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       1      14     125      83     106       3       1      71      74
gene2      18       1       2     334       8       4       1       2     191
gene3     398       4       3      46      96       5       2       3      36
gene4       1      46      20     295      54       2       2       3    1078
gene5     112     307      41       1      32       6       1      50      10
gene6     125       2       1      64       7      86      16      97      56
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1        1      113       60       18        5        1       21
gene2        1       25        1        3      122      375      568      185
gene3        4       36        2      344      808      339       44        1
gene4       37        8        1        1      102      230        1      249
gene5        1       36        2      136       36        1      103        4
gene6       61        1        4      269       41      122      154        4
      sample18 sample19 sample20
gene1      417      165        2
gene2        6       84       14
gene3      256      315       59
gene4       81      589      328
gene5       92      342       10
gene6       35      129      146

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 61.62516 1.2517649 -0.3978103 -0.3072051    1
sample2 63.07291 0.9409884  0.9133252 -1.4889276    2
sample3 63.12365 0.4793448  0.9962835 -0.3014775    0
sample4 63.07130 0.6407252 -0.8100224 -0.1664305    1
sample5 34.41759 0.9836666  0.4597228 -0.3196812    1
sample6 51.76991 1.1872650 -0.8454540 -0.3558961    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   65.9010   1.00009 0.0151460  0.902357  0.938403   198.691   205.661
gene2   87.5544   1.00006 0.7902230  0.374080  0.688780   204.613   211.583
gene3  101.4641   1.00005 1.9208547  0.165787  0.406354   227.696   234.666
gene4  107.4342   1.00019 0.0686016  0.793696  0.938403   227.746   234.716
gene5   51.7667   1.00012 0.0273460  0.868969  0.938403   210.255   217.225
gene6   56.5872   1.15916 0.3205784  0.813923  0.938403   216.946   224.075

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   65.9010  0.233524  0.454366  0.5139564 0.6072825  0.820652   198.691
gene2   87.5544 -1.135195  0.501517 -2.2635232 0.0236035  0.214104   204.613
gene3  101.4641 -0.408630  0.487602 -0.8380405 0.4020079  0.758445   227.696
gene4  107.4342 -0.036771  0.527643 -0.0696891 0.9444411  0.962649   227.746
gene5   51.7667  0.670380  0.495330  1.3534004 0.1759278  0.487766   210.255
gene6   56.5872 -0.393224  0.421550 -0.9328036 0.3509214  0.758445   216.946
            BIC
      <numeric>
gene1   205.661
gene2   211.583
gene3   234.666
gene4   234.716
gene5   217.225
gene6   224.075

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   65.9010 -3.000087  1.071483 -2.799938 0.00511125 0.0718983   198.691
gene2   87.5544  2.390498  1.208596  1.977913 0.04793849 0.2438920   204.613
gene3  101.4641  1.977628  1.144369  1.728139 0.08396335 0.2998691   227.696
gene4  107.4342  1.866692  1.226441  1.522040 0.12799912 0.3345118   227.746
gene5   51.7667 -0.433153  1.146271 -0.377880 0.70551964 0.9045124   210.255
gene6   56.5872  0.525025  0.972699  0.539762 0.58936137 0.8159530   216.946
            BIC
      <numeric>
gene1   205.661
gene2   211.583
gene3   234.666
gene4   234.716
gene5   217.225
gene6   224.075

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene22  149.8081   1.00084  14.28091 0.000158832 0.00794161   220.149   227.120
gene10  132.2014   1.00004  10.72449 0.001057650 0.02644125   237.050   244.020
gene33   44.3178   1.00036   9.50189 0.002055727 0.03426212   191.913   198.883
gene46   76.9610   1.00004   8.50563 0.003541675 0.04399800   213.156   220.127
gene27   92.8809   1.00003   8.11131 0.004399800 0.04399800   198.918   205.889
gene13   25.7498   1.00018   7.44596 0.006359302 0.05299418   157.055   164.025
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.1.1 (2021-08-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows Server x64 (build 17763)

Matrix products: default

locale:
[1] LC_COLLATE=C                          
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] ggplot2_3.3.5               BiocParallel_1.28.0        
 [3] NBAMSeq_1.10.0              SummarizedExperiment_1.24.0
 [5] Biobase_2.54.0              GenomicRanges_1.46.0       
 [7] GenomeInfoDb_1.30.0         IRanges_2.28.0             
 [9] S4Vectors_0.32.0            BiocGenerics_0.40.0        
[11] MatrixGenerics_1.6.0        matrixStats_0.61.0         

loaded via a namespace (and not attached):
 [1] httr_1.4.2             sass_0.4.0             bit64_4.0.5           
 [4] jsonlite_1.7.2         splines_4.1.1          bslib_0.3.1           
 [7] assertthat_0.2.1       highr_0.9              blob_1.2.2            
[10] GenomeInfoDbData_1.2.7 yaml_2.2.1             pillar_1.6.4          
[13] RSQLite_2.2.8          lattice_0.20-45        glue_1.4.2            
[16] digest_0.6.28          RColorBrewer_1.1-2     XVector_0.34.0        
[19] colorspace_2.0-2       htmltools_0.5.2        Matrix_1.3-4          
[22] DESeq2_1.34.0          XML_3.99-0.8           pkgconfig_2.0.3       
[25] genefilter_1.76.0      zlibbioc_1.40.0        purrr_0.3.4           
[28] xtable_1.8-4           snow_0.4-3             scales_1.1.1          
[31] tibble_3.1.5           annotate_1.72.0        mgcv_1.8-38           
[34] KEGGREST_1.34.0        farver_2.1.0           generics_0.1.1        
[37] ellipsis_0.3.2         withr_2.4.2            cachem_1.0.6          
[40] survival_3.2-13        magrittr_2.0.1         crayon_1.4.1          
[43] memoise_2.0.0          evaluate_0.14          fansi_0.5.0           
[46] nlme_3.1-153           tools_4.1.1            lifecycle_1.0.1       
[49] stringr_1.4.0          locfit_1.5-9.4         munsell_0.5.0         
[52] DelayedArray_0.20.0    AnnotationDbi_1.56.0   Biostrings_2.62.0     
[55] compiler_4.1.1         jquerylib_0.1.4        rlang_0.4.12          
[58] grid_4.1.1             RCurl_1.98-1.5         labeling_0.4.2        
[61] bitops_1.0-7           rmarkdown_2.11         gtable_0.3.0          
[64] DBI_1.1.1              R6_2.5.1               knitr_1.36            
[67] dplyr_1.0.7            fastmap_1.1.0          bit_4.0.4             
[70] utf8_1.2.2             stringi_1.7.5          parallel_4.1.1        
[73] Rcpp_1.0.7             vctrs_0.3.8            geneplotter_1.72.0    
[76] png_0.1-7              tidyselect_1.1.1       xfun_0.27             

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.