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      10      52     394       3      52      37      26     240
gene2      12     108      35       7     449     165      10       3       3
gene3       1       3       1       5     142       3     175       1       4
gene4     184       2      19       5      30     192       3      91       1
gene5      15       1       7     134      12       1       9      24       9
gene6       1       1     360      78       8     107       1      53       9
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       29       82        1        3      938        3      914      110
gene2        4        1       16       10        1       77        9       38
gene3      432      291       70      162        7        1      133        1
gene4       35      167      250       21        4       47        5       94
gene5        1      103       33       15       19       75       66        7
gene6      512      249      179      103       16      141      287       89
      sample18 sample19 sample20
gene1      125        1       53
gene2      247      131        1
gene3      137       56       53
gene4        1      170       62
gene5       33       31       23
gene6        2        5        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 48.44995  1.3551550 -0.5319536 -0.1600502    1
sample2 45.76193  0.8388865  2.5783154 -1.3113475    0
sample3 63.59380  0.7627634 -0.7466934  0.3289092    0
sample4 68.08355  0.5425361  1.0341969  2.4307850    2
sample5 39.89988  0.1851019  0.3405028  2.0734438    1
sample6 74.29516 -0.5952411  0.4229664  1.3760040    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  116.5672   1.00016  0.849784  0.356635  0.715956   230.676   237.647
gene2   59.8064   1.00006  1.137879  0.286177  0.681375   207.195   214.165
gene3   77.1961   1.00009  0.753639  0.385381  0.715956   211.460   218.431
gene4   52.4473   1.00013  0.234743  0.628247  0.842867   216.667   223.638
gene5   30.6428   1.00007  2.679565  0.101679  0.423662   191.012   197.983
gene6   81.8056   1.00010  0.837376  0.360172  0.715956   223.706   230.676

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  116.5672  0.5566137  0.399071  1.3947730 0.1630843  0.543614   230.676
gene2   59.8064  0.5799572  0.387217  1.4977562 0.1341966  0.535146   207.195
gene3   77.1961 -0.7856393  0.406838 -1.9310869 0.0534723  0.381945   211.460
gene4   52.4473 -0.0068902  0.360818 -0.0190961 0.9847645  0.994448   216.667
gene5   30.6428 -0.0807033  0.318230 -0.2536008 0.7998039  0.979068   191.012
gene6   81.8056 -0.9607749  0.383385 -2.5060316 0.0122095  0.203491   223.706
            BIC
      <numeric>
gene1   237.647
gene2   214.165
gene3   218.431
gene4   223.638
gene5   197.983
gene6   230.676

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  116.5672  0.501069  1.119703  0.447502 0.6545130  0.884477   230.676
gene2   59.8064 -1.872925  1.097872 -1.705959 0.0880157  0.258026   207.195
gene3   77.1961 -0.837818  1.140761 -0.734438 0.4626818  0.722940   211.460
gene4   52.4473  0.269848  1.014955  0.265872 0.7903378  0.938244   216.667
gene5   30.6428  0.968101  0.892847  1.084285 0.2782382  0.535074   191.012
gene6   81.8056 -0.837772  1.069607 -0.783252 0.4334794  0.699160   223.706
            BIC
      <numeric>
gene1   237.647
gene2   214.165
gene3   218.431
gene4   223.638
gene5   197.983
gene6   230.676

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene24   66.9698   1.00007  14.24479 0.000161433 0.00807163   197.279   204.250
gene45   88.3147   1.00006  12.31719 0.000448948 0.01122370   197.037   204.008
gene38   52.1314   1.00008   7.75358 0.005363761 0.08939601   196.536   203.507
gene33   62.0064   1.00003   4.86689 0.027380740 0.24763456   195.828   202.798
gene49  141.0853   1.00004   4.74832 0.029333213 0.24763456   232.136   239.106
gene9    55.4457   1.00008   4.72608 0.029716148 0.24763456   205.921   212.891
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 beta (2024-04-14 r86421)
Platform: x86_64-apple-darwin20
Running under: macOS Monterey 12.7.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

locale:
[1] en_US.UTF-8/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_1.38.0        
 [3] NBAMSeq_1.20.0              SummarizedExperiment_1.34.0
 [5] Biobase_2.64.0              GenomicRanges_1.56.0       
 [7] GenomeInfoDb_1.40.0         IRanges_2.38.0             
 [9] S4Vectors_0.42.0            BiocGenerics_0.50.0        
[11] MatrixGenerics_1.16.0       matrixStats_1.3.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.44.0         gtable_0.3.5            xfun_0.43              
 [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_1.66.0    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_2.1.1            compiler_4.4.0         
[22] Biostrings_2.72.0       munsell_0.5.1           DESeq2_1.44.0          
[25] codetools_0.2-20        htmltools_0.5.8.1       sass_0.4.9             
[28] yaml_2.3.8              pillar_1.9.0            crayon_1.5.2           
[31] jquerylib_0.1.4         DelayedArray_0.30.0     cachem_1.0.8           
[34] abind_1.4-5             nlme_3.1-164            genefilter_1.86.0      
[37] tidyselect_1.2.1        locfit_1.5-9.9          digest_0.6.35          
[40] dplyr_1.1.4             labeling_0.4.3          splines_4.4.0          
[43] fastmap_1.1.1           grid_4.4.0              colorspace_2.1-0       
[46] cli_3.6.2               SparseArray_1.4.0       magrittr_2.0.3         
[49] S4Arrays_1.4.0          survival_3.6-4          XML_3.99-0.16.1        
[52] utf8_1.2.4              withr_3.0.0             scales_1.3.0           
[55] UCSC.utils_1.0.0        bit64_4.0.5             rmarkdown_2.26         
[58] XVector_0.44.0          httr_1.4.7              bit_4.0.5              
[61] png_0.1-8               memoise_2.0.1           evaluate_0.23          
[64] knitr_1.46              mgcv_1.9-1              rlang_1.1.3            
[67] Rcpp_1.0.12             DBI_1.2.2               xtable_1.8-4           
[70] glue_1.7.0              annotate_1.82.0         jsonlite_1.8.8         
[73] R6_2.5.1                zlibbioc_1.50.0        

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.