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     362      99      30     198      50     205    1004       1       4
gene2      68     203      21       1       3       7     383     136       1
gene3     100       2      72     411       1      94       1      24    1016
gene4      75       1       5       3     239     136       1     112     159
gene5       1       2       2     247       1      14       8      42       1
gene6      99       4     161       1      58     292      84      78     327
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1      114      137      621       86       37       55      390
gene2        1        1       59      302        4      120        1        1
gene3        2      214      107        2        3        1       14      350
gene4      154        5        1        1      257      202        8       60
gene5       91        3        1       15      611       11      133       55
gene6        6      419       75        2      124       11       28      208
      sample18 sample19 sample20
gene1        4        1       66
gene2        1        3       29
gene3      133       18        1
gene4        9      944       19
gene5        2      449        1
gene6        1        1       78

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 71.46650 -0.5844264 -0.4820340 -0.4881706    2
sample2 68.09191 -0.8131958 -0.2271750  0.6425904    2
sample3 60.89671  0.7265568 -1.0284718 -0.3172808    1
sample4 57.37460  1.3896376  0.2626334 -0.3929028    1
sample5 58.91808 -0.1657358 -0.1899554 -0.1090908    2
sample6 34.87496 -0.9335635 -1.2951848 -0.6174054    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  150.7387   1.00013  1.249270  0.263789  0.628069   239.461   246.431
gene2   64.5329   1.00008  0.309777  0.577916  0.760416   196.604   203.574
gene3   87.0460   1.00013  2.062489  0.151060  0.545348   214.961   221.931
gene4   83.6408   1.00005  1.688653  0.193812  0.545348   221.024   227.994
gene5   67.0265   1.00009  0.705505  0.401047  0.661271   195.399   202.369
gene6   73.4943   1.00008  0.773750  0.379115  0.661271   227.415   234.385

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  150.7387  0.712834  0.419415  1.699592 0.0892077  0.319007   239.461
gene2   64.5329  0.243510  0.525999  0.462948 0.6434019  0.804252   196.604
gene3   87.0460 -0.458662  0.488137 -0.939618 0.3474133  0.637882   214.961
gene4   83.6408 -0.959662  0.488031 -1.966395 0.0492530  0.262808   221.024
gene5   67.0265  0.320697  0.502104  0.638706 0.5230142  0.670531   195.399
gene6   73.4943 -0.988854  0.451283 -2.191208 0.0284368  0.203120   227.415
            BIC
      <numeric>
gene1   246.431
gene2   203.574
gene3   221.931
gene4   227.994
gene5   202.369
gene6   234.385

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  150.7387  1.020057   1.02308  0.997048 0.3187410  0.667994   239.461
gene2   64.5329  1.388972   1.28611  1.079976 0.2801528  0.667994   196.604
gene3   87.0460 -2.210757   1.18267 -1.869291 0.0615823  0.621327   214.961
gene4   83.6408 -0.980174   1.17224 -0.836155 0.4030677  0.683528   221.024
gene5   67.0265 -1.887256   1.22779 -1.537114 0.1242654  0.621327   195.399
gene6   73.4943 -2.100280   1.09421 -1.919446 0.0549279  0.621327   227.415
            BIC
      <numeric>
gene1   246.431
gene2   203.574
gene3   221.931
gene4   227.994
gene5   202.369
gene6   234.385

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
       <numeric> <numeric> <numeric>   <numeric>   <numeric> <numeric>
gene29   65.3758   1.00005  19.27253 1.10635e-05 0.000553173   192.335
gene8    68.7211   1.00009   5.86938 1.54103e-02 0.296901740   208.664
gene23   25.8957   1.00002   5.41628 1.99521e-02 0.296901740   178.977
gene41  139.3659   1.00104   5.12524 2.37521e-02 0.296901740   235.926
gene42   45.6660   1.00008   4.53856 3.31486e-02 0.331485615   195.997
gene47   35.3567   1.00004   3.34273 6.75148e-02 0.545348067   183.351
             BIC
       <numeric>
gene29   199.305
gene8    215.634
gene23   185.947
gene41   242.898
gene42   202.967
gene47   190.321

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_1.46.0        
 [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_0.50.3            BiocGenerics_0.58.1        
[11] generics_0.1.4              MatrixGenerics_1.24.0      
[13] matrixStats_1.5.0           rmarkdown_2.32             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.52.2      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_1.74.0
[10] RSQLite_3.53.3       blob_1.3.0           Matrix_1.7-6        
[13] RColorBrewer_1.1-3   S7_0.2.2             lifecycle_1.0.5     
[16] compiler_4.6.1       farver_2.1.2         Biostrings_2.80.2   
[19] DESeq2_1.52.0        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_0.38.2  cachem_1.1.0         abind_1.4-8         
[31] nlme_3.1-171         genefilter_1.94.0    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_1.12.3   S4Arrays_1.12.1     
[43] survival_3.8-12      XML_3.99-0.24        withr_3.0.3         
[46] scales_1.4.0         bit64_4.8.6          XVector_0.52.0      
[49] httr_1.4.9           bit_4.6.0            otel_0.2.0          
[52] png_0.1-9            memoise_2.0.1        evaluate_1.0.5      
[55] knitr_1.52           mgcv_1.9-4           rlang_1.3.0         
[58] Rcpp_1.1.2           xtable_1.8-8         glue_1.8.1          
[61] DBI_1.3.0            annotate_1.90.0      jsonlite_2.0.0      
[64] R6_2.6.1