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       2       1     220       7       2     680      31     102       3
gene2      27      33     163      38       2     127      38      17      11
gene3     239       2     114     169      58       1     191      16     104
gene4     111      12      14      11       1     428     140      61       2
gene5       2      17      46       2      10      62     696      12       7
gene6      33       5     602      22     378       1       4      55       9
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      163        1       39      107       16      236        2       33
gene2       44      447       44        1        3        1        2      377
gene3        1        1      113      133      942       50        1      206
gene4       47       63        1      109        9      132       16      197
gene5        3        1        9        1        6       33      190      141
gene6      160       54      252      635        4       34        7       39
      sample18 sample19 sample20
gene1        1        6        8
gene2       58      283      173
gene3       14      323       14
gene4       26        6      144
gene5       53       24        9
gene6       18        3      240

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 55.98011  1.63751205 -1.0997371 -1.4039810    1
sample2 34.13251 -0.30089995 -1.0545540  0.8582900    2
sample3 35.45191  1.06459769 -0.8992885  1.5800864    1
sample4 23.35149  0.36402180 -0.2432098  0.8107233    0
sample5 63.07076  1.18663274  0.1002464 -1.4819245    1
sample6 30.20543  0.08313703 -1.1940850  1.0330631    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   59.7293   1.00013  0.877717 0.3488883  0.625390   203.922   210.892
gene2   89.4233   1.00007  0.152211 0.6965176  0.735514   221.021   227.991
gene3  130.2202   1.00005  0.187691 0.6648821  0.722698   234.136   241.106
gene4   66.8300   1.00009  0.371514 0.5422801  0.646065   221.517   228.488
gene5   93.6086   1.00012  3.020610 0.0822465  0.316333   201.164   208.134
gene6   96.5862   1.00005  0.795308 0.3725290  0.625390   226.890   233.860

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   59.7293  0.393588  0.561928  0.700425 0.48366208 0.7205455   203.922
gene2   89.4233  0.119313  0.512014  0.233027 0.81574030 0.9083350   221.021
gene3  130.2202 -0.284248  0.559786 -0.507781 0.61160723 0.8047464   234.136
gene4   66.8300 -0.194596  0.520177 -0.374096 0.70833308 0.8854163   221.517
gene5   93.6086 -1.505587  0.555575 -2.709962 0.00672908 0.0560757   201.164
gene6   96.5862  0.500417  0.512661  0.976118 0.32900615 0.6580123   226.890
            BIC
      <numeric>
gene1   210.892
gene2   227.991
gene3   241.106
gene4   228.488
gene5   208.134
gene6   233.860

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
      <numeric>   <numeric> <numeric>   <numeric>  <numeric> <numeric>
gene1   59.7293  1.02057436   1.45589  0.70099645 0.48330523 0.8417310
gene2   89.4233 -1.99492602   1.32965 -1.50033795 0.13352688 0.3709080
gene3  130.2202 -4.86829784   1.55995 -3.12080897 0.00180355 0.0300592
gene4   66.8300  1.16090818   1.34767  0.86141666 0.38900860 0.7463774
gene5   93.6086  0.00418844   1.42983  0.00292932 0.99766274 0.9976627
gene6   96.5862 -2.83852425   1.38238 -2.05336560 0.04003713 0.1662133
            AIC       BIC
      <numeric> <numeric>
gene1   203.922   210.892
gene2   221.021   227.991
gene3   234.136   241.106
gene4   221.517   228.488
gene5   201.164   208.134
gene6   226.890   233.860

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene15   93.1031   1.00004  17.30777 3.27278e-05 0.00163639   204.871   211.841
gene45  119.5809   1.00010  10.01116 1.55687e-03 0.02693888   214.326   221.297
gene13   63.7973   1.00004   9.94162 1.61633e-03 0.02693888   209.394   216.364
gene31   94.9188   1.00006   6.08822 1.36145e-02 0.15559727   226.186   233.156
gene46   41.8465   1.00004   5.85245 1.55597e-02 0.15559727   184.418   191.388
gene19  140.9082   1.00007   5.26594 2.17545e-02 0.16285409   236.081   243.052
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.4.1 (2024-06-14)
Platform: aarch64-apple-darwin20
Running under: macOS Ventura 13.6.7

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

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_3.5.1               BiocParallel_1.40.0        
 [3] NBAMSeq_1.22.0              SummarizedExperiment_1.36.0
 [5] Biobase_2.66.0              GenomicRanges_1.58.0       
 [7] GenomeInfoDb_1.42.0         IRanges_2.40.0             
 [9] S4Vectors_0.44.0            BiocGenerics_0.52.0        
[11] MatrixGenerics_1.18.0       matrixStats_1.4.1          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.46.0         gtable_0.3.6            xfun_0.49              
 [4] bslib_0.8.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.4.1             generics_0.1.3          parallel_4.4.1         
[10] RSQLite_2.3.7           tibble_3.2.1            fansi_1.0.6            
[13] AnnotationDbi_1.68.0    blob_1.2.4              pkgconfig_2.0.3        
[16] Matrix_1.7-1            lifecycle_1.0.4         GenomeInfoDbData_1.2.13
[19] farver_2.1.2            compiler_4.4.1          Biostrings_2.74.0      
[22] munsell_0.5.1           DESeq2_1.46.0           codetools_0.2-20       
[25] htmltools_0.5.8.1       sass_0.4.9              yaml_2.3.10            
[28] pillar_1.9.0            crayon_1.5.3            jquerylib_0.1.4        
[31] DelayedArray_0.32.0     cachem_1.1.0            abind_1.4-8            
[34] nlme_3.1-166            genefilter_1.88.0       tidyselect_1.2.1       
[37] locfit_1.5-9.10         digest_0.6.37           dplyr_1.1.4            
[40] labeling_0.4.3          splines_4.4.1           fastmap_1.2.0          
[43] grid_4.4.1              colorspace_2.1-1        cli_3.6.3              
[46] SparseArray_1.6.0       magrittr_2.0.3          S4Arrays_1.6.0         
[49] survival_3.7-0          XML_3.99-0.17           utf8_1.2.4             
[52] withr_3.0.2             scales_1.3.0            UCSC.utils_1.2.0       
[55] bit64_4.5.2             rmarkdown_2.29          XVector_0.46.0         
[58] httr_1.4.7              bit_4.5.0               png_0.1-8              
[61] memoise_2.0.1           evaluate_1.0.1          knitr_1.49             
[64] mgcv_1.9-1              rlang_1.1.4             Rcpp_1.0.13-1          
[67] DBI_1.2.3               xtable_1.8-4            glue_1.8.0             
[70] annotate_1.84.0         jsonlite_1.8.9          R6_2.5.1               
[73] zlibbioc_1.52.0        

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.