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      63       1      49     182       1     119     229       3       1
gene2     165      79     457       1     372      11      82      72      43
gene3      72     238      81     149      78       2      62      17     350
gene4     124       4      45       4       1      25     211     372     126
gene5     179      69      17       9     107     224       1       6       6
gene6       8      24       7     515      62      17       2     397      87
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       81       25        6       38        2       80        1      457
gene2      383      485        7       65        3       14      660        8
gene3       34      141       15       36        5      210       20        4
gene4        3       76        2       85       12       35      164       10
gene5        8       27        1       23      167        1      426       20
gene6       18      413       51      102       24       12        1      115
      sample18 sample19 sample20
gene1       49       66        1
gene2        4      253        5
gene3      145      382       18
gene4        7        1       49
gene5       28        1      116
gene6        3      155      529

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 79.08041 -0.3993478  0.9172095  0.1333777    1
sample2 40.53707  1.3645392 -0.2970013  0.4767594    0
sample3 57.76781  0.1044263  0.8023012  0.2832003    0
sample4 33.82920  0.8441772  0.6410707 -1.2560859    0
sample5 66.67510 -0.1217728 -0.7880622  0.2466329    1
sample6 54.30309 -0.7365714 -1.3511212  0.2584657    1

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   78.2540   1.00003  0.355782 0.5508994  0.810146   212.260   219.231
gene2  182.2583   1.00033  2.739709 0.0979277  0.305704   250.547   257.518
gene3   92.6688   1.00007  0.486304 0.4856130  0.758770   235.198   242.168
gene4   64.5192   1.00003  1.722143 0.1894382  0.430541   212.931   219.901
gene5   91.6361   1.00003  3.145441 0.0761400  0.253800   217.751   224.721
gene6  102.3758   1.00007  3.791063 0.0515417  0.219680   227.028   233.999

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   78.2540  0.9017412  0.629035  1.433530 0.1517065  0.541809   212.260
gene2  182.2583 -0.6071377  0.638470 -0.950926 0.3416418  0.617891   250.547
gene3   92.6688 -0.2177677  0.501251 -0.434448 0.6639628  0.851234   235.198
gene4   64.5192 -1.2291159  0.587317 -2.092763 0.0363703  0.454629   212.931
gene5   91.6361 -0.0814978  0.639349 -0.127470 0.8985685  0.990552   217.751
gene6  102.3758  0.8610738  0.512917  1.678779 0.0931951  0.489732   227.028
            BIC
      <numeric>
gene1   219.231
gene2   257.518
gene3   242.168
gene4   219.901
gene5   224.721
gene6   233.999

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   78.2540  1.557712  1.246583  1.249585 0.2114511  0.459676   212.260
gene2  182.2583 -1.269328  1.263953 -1.004253 0.3152566  0.569163   250.547
gene3   92.6688  0.178472  0.994575  0.179446 0.8575876  0.912327   235.198
gene4   64.5192 -1.619720  1.165476 -1.389750 0.1646047  0.457235   212.931
gene5   91.6361 -1.225424  1.266665 -0.967441 0.3333236  0.569163   217.751
gene6  102.3758  1.846233  1.017609  1.814286 0.0696337  0.290140   227.028
            BIC
      <numeric>
gene1   219.231
gene2   257.518
gene3   242.168
gene4   219.901
gene5   224.721
gene6   233.999

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene46  121.9149   1.00008  15.75573 7.18751e-05 0.00359375   208.512   215.483
gene16  139.2076   1.00028   9.93699 1.62335e-03 0.04058372   209.654   216.624
gene10   93.1198   1.00008   8.07722 4.48576e-03 0.06930084   194.311   201.281
gene44  103.1979   1.00008   7.69303 5.54407e-03 0.06930084   213.820   220.791
gene40  118.5934   1.00006   6.40424 1.13888e-02 0.11388815   229.466   236.437
gene17  113.7494   1.00012   5.57733 1.81987e-02 0.15165601   202.401   209.371
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 Patched (2021-08-22 r80813)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/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_3.3.5               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           scales_1.1.1           tibble_3.1.5          
[31] annotate_1.72.0        mgcv_1.8-38            KEGGREST_1.34.0       
[34] farver_2.1.0           generics_0.1.1         ellipsis_0.3.2        
[37] withr_2.4.2            cachem_1.0.6           survival_3.2-13       
[40] magrittr_2.0.1         crayon_1.4.1           memoise_2.0.0         
[43] evaluate_0.14          fansi_0.5.0            nlme_3.1-153          
[46] tools_4.1.1            lifecycle_1.0.1        stringr_1.4.0         
[49] locfit_1.5-9.4         munsell_0.5.0          DelayedArray_0.20.0   
[52] AnnotationDbi_1.56.0   Biostrings_2.62.0      compiler_4.1.1        
[55] jquerylib_0.1.4        rlang_0.4.12           grid_4.1.1            
[58] RCurl_1.98-1.5         labeling_0.4.2         bitops_1.0-7          
[61] rmarkdown_2.11         gtable_0.3.0           DBI_1.1.1             
[64] R6_2.5.1               knitr_1.36             dplyr_1.0.7           
[67] fastmap_1.1.0          bit_4.0.4              utf8_1.2.2            
[70] stringi_1.7.5          parallel_4.1.1         Rcpp_1.0.7            
[73] vctrs_0.3.8            geneplotter_1.72.0     png_0.1-7             
[76] 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.