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       7       5      96       6     109      21       7      46      37
gene2       1      57     190      97     213       1      74     867      49
gene3       1      11      83     195       2     121     288      10      64
gene4      33     373     126      58      10      58     339     143      72
gene5      17      66     719       4      30      71       1      54       1
gene6       1       4      24       1       1     116       6      17       8
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      120       16      104      194        1       24       18      168
gene2      296       54       62      185        1      233       52      306
gene3       41        4        1        1      157        2       41       72
gene4        6        1        1        3       93      550       55      211
gene5       60       12      548        2      257      118       49       12
gene6      416       27        1        1       46      159      197      116
      sample18 sample19 sample20
gene1       20        5       17
gene2       36       40        1
gene3       36      336      805
gene4        1       29      237
gene5        4       27       82
gene6       98        4      616

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 28.65312 -0.8103270  1.98174321 -0.1919243    0
sample2 53.45100 -0.3180619 -0.09926992 -0.2116536    1
sample3 31.35403 -0.2295486 -0.46044418  0.4566301    2
sample4 65.41978  0.2195668  1.54815427  0.8581354    0
sample5 75.81841  0.2897221 -1.20943558  0.4738816    1
sample6 35.60605  0.8436993 -0.32202641 -0.6438498    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   45.2064   1.00008 0.17650904 0.6744367  0.807882   207.764   214.734
gene2  132.3282   1.00008 0.17175108 0.6786206  0.807882   243.256   250.226
gene3   74.6210   1.00025 0.00130449 0.9748719  0.994767   217.664   224.635
gene4  100.3924   1.00008 2.46764143 0.1162332  0.371877   237.495   244.465
gene5   80.6177   1.00010 5.69143342 0.0170548  0.120953   219.484   226.455
gene6   82.2199   1.00010 0.80869480 0.3685670  0.658155   212.160   219.131

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   45.2064  0.5597904  0.418402  1.3379234  0.180921  0.393307   207.764
gene2  132.3282  0.6977581  0.479051  1.4565434  0.145242  0.369934   243.256
gene3   74.6210 -0.7433422  0.472541 -1.5730759  0.115701  0.369934   217.664
gene4  100.3924 -0.7639954  0.497794 -1.5347624  0.124842  0.369934   237.495
gene5   80.6177 -0.0395956  0.458518 -0.0863555  0.931184  0.931184   219.484
gene6   82.2199 -0.8577989  0.535290 -1.6024949  0.109046  0.369934   212.160
            BIC
      <numeric>
gene1   214.734
gene2   250.226
gene3   224.635
gene4   244.465
gene5   226.455
gene6   219.131

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   45.2064 -0.0187359  0.962016 -0.0194756  0.984462  0.998791   207.764
gene2  132.3282  1.0443612  1.101365  0.9482423  0.343006  0.775683   243.256
gene3   74.6210  0.9340582  1.069404  0.8734377  0.382425  0.775683   217.664
gene4  100.3924  0.4748084  1.141767  0.4158541  0.677517  0.880538   237.495
gene5   80.6177  1.1375227  1.058841  1.0743089  0.282684  0.775683   219.484
gene6   82.2199  0.9920276  1.220882  0.8125503  0.416476  0.775683   212.160
            BIC
      <numeric>
gene1   214.734
gene2   250.226
gene3   224.635
gene4   244.465
gene5   226.455
gene6   219.131

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene24   69.8719   1.00004  10.01762 0.00155108 0.0274438   210.431   217.401
gene31   89.1033   1.00013   9.96574 0.00159709 0.0274438   229.722   236.693
gene9    62.8589   1.00007   9.90807 0.00164663 0.0274438   209.236   216.206
gene20  115.1506   1.00005   9.13542 0.00250821 0.0313527   222.391   229.361
gene29   95.6909   1.00009   6.40075 0.01141487 0.1021206   222.552   229.522
gene48  124.0337   1.00004   6.27399 0.01225447 0.1021206   225.245   232.215
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 Under development (unstable) (2025-03-01 r87860 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows Server 2022 x64 (build 20348)

Matrix products: default
  LAPACK version 3.12.0

locale:
[1] LC_COLLATE=C                          
[2] LC_CTYPE=English_United States.utf8   
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.utf8    

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_3.5.1               BiocParallel_1.41.2        
 [3] NBAMSeq_1.23.0              SummarizedExperiment_1.37.0
 [5] Biobase_2.67.0              GenomicRanges_1.59.1       
 [7] GenomeInfoDb_1.43.4         IRanges_2.41.3             
 [9] S4Vectors_0.45.4            BiocGenerics_0.53.6        
[11] generics_0.1.3              MatrixGenerics_1.19.1      
[13] matrixStats_1.5.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.47.0         gtable_0.3.6            xfun_0.51              
 [4] bslib_0.9.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.5.0             parallel_4.5.0          tibble_3.2.1           
[10] AnnotationDbi_1.69.0    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_2.75.4       munsell_0.5.1           DESeq2_1.47.5          
[22] codetools_0.2-20        snow_0.4-4              htmltools_0.5.8.1      
[25] sass_0.4.9              yaml_2.3.10             pillar_1.10.1          
[28] crayon_1.5.3            jquerylib_0.1.4         DelayedArray_0.33.6    
[31] cachem_1.1.0            abind_1.4-8             nlme_3.1-167           
[34] genefilter_1.89.0       tidyselect_1.2.1        locfit_1.5-9.12        
[37] digest_0.6.37           dplyr_1.1.4             labeling_0.4.3         
[40] splines_4.5.0           fastmap_1.2.0           grid_4.5.0             
[43] colorspace_2.1-1        cli_3.6.4               SparseArray_1.7.7      
[46] magrittr_2.0.3          S4Arrays_1.7.3          survival_3.8-3         
[49] XML_3.99-0.18           withr_3.0.2             scales_1.3.0           
[52] UCSC.utils_1.3.1        bit64_4.6.0-1           rmarkdown_2.29         
[55] XVector_0.47.2          httr_1.4.7              bit_4.6.0              
[58] png_0.1-8               memoise_2.0.1           evaluate_1.0.3         
[61] knitr_1.50              mgcv_1.9-1              rlang_1.1.5            
[64] Rcpp_1.0.14             xtable_1.8-4            glue_1.8.0             
[67] DBI_1.2.3               annotate_1.85.0         jsonlite_1.9.1         
[70] 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.