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     301      76       7       1     523      22     268     114      59
gene2     130     262      23      13      97     325       6      68     204
gene3     454     168       1      22       2     148      13     352       3
gene4      34     234      51       2     208      54       8     193      28
gene5      11     468      27       1       1      75      15       1     899
gene6       4      56     156     186      24       1     119      93       1
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       16      149      158      115       19        5        9       28
gene2        1        1        5        7       55        7      222       68
gene3        7       13       64       11        1        2      106       45
gene4      206       19       46        1      178      319      229      775
gene5        1       37       14       46       35       54      255       26
gene6      121       66       90      272        3       13      128        6
      sample18 sample19 sample20
gene1       53       29        1
gene2        1       10        1
gene3       84       50       14
gene4      202      273        9
gene5      152        8      269
gene6        1      165        1

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 36.67279  1.33351808 -1.815513148  0.26370699    0
sample2 35.36804 -0.83583927 -0.790266252 -2.43361280    1
sample3 37.25504 -1.08571507  0.007593744  0.05564406    1
sample4 64.83742 -0.17374276 -0.240979010  0.55838657    2
sample5 36.95051 -0.00803284 -1.752551858 -3.50006262    2
sample6 53.36819 -1.97145100  1.339464343  0.48793539    0

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   65.1262   1.00012 0.19779512 0.6565476  0.820908   226.604   233.574
gene2   64.7553   1.00005 0.42405558 0.5149499  0.820908   211.279   218.250
gene3   54.9511   1.00018 0.00381677 0.9518291  0.954606   205.547   212.517
gene4  134.6692   1.00004 0.27619095 0.5992381  0.820908   252.458   259.428
gene5  121.4099   1.00017 2.87008131 0.0902861  0.410392   226.122   233.092
gene6   65.7235   1.00009 1.10861883 0.2924203  0.595862   217.974   224.945

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   65.1262  0.2338915  0.350751  0.666830 0.50488066 0.8948568   226.604
gene2   64.7553 -0.7554963  0.391295 -1.930757 0.05351306 0.3869572   211.279
gene3   54.9511 -1.1164631  0.357613 -3.121984 0.00179637 0.0875513   205.547
gene4  134.6692 -0.0459519  0.373952 -0.122882 0.90220079 0.9206131   252.458
gene5  121.4099  0.2506278  0.413575  0.606003 0.54451302 0.8948568   226.122
gene6   65.7235 -0.4201158  0.388017 -1.082727 0.27892973 0.8203816   217.974
            BIC
      <numeric>
gene1   233.574
gene2   218.250
gene3   212.517
gene4   259.428
gene5   233.092
gene6   224.945

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   65.1262  0.663021  0.824177  0.804465 0.4211287  0.638651   226.604
gene2   64.7553 -1.648574  0.915091 -1.801541 0.0716177  0.275453   211.279
gene3   54.9511 -1.334259  0.814570 -1.637991 0.1014235  0.338078   205.547
gene4  134.6692 -1.622770  0.880143 -1.843757 0.0652185  0.271744   252.458
gene5  121.4099 -1.261539  0.976117 -1.292406 0.1962166  0.545046   226.122
gene6   65.7235  0.954959  0.910726  1.048569 0.2943766  0.574153   217.974
            BIC
      <numeric>
gene1   233.574
gene2   218.250
gene3   212.517
gene4   259.428
gene5   233.092
gene6   224.945

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene39  156.1090   1.00011  15.78134 7.07333e-05 0.00353667   207.235   214.205
gene12  105.8409   1.00005  12.34760 4.41854e-04 0.01104636   213.983   220.953
gene38   37.8851   1.00005  10.05135 1.52300e-03 0.02179965   189.188   196.158
gene44  141.3677   1.00018   9.80395 1.74397e-03 0.02179965   238.575   245.545
gene22  106.2786   1.00011   8.91235 2.83456e-03 0.02834562   226.302   233.272
gene23   22.6642   1.00004   7.53431 6.05443e-03 0.05045359   168.987   175.957
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.3.1 (2023-06-16)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.6.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

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_3.4.2               BiocParallel_1.36.0        
 [3] NBAMSeq_1.18.0              SummarizedExperiment_1.32.0
 [5] Biobase_2.62.0              GenomicRanges_1.54.1       
 [7] GenomeInfoDb_1.38.0         IRanges_2.36.0             
 [9] S4Vectors_0.40.1            BiocGenerics_0.48.1        
[11] MatrixGenerics_1.14.0       matrixStats_1.0.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.42.0         gtable_0.3.3            xfun_0.39              
 [4] bslib_0.5.0             lattice_0.21-8          vctrs_0.6.3            
 [7] tools_4.3.1             bitops_1.0-7            generics_0.1.3         
[10] parallel_4.3.1          RSQLite_2.3.1           AnnotationDbi_1.64.1   
[13] tibble_3.2.1            fansi_1.0.4             highr_0.10             
[16] blob_1.2.4              pkgconfig_2.0.3         Matrix_1.6-0           
[19] lifecycle_1.0.3         GenomeInfoDbData_1.2.10 farver_2.1.1           
[22] compiler_4.3.1          Biostrings_2.70.1       munsell_0.5.0          
[25] DESeq2_1.42.0           codetools_0.2-19        htmltools_0.5.5        
[28] sass_0.4.6              RCurl_1.98-1.12         yaml_2.3.7             
[31] pillar_1.9.0            crayon_1.5.2            jquerylib_0.1.4        
[34] DelayedArray_0.28.0     cachem_1.0.8            abind_1.4-5            
[37] nlme_3.1-162            genefilter_1.84.0       tidyselect_1.2.0       
[40] locfit_1.5-9.8          digest_0.6.33           dplyr_1.1.2            
[43] labeling_0.4.2          splines_4.3.1           fastmap_1.1.1          
[46] grid_4.3.1              colorspace_2.1-0        cli_3.6.1              
[49] SparseArray_1.2.0       magrittr_2.0.3          S4Arrays_1.2.0         
[52] survival_3.5-5          XML_3.99-0.14           utf8_1.2.3             
[55] withr_2.5.0             scales_1.2.1            bit64_4.0.5            
[58] rmarkdown_2.23          XVector_0.42.0          httr_1.4.6             
[61] bit_4.0.5               png_0.1-8               memoise_2.0.1          
[64] evaluate_0.21           knitr_1.43              mgcv_1.9-0             
[67] rlang_1.1.1             Rcpp_1.0.11             DBI_1.1.3              
[70] xtable_1.8-4            glue_1.6.2              annotate_1.80.0        
[73] jsonlite_1.8.7          R6_2.5.1                zlibbioc_1.48.0        

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.