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:

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       1     622       3       1      55     480       5     123     107
gene2      44     105      73       1      22     297     431       1     443
gene3      40     377     172      30      25       8       5      23     135
gene4       2     137      20      96       8       3     145       1       9
gene5      29      36      93      44     149       1      54     146       1
gene6       5       1     265      12      21     275       1       1      33
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      612       38       21        2        3       80      108       89
gene2       14       27       83       43        4       13       50        1
gene3        1      831       35        9      173        5      164        5
gene4        2      104      294      114       85      120      260        1
gene5       19       14       24       54       28       25       12       54
gene6       99        1      412       10       74        1       51       80
      sample18 sample19 sample20
gene1       41        6      324
gene2        4      132      213
gene3       46      343      193
gene4        6        1        4
gene5       31       70        2
gene6        8       39       53

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 23.46853 -0.8107729  1.1672727 -0.9758171    2
sample2 30.11858 -0.1677050 -0.8317767 -0.9979414    1
sample3 75.40656  0.5406788 -0.5764541 -0.1479813    1
sample4 41.90524 -0.1856598 -0.9826310  2.0318533    2
sample5 76.04125  2.0879219  1.7203353 -0.3404363    1
sample6 42.80713 -0.8261199  0.8607129 -0.4904841    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:

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.

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  108.0045   1.00006  0.543868 0.4609310  0.746769   234.980   241.950
gene2   86.8759   1.00006  0.272677 0.6015919  0.791378   229.024   235.995
gene3  123.5539   1.00007  0.249200 0.6176760  0.791378   235.126   242.096
gene4   49.9436   1.00018  0.865087 0.3522740  0.715972   206.312   213.282
gene5   40.6054   1.00004  1.491237 0.2220338  0.580245   206.313   213.284
gene6   59.9212   1.00004  2.728438 0.0985781  0.410742   210.434   217.404

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  108.0045 -0.3618531  0.436487 -0.8290125  0.407097  0.709718   234.980
gene2   86.8759 -0.2633533  0.412891 -0.6378281  0.523586  0.805055   229.024
gene3  123.5539  0.2043466  0.378848  0.5393888  0.589619  0.805055   235.126
gene4   49.9436 -0.5430207  0.391187 -1.3881369  0.165095  0.405787   206.312
gene5   40.6054  0.4888901  0.330508  1.4792065  0.139085  0.386348   206.313
gene6   59.9212 -0.0410265  0.415154 -0.0988223  0.921279  0.980084   210.434
            BIC
      <numeric>
gene1   241.950
gene2   235.995
gene3   242.096
gene4   213.282
gene5   213.284
gene6   217.404

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  108.0045  0.697545  1.122008  0.621693 0.53414365  0.763516   234.980
gene2   86.8759 -0.690297  1.059487 -0.651539 0.51469874  0.763516   229.024
gene3  123.5539 -2.543048  0.973513 -2.612238 0.00899515  0.112439   235.126
gene4   49.9436 -0.222265  1.000601 -0.222131 0.82421154  0.925469   206.312
gene5   40.6054  0.731280  0.853571  0.856731 0.39159370  0.716784   206.313
gene6   59.9212  1.491542  1.066900  1.398014 0.16210879  0.470570   210.434
            BIC
      <numeric>
gene1   241.950
gene2   235.995
gene3   242.096
gene4   213.282
gene5   213.284
gene6   217.404

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene38  104.8909   1.00010   6.82526 0.00899020  0.223544   219.327   226.298
gene30   55.8566   1.00006   6.77117 0.00926886  0.223544   209.464   216.434
gene28  105.8213   1.00007   5.64262 0.01753244  0.223544   215.458   222.428
gene40   23.3175   1.00009   5.60820 0.01788352  0.223544   171.626   178.596
gene49   66.8204   1.00006   4.05882 0.04395746  0.375988   203.090   210.060
gene29   57.4066   1.00008   4.01471 0.04511861  0.375988   215.849   222.819
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.5.0 Patched (2025-04-21 r88169)
Platform: x86_64-apple-darwin20
Running under: macOS Monterey 12.7.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

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

other attached packages:
 [1] ggplot2_3.5.2               BiocParallel_1.43.0        
 [3] NBAMSeq_1.25.0              SummarizedExperiment_1.39.0
 [5] Biobase_2.69.0              GenomicRanges_1.61.0       
 [7] GenomeInfoDb_1.45.0         IRanges_2.43.0             
 [9] S4Vectors_0.47.0            BiocGenerics_0.55.0        
[11] generics_0.1.3              MatrixGenerics_1.21.0      
[13] matrixStats_1.5.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.49.0         gtable_0.3.6            xfun_0.52              
 [4] bslib_0.9.0             lattice_0.22-7          vctrs_0.6.5            
 [7] tools_4.5.0             parallel_4.5.0          tibble_3.2.1           
[10] AnnotationDbi_1.71.0    RSQLite_2.3.9           blob_1.2.4             
[13] pkgconfig_2.0.3         Matrix_1.7-3            lifecycle_1.0.4        
[16] GenomeInfoDbData_1.2.14 farver_2.1.2            compiler_4.5.0         
[19] Biostrings_2.77.0       munsell_0.5.1           DESeq2_1.49.0          
[22] codetools_0.2-20        htmltools_0.5.8.1       sass_0.4.10            
[25] yaml_2.3.10             pillar_1.10.2           crayon_1.5.3           
[28] jquerylib_0.1.4         DelayedArray_0.35.1     cachem_1.1.0           
[31] abind_1.4-8             nlme_3.1-168            genefilter_1.91.0      
[34] tidyselect_1.2.1        locfit_1.5-9.12         digest_0.6.37          
[37] dplyr_1.1.4             labeling_0.4.3          splines_4.5.0          
[40] fastmap_1.2.0           grid_4.5.0              colorspace_2.1-1       
[43] cli_3.6.5               SparseArray_1.9.0       magrittr_2.0.3         
[46] S4Arrays_1.9.0          survival_3.8-3          XML_3.99-0.18          
[49] withr_3.0.2             scales_1.3.0            UCSC.utils_1.5.0       
[52] bit64_4.6.0-1           rmarkdown_2.29          XVector_0.49.0         
[55] httr_1.4.7              bit_4.6.0               png_0.1-8              
[58] memoise_2.0.1           evaluate_1.0.3          knitr_1.50             
[61] mgcv_1.9-3              rlang_1.1.6             Rcpp_1.0.14            
[64] xtable_1.8-4            glue_1.8.0              DBI_1.2.3              
[67] annotate_1.87.0         jsonlite_2.0.0          R6_2.6.1               

References

Di, Y, DW Schafer, JS Cumbie, and JH Chang. 2015. “NBPSeq: Negative Binomial Models for Rna-Sequencing Data.” R Package Version 0.3. 0, URL Http://CRAN. R-Project. Org/Package= NBPSeq.

Love, Michael I, Wolfgang Huber, and Simon Anders. 2014. “Moderated Estimation of Fold Change and Dispersion for Rna-Seq Data with Deseq2.” Genome Biology 15 (12): 550.

Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “EdgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.

Wood, Simon, and Maintainer Simon Wood. 2015. “Package ’Mgcv’.” R Package Version 1: 29.

Zhou, Yi-Hui, Kai Xia, and Fred A Wright. 2011. “A Powerful and Flexible Approach to the Analysis of Rna Sequence Count Data.” Bioinformatics 27 (19): 2672–8.