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       2      14       3     107     139     566       4     152     333
gene2      17     120     232      44      64     172       1      82      25
gene3     195       3     164      89       1      10      66     577       1
gene4     996      15      16      55       1      42      28      31      78
gene5      26       6      10      63      10     138       9     205      21
gene6     165       9      52     113      66      33     489      15       3
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       53        3       64       63      108        2        4       18
gene2      118        8      325      144        2       10        6       11
gene3        1       13       22        1      271       15        4        1
gene4        9       13      610      400       44        1        3       10
gene5        1      136       19        2        6      855        1       94
gene6       20      317        1      330        3        4        7        9
      sample18 sample19 sample20
gene1        2       23       42
gene2        9        7      320
gene3       50       76        1
gene4      221      184       34
gene5        1       25      168
gene6      104        2       56

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 47.47630 -0.50844573  0.8444654  1.7657766    2
sample2 27.09050  3.00503740 -1.1390582 -0.3297468    1
sample3 45.10318  0.67057257 -0.2991542 -1.0058662    2
sample4 66.43527 -0.64650174 -0.2173750 -0.6524994    0
sample5 52.81253 -0.08645734  1.3812596 -0.1688391    0
sample6 73.25089 -0.42856981 -0.5161098 -0.3328764    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   81.5905   1.00011 4.250535345 0.0392339  0.217966   220.821   227.791
gene2   81.7964   1.00006 0.083289376 0.7729888  0.962631   227.037   234.007
gene3   57.3312   1.00021 0.514968064 0.4732035  0.845006   202.164   209.134
gene4  106.7823   1.00010 0.186583574 0.6658814  0.962631   233.508   240.478
gene5   81.8982   1.00007 0.000342507 0.9870132  0.988737   208.308   215.278
gene6   73.9153   1.00017 0.994122571 0.3188422  0.693135   224.998   231.968

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   81.5905 -0.0917766  0.316776 -0.289721 0.77202980 0.9223307   220.821
gene2   81.7964  0.3209239  0.298478  1.075201 0.28228493 0.5818009   227.037
gene3   57.3312 -0.9287660  0.327820 -2.833161 0.00460901 0.0749855   202.164
gene4  106.7823  0.1178443  0.314359  0.374872 0.70775572 0.9073791   233.508
gene5   81.8982 -0.8746992  0.298906 -2.926332 0.00342984 0.0749855   208.308
gene6   73.9153 -0.2429122  0.324901 -0.747650 0.45467103 0.7116158   224.998
            BIC
      <numeric>
gene1   227.791
gene2   234.007
gene3   209.134
gene4   240.478
gene5   215.278
gene6   231.968

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   81.5905  0.00487856  1.013834  0.0048120 0.9961606  0.996161   220.821
gene2   81.7964 -0.02766236  0.958122 -0.0288715 0.9769671  0.996161   227.037
gene3   57.3312  2.10487296  1.040255  2.0234195 0.0430299  0.269747   202.164
gene4  106.7823 -0.60462447  1.006321 -0.6008264 0.5479556  0.899988   233.508
gene5   81.8982  2.31029578  0.958465  2.4104119 0.0159345  0.199181   208.308
gene6   73.9153 -0.51812941  1.040175 -0.4981174 0.6184013  0.899988   224.998
            BIC
      <numeric>
gene1   227.791
gene2   234.007
gene3   209.134
gene4   240.478
gene5   215.278
gene6   231.968

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>
gene9    43.8037   1.00006  12.08903 0.000507588 0.0169980   179.439   186.410
gene31   35.8852   1.00010  11.54452 0.000679919 0.0169980   182.119   189.089
gene30   98.8739   1.00008   8.79875 0.003015749 0.0455271   225.777   232.747
gene19  100.5479   1.00005   8.45476 0.003642166 0.0455271   227.430   234.400
gene32   38.8564   1.29690   6.82945 0.010638396 0.1063840   186.422   193.688
gene38   63.2716   1.00013   6.07410 0.013726559 0.1143880   209.216   216.186

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_1.62.0       
 [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           rmarkdown_2.30             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.50.0      gtable_0.3.6         xfun_0.54           
 [4] bslib_0.9.0          lattice_0.22-7       vctrs_0.6.5         
 [7] tools_4.5.2          parallel_4.5.2       AnnotationDbi_1.72.0
[10] RSQLite_2.4.4        blob_1.2.4           Matrix_1.7-4        
[13] RColorBrewer_1.1-3   S7_0.2.1             lifecycle_1.0.4     
[16] compiler_4.5.2       farver_2.1.2         Biostrings_2.78.0   
[19] DESeq2_1.50.2        codetools_0.2-20     htmltools_0.5.8.1   
[22] sys_3.4.3            buildtools_1.0.0     sass_0.4.10         
[25] yaml_2.3.10          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_0.6.38        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_1.10.2   S4Arrays_1.10.0     
[43] survival_3.8-3       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_1.50          
[55] mgcv_1.9-4           rlang_1.1.6          Rcpp_1.1.0          
[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