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       3    1100     167      72     238     232      74     108     497
gene2      12       1     131      60      14      13      11     140      54
gene3      12     209     334      21     175      20     460     171      46
gene4      13      54       3       9      38     588       4       1       5
gene5      57     148       2      52     150      36       3      28      24
gene6      38     111     378     178      88     151      23     326       1
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       13        1        3        2       68        1       14        1
gene2        2        6       52      940      192       73        1       12
gene3        1        1       26      201        2       13       23      113
gene4        1        7        8      445        1       62       44        1
gene5      489       27        2       18       11      157      115      174
gene6       21      399      191     1024        1       16      109      197
      sample18 sample19 sample20
gene1      353        1       24
gene2       18       27        3
gene3       45      135      348
gene4      144        1        1
gene5       59       33       10
gene6       20      145        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 60.89504  0.2867188 -0.9660655  0.59879712    1
sample2 41.43134 -0.6325066  1.6286422  0.77715354    0
sample3 27.70834 -0.6552219  0.8297284 -0.06018658    2
sample4 37.58138 -0.1784748  2.6503799  1.82794968    2
sample5 26.88234 -1.3387167  2.2828828 -1.51035477    2
sample6 33.81681 -1.0825636  0.6167613 -0.85197024    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  128.0058   1.00025 0.8346790  0.360887  0.694014   226.723   233.693
gene2   87.3451   1.00003 0.2729840  0.601366  0.848077   212.463   219.433
gene3   84.4142   1.00005 0.0404992  0.840661  0.955296   231.523   238.494
gene4   65.1228   1.00004 2.0378143  0.153436  0.655630   190.777   197.747
gene5   83.7423   1.00005 0.8953343  0.344037  0.694014   222.720   229.690
gene6  161.7722   1.00005 0.6991959  0.403050  0.746388   251.171   258.141

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  128.0058 -1.4642664  0.537110 -2.726195 0.00640691  0.106782   226.723
gene2   87.3451  1.5738552  0.483859  3.252715 0.00114308  0.028577   212.463
gene3   84.4142 -0.8051793  0.428001 -1.881254 0.05993743  0.369699   231.523
gene4   65.1228  0.0589299  0.532607  0.110644 0.91189856  0.965502   190.777
gene5   83.7423 -0.8066308  0.424815 -1.898782 0.05759312  0.369699   222.720
gene6  161.7722  0.1271021  0.482001  0.263697 0.79201355  0.920946   251.171
            BIC
      <numeric>
gene1   233.693
gene2   219.433
gene3   238.494
gene4   197.747
gene5   229.690
gene6   258.141

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  128.0058 -0.760557  1.130682 -0.672653 0.5011678  0.746207   226.723
gene2   87.3451  0.491204  1.017718  0.482652 0.6293428  0.802816   212.463
gene3   84.4142 -1.713778  0.903308 -1.897225 0.0577983  0.346413   231.523
gene4   65.1228 -1.092411  1.120492 -0.974939 0.3295903  0.746207   190.777
gene5   83.7423 -0.922870  0.899891 -1.025536 0.3051104  0.746207   222.720
gene6  161.7722 -0.840060  1.017388 -0.825702 0.4089729  0.746207   251.171
            BIC
      <numeric>
gene1   233.693
gene2   219.433
gene3   238.494
gene4   197.747
gene5   229.690
gene6   258.141

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene27   65.3540   1.00008   7.63320 0.00573257  0.167029   201.435   208.405
gene16   74.9659   1.00012   7.22646 0.00719012  0.167029   217.738   224.708
gene48   60.5203   1.00016   6.63237 0.01002172  0.167029   204.697   211.667
gene31   34.7013   1.00008   5.93522 0.01484535  0.185567   178.318   185.288
gene26  104.1157   1.00008   5.24012 0.02207251  0.220725   234.108   241.078
gene12   73.4832   1.00012   4.89543 0.02693193  0.224433   188.920   195.890
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.2.1 (2022-06-23)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.0

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

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

other attached packages:
 [1] ggplot2_3.3.6               BiocParallel_1.32.1        
 [3] NBAMSeq_1.14.0              SummarizedExperiment_1.28.0
 [5] Biobase_2.58.0              GenomicRanges_1.50.1       
 [7] GenomeInfoDb_1.34.2         IRanges_2.32.0             
 [9] S4Vectors_0.36.0            BiocGenerics_0.44.0        
[11] MatrixGenerics_1.10.0       matrixStats_0.62.0         

loaded via a namespace (and not attached):
 [1] httr_1.4.3             sass_0.4.1             bit64_4.0.5           
 [4] jsonlite_1.8.0         splines_4.2.1          bslib_0.3.1           
 [7] assertthat_0.2.1       highr_0.9              blob_1.2.3            
[10] GenomeInfoDbData_1.2.8 yaml_2.3.5             pillar_1.7.0          
[13] RSQLite_2.2.14         lattice_0.20-45        glue_1.6.2            
[16] digest_0.6.29          RColorBrewer_1.1-3     XVector_0.38.0        
[19] colorspace_2.0-3       htmltools_0.5.2        Matrix_1.4-1          
[22] DESeq2_1.38.0          XML_3.99-0.10          pkgconfig_2.0.3       
[25] genefilter_1.80.0      zlibbioc_1.44.0        purrr_0.3.4           
[28] xtable_1.8-4           scales_1.2.0           tibble_3.1.7          
[31] annotate_1.76.0        mgcv_1.8-40            KEGGREST_1.38.0       
[34] farver_2.1.1           generics_0.1.3         ellipsis_0.3.2        
[37] withr_2.5.0            cachem_1.0.6           cli_3.3.0             
[40] survival_3.3-1         magrittr_2.0.3         crayon_1.5.1          
[43] memoise_2.0.1          evaluate_0.15          fansi_1.0.3           
[46] nlme_3.1-158           tools_4.2.1            lifecycle_1.0.1       
[49] stringr_1.4.0          locfit_1.5-9.6         munsell_0.5.0         
[52] DelayedArray_0.24.0    AnnotationDbi_1.60.0   Biostrings_2.66.0     
[55] compiler_4.2.1         jquerylib_0.1.4        rlang_1.0.4           
[58] grid_4.2.1             RCurl_1.98-1.7         labeling_0.4.2        
[61] bitops_1.0-7           rmarkdown_2.14         gtable_0.3.0          
[64] codetools_0.2-18       DBI_1.1.3              R6_2.5.1              
[67] knitr_1.39             dplyr_1.0.9            fastmap_1.1.0         
[70] bit_4.0.4              utf8_1.2.2             stringi_1.7.8         
[73] parallel_4.2.1         Rcpp_1.0.9             vctrs_0.4.1           
[76] geneplotter_1.76.0     png_0.1-7              tidyselect_1.1.2      
[79] xfun_0.31             

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.