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     460       3     112       7     169     193       1      48     113
gene2      20      87      18     116     104       1      97     131       2
gene3     145       1     308       1       2      11     518      13     167
gene4       6      41       3      64       7     443      97       1      81
gene5      87      78     101     265     226      48     294       3      17
gene6      17       2     278      44       7       1       1     190      16
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1       96      107      313        3        4      164       52
gene2        6        1        2       30       18      823        4       91
gene3       68        1      501       30        4        1       29      203
gene4       47        7        1      123       53        1      301        1
gene5        6      361        4        3       22       17       12      120
gene6       35       11       24        7        2       66       31        3
      sample18 sample19 sample20
gene1        2        3        1
gene2       12        2        1
gene3       97       10        1
gene4      139       99      459
gene5        1      192       30
gene6       36      375        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 43.55917  0.14441736  0.2170695  0.29533464    0
sample2 44.54108  0.04735797 -1.9367028 -1.03447526    0
sample3 50.55432 -0.15526302 -0.3529096  1.13821197    1
sample4 49.28225  0.63080142 -0.9912898  1.51487020    1
sample5 77.17409 -0.74588880 -0.9599302  0.04746719    1
sample6 58.17694 -0.60488350  0.4614916  0.30359403    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   74.4412   1.00035  0.194819 0.65946924 0.8761276   221.448   228.418
gene2   64.1794   1.00007  0.754757 0.38496256 0.7128936   195.705   202.675
gene3  117.5126   1.00007  7.751152 0.00537017 0.0615892   214.630   221.600
gene4   82.0960   1.00019  2.428189 0.11922995 0.4985112   220.822   227.793
gene5   81.6149   1.00006  0.577739 0.44721330 0.7453555   232.616   239.586
gene6   48.8434   1.00006  4.001230 0.04548056 0.2706168   193.350   200.320

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   74.4412 -0.0163594  0.514361 -0.0318054 0.97462728 0.9873423   221.448
gene2   64.1794  1.2048230  0.444033  2.7133627 0.00666042 0.0832552   195.705
gene3  117.5126 -0.6940381  0.514544 -1.3488408 0.17738811 0.4223526   214.630
gene4   82.0960  0.4720981  0.479506  0.9845514 0.32484448 0.6247009   220.822
gene5   81.6149 -0.3061529  0.477210 -0.6415472 0.52116724 0.6514591   232.616
gene6   48.8434  0.6037654  0.444066  1.3596302 0.17394699 0.4223526   193.350
            BIC
      <numeric>
gene1   228.418
gene2   202.675
gene3   221.600
gene4   227.793
gene5   239.586
gene6   200.320

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   74.4412 -1.146477   1.15186 -0.995326 0.31957781 0.5918108   221.448
gene2   64.1794 -2.736695   1.02555 -2.668511 0.00761882 0.0761882   195.705
gene3  117.5126  1.305511   1.15185  1.133400 0.25704614 0.5918108   214.630
gene4   82.0960  0.374798   1.07307  0.349276 0.72688195 0.8407138   220.822
gene5   81.6149  1.097137   1.06886  1.026458 0.30467555 0.5918108   232.616
gene6   48.8434  1.368122   1.01327  1.350207 0.17694946 0.5918108   193.350
            BIC
      <numeric>
gene1   228.418
gene2   202.675
gene3   221.600
gene4   227.793
gene5   239.586
gene6   200.320

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene50   74.5009   1.00010  15.42810 0.00008659 0.0043295   211.289   218.259
gene38  124.4731   1.00007  10.59859 0.00113236 0.0192165   237.112   244.082
gene30   69.3954   1.00007  10.56512 0.00115299 0.0192165   211.730   218.700
gene3   117.5126   1.00007   7.75115 0.00537017 0.0615892   214.630   221.600
gene18  128.0077   1.00007   7.45053 0.00634483 0.0615892   221.461   228.431
gene25   91.5350   1.00009   7.17646 0.00739071 0.0615892   211.355   218.325
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.4.0 RC (2024-04-16 r86468 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows Server 2022 x64 (build 20348)

Matrix products: default


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_1.39.0        
 [3] NBAMSeq_1.21.0              SummarizedExperiment_1.35.0
 [5] Biobase_2.65.0              GenomicRanges_1.57.0       
 [7] GenomeInfoDb_1.41.0         IRanges_2.39.0             
 [9] S4Vectors_0.43.0            BiocGenerics_0.51.0        
[11] MatrixGenerics_1.17.0       matrixStats_1.3.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.45.0         gtable_0.3.5            xfun_0.44              
 [4] bslib_0.7.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.4.0             generics_0.1.3          parallel_4.4.0         
[10] RSQLite_2.3.6           tibble_3.2.1            fansi_1.0.6            
[13] AnnotationDbi_1.67.0    highr_0.10              blob_1.2.4             
[16] pkgconfig_2.0.3         Matrix_1.7-0            lifecycle_1.0.4        
[19] GenomeInfoDbData_1.2.12 farver_2.1.2            compiler_4.4.0         
[22] Biostrings_2.73.0       munsell_0.5.1           DESeq2_1.45.0          
[25] codetools_0.2-20        snow_0.4-4              htmltools_0.5.8.1      
[28] sass_0.4.9              yaml_2.3.8              pillar_1.9.0           
[31] crayon_1.5.2            jquerylib_0.1.4         DelayedArray_0.31.1    
[34] cachem_1.0.8            abind_1.4-5             nlme_3.1-164           
[37] genefilter_1.87.0       tidyselect_1.2.1        locfit_1.5-9.9         
[40] digest_0.6.35           dplyr_1.1.4             labeling_0.4.3         
[43] splines_4.4.0           fastmap_1.2.0           grid_4.4.0             
[46] colorspace_2.1-0        cli_3.6.2               SparseArray_1.5.4      
[49] magrittr_2.0.3          S4Arrays_1.5.0          survival_3.6-4         
[52] XML_3.99-0.16.1         utf8_1.2.4              withr_3.0.0            
[55] scales_1.3.0            UCSC.utils_1.1.0        bit64_4.0.5            
[58] rmarkdown_2.26          XVector_0.45.0          httr_1.4.7             
[61] bit_4.0.5               png_0.1-8               memoise_2.0.1          
[64] evaluate_0.23           knitr_1.46              mgcv_1.9-1             
[67] rlang_1.1.3             Rcpp_1.0.12             DBI_1.2.2              
[70] xtable_1.8-4            glue_1.7.0              annotate_1.83.0        
[73] jsonlite_1.8.8          R6_2.5.1                zlibbioc_1.51.0        

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): 2672–8.