   70.2925   1.00007 0.47257226  0.491830  0.683097   210.137   217.107
gene5   68.1473   1.00008 0.16779685  0.682166  0.852554   227.500   234.470
gene6   62.5698   1.00006 0.19525218  0.658574  0.852554   216.654   223.624

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   62.5795  1.193725  0.482201  2.475573 0.0133022  0.137443   200.844
gene2   49.2855  0.211859  0.498410  0.425069 0.6707862  0.859982   209.057
gene3  147.6528 -0.645195  0.491997 -1.311380 0.1897294  0.493094   244.713
gene4   70.2925 -0.602794  0.471338 -1.278901 0.2009319  0.493094   210.137
gene5   68.1473 -0.212429  0.448893 -0.473230 0.6360493  0.859982   227.500
gene6   62.5698  1.032723  0.429373  2.405189 0.0161641  0.137443   216.654
            BIC
      <numeric>
gene1   207.815
gene2   216.027
gene3   251.683
gene4   217.107
gene5   234.470
gene6   223.624

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   62.5795  2.2770307  1.021623  2.228837 0.0258247  0.258247   200.844
gene2   49.2855 -0.0408023  1.059498 -0.038511 0.9692802  0.989061   209.057
gene3  147.6528 -1.4016881  1.045345 -1.340886 0.1799575  0.562367   244.713
gene4   70.2925 -2.4125740  1.002978 -2.405411 0.0161543  0.258247   210.137
gene5   68.1473 -0.4423372  0.955427 -0.462973 0.6433837  0.953164   227.500
gene6   62.5698  1.7687594  0.908419  1.947075 0.0515257  0.368041   216.654
            BIC
      <numeric>
gene1   207.815
gene2   216.027
gene3   251.683
gene4   217.107
gene5   234.470
gene6   223.624

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>
gene50  103.2176   1.00005  10.32925 0.00130974 0.0416764   222.568   229.538
gene29  112.0500   1.00004   9.21630 0.00239955 0.0416764   215.376   222.346
gene8   169.0703   1.00004   9.14092 0.00250059 0.0416764   227.629   234.599
gene19  117.1119   1.00006   6.47899 0.01091870 0.1248261   234.559   241.529
gene43   68.6785   1.00018   6.17377 0.01296791 0.1248261   205.487   212.457
gene22  111.9889   1.00018   5.70075 0.01697420 0.1248261   244.531   251.502

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 26.04.1 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_2.73.2              GenomicRanges_1.65.4       
 [7] Seqinfo_1.3.2               IRanges_2.47.5             
 [9] S4Vectors_0.51.10           BiocGenerics_0.59.12       
[11] generics_0.1.4              MatrixGenerics_1.25.0      
[13] matrixStats_1.5.0           rmarkdown_2.32             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.53.6      gtable_0.3.6         xfun_0.61           
 [4] bslib_0.12.0         lattice_0.23-1       vctrs_0.7.3         
 [7] tools_4.6.1          parallel_4.6.1       AnnotationDbi_1.75.2
[10] RSQLite_3.53.3       blob_1.3.0           BiocBaseUtils_1.15.1
[13] Matrix_1.7-6         RColorBrewer_1.1-3   S7_0.2.2            
[16] lifecycle_1.0.5      compiler_4.6.1       farver_2.1.2        
[19] Biostrings_2.81.9    DESeq2_1.53.3        codetools_0.2-20    
[22] htmltools_0.5.9      sys_3.4.3            buildtools_1.0.0    
[25] sass_0.4.10          yaml_2.3.12          crayon_1.5.3        
[28] jquerylib_0.1.4      DelayedArray_0.39.6  cachem_1.1.0        
[31] abind_1.4-8          nlme_3.1-171         genefilter_1.95.0   
[34] locfit_1.5-9.12      digest_0.6.39        labeling_0.4.3      
[37] splines_4.6.1        maketools_1.3.2      fastmap_1.2.0       
[40] grid_4.6.1           cli_3.6.6            SparseArray_1.13.2  
[43] S4Arrays_1.13.0      survival_3.8-12      XML_3.99-0.24       
[46] withr_3.0.3          scales_1.4.0         bit64_4.8.6         
[49] XVector_0.53.0       httr_1.4.9           bit_4.6.0           
[52] otel_0.2.0           png_0.1-9            memoise_2.0.1       
[55] evaluate_1.0.5       knitr_1.52           mgcv_1.9-4          
[58] rlang_1.3.0          Rcpp_1.1.2           xtable_1.8-8        
[61] glue_1.8.1           DBI_1.3.0            annotate_1.91.0     
[64] jsonlite_2.0.0       R6_2.6.1