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      95      75      25      15       1      13       9     122      78
gene2       5       4       1      17      14      32     179       1       1
gene3       2     112      49      29     737      41     189      52      13
gene4      12       4      60     426     502       3     315      88     379
gene5      40       2      10      21      18      24       1      78      63
gene6     455      55     155     482     317       1      64      31       1
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1      505        1       53       18        1      297      180
gene2      109        2        1      142        1       45        1        3
gene3        3       66      433      491        1       44       34        1
gene4      229       93        2       10       33        7      269       60
gene5      137       59      154       45       38        3      309      426
gene6        1      176        7        1        2        1       21        1
      sample18 sample19 sample20
gene1      117       42       70
gene2       42      425       46
gene3       21       41        7
gene4      124      256        4
gene5       24        6      773
gene6      282        2      584

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 27.34509  1.3950252 -0.86961843  1.559718431    2
sample2 38.82249  0.6909785 -1.14926454 -0.005511607    2
sample3 22.28316  2.3473260  0.88241085 -0.624859041    2
sample4 52.22037  0.5876980 -0.77637298 -0.376341252    0
sample5 33.31987 -1.6537328  0.44375437 -0.788551373    1
sample6 50.81314  1.5055999 -0.05318027  0.281177932    1

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   68.2967   1.00006 1.3829747  0.239630  0.499367   225.925   232.896
gene2   42.5276   1.00013 2.0997861  0.147363  0.449838   194.148   201.118
gene3   87.9044   1.00012 0.3816055  0.536811  0.813349   231.892   238.862
gene4   91.8586   1.00012 0.6792965  0.409926  0.732010   240.280   247.250
gene5   87.6959   1.00053 0.0211743  0.885951  0.914422   232.614   239.585
gene6   88.3517   1.00013 1.9435339  0.163294  0.449838   218.065   225.035

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   68.2967  0.476100  0.454574  1.047353 0.2949370  0.641442   225.925
gene2   42.5276 -0.409998  0.501045 -0.818286 0.4131938  0.645615   194.148
gene3   87.9044 -0.553788  0.458570 -1.207640 0.2271859  0.641442   231.892
gene4   91.8586 -0.388925  0.403980 -0.962733 0.3356814  0.641442   240.280
gene5   87.6959 -0.621959  0.440800 -1.410978 0.1582510  0.565182   232.614
gene6   88.3517  0.925041  0.494261  1.871563 0.0612671  0.340373   218.065
            BIC
      <numeric>
gene1   232.896
gene2   201.118
gene3   238.862
gene4   247.250
gene5   239.585
gene6   225.035

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   68.2967 -1.200968   1.12625 -1.0663387  0.286271  0.624520   225.925
gene2   42.5276 -0.840691   1.24075 -0.6775676  0.498046  0.690239   194.148
gene3   87.9044  0.319122   1.13285  0.2816989  0.778174  0.849418   231.892
gene4   91.8586 -0.907549   0.99979 -0.9077401  0.364016  0.624520   240.280
gene5   87.6959 -0.838869   1.09044 -0.7692931  0.441719  0.675674   232.614
gene6   88.3517 -0.113209   1.22939 -0.0920857  0.926630  0.943969   218.065
            BIC
      <numeric>
gene1   232.896
gene2   201.118
gene3   238.862
gene4   247.250
gene5   239.585
gene6   225.035

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric> <numeric> <numeric> <numeric>
gene46   62.2706   1.00009  13.20936 0.000278748 0.0139374   205.376   212.346
gene38  131.1233   1.00006   8.53648 0.003481852 0.0654754   225.018   231.988
gene33   74.7865   1.00007   8.31729 0.003928524 0.0654754   199.203   206.173
gene31   61.9187   1.00138   7.31453 0.006850542 0.0856318   209.838   216.810
gene7    68.4228   1.00021   5.97739 0.014491945 0.1294200   214.149   221.119
gene24  130.4832   1.00005   5.85593 0.015530405 0.1294200   207.197   214.167
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 RC (2025-04-04 r88126)
Platform: aarch64-apple-darwin20
Running under: macOS Ventura 13.7.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/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_1.42.0        
 [3] NBAMSeq_1.24.0              SummarizedExperiment_1.38.0
 [5] Biobase_2.68.0              GenomicRanges_1.60.0       
 [7] GenomeInfoDb_1.44.0         IRanges_2.42.0             
 [9] S4Vectors_0.46.0            BiocGenerics_0.54.0        
[11] generics_0.1.3              MatrixGenerics_1.20.0      
[13] matrixStats_1.5.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.48.0         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_1.70.0    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_2.76.0       munsell_0.5.1           DESeq2_1.48.0          
[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_0.34.0     cachem_1.1.0           
[31] abind_1.4-8             nlme_3.1-168            genefilter_1.90.0      
[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_3.6.4               SparseArray_1.8.0       magrittr_2.0.3         
[46] S4Arrays_1.8.0          survival_3.8-3          XML_3.99-0.18          
[49] withr_3.0.2             scales_1.3.0            UCSC.utils_1.4.0       
[52] bit64_4.6.0-1           rmarkdown_2.29          XVector_0.48.0         
[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_1.86.0         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): 2672–78.