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     446      18       5     114       1      17     268      77       4
gene2       2    1041      65      69       1      30     107       5      93
gene3     149      33      41       1     596      28       4     277       4
gene4       4      25       1     117     350       1      45       1       7
gene5       1       1     183       3      40     121      54     104       7
gene6      55     311      46     185      80       8       7     314     388
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1      526        8        2       75        1       83       63
gene2       68      123      187      374      270        1        7       93
gene3       23      902      190       19        2      404      208      416
gene4        1       71      277        9        1       19      144      256
gene5      219       19        1       39      357       98        3      205
gene6        1      288        3        5       29      304      250      170
      sample18 sample19 sample20
gene1       84       12       33
gene2      114        1       24
gene3      291       10       22
gene4      396      138       45
gene5        3      411        1
gene6        4        1     1248

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 78.10198 -0.81127774  0.53652198  0.06041413    2
sample2 79.68947 -0.93061246 -0.49188994  0.22510731    2
sample3 55.57142 -1.61657423 -0.00211368 -1.99680180    2
sample4 31.35824 -1.64441510 -0.64734406 -0.51095132    0
sample5 64.71446  0.93059106 -0.51393640  0.53077575    0
sample6 31.29346 -0.06354946  2.43150745  1.00077676    0

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   47.6045   1.00007 0.1075551 0.7429988  0.807607   215.264   222.234
gene2  112.3051   1.00012 0.7550910 0.3849241  0.620845   238.963   245.933
gene3  131.2139   1.00006 0.3414903 0.5589805  0.716642   236.529   243.499
gene4   86.2382   1.00009 1.7460638 0.1863789  0.438074   220.545   227.515
gene5   79.9994   1.00060 5.3609924 0.0206822  0.139526   220.120   227.090
gene6  128.6477   1.00010 0.0921174 0.7616830  0.810301   246.775   253.745

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   47.6045 -0.1444526  0.377166 -0.3829949 0.701723518 0.8996455   215.264
gene2  112.3051 -0.0408527  0.408829 -0.0999261 0.920402997 0.9204030   238.963
gene3  131.2139  1.1712584  0.328651  3.5638376 0.000365472 0.0060912   236.529
gene4   86.2382  0.7297367  0.411517  1.7732823 0.076181944 0.1914186   220.545
gene5   79.9994 -0.4627939  0.408238 -1.1336370 0.256946852 0.4430118   220.120
gene6  128.6477  0.2677766  0.395393  0.6772414 0.498252789 0.7312441   246.775
            BIC
      <numeric>
gene1   222.234
gene2   245.933
gene3   243.499
gene4   227.515
gene5   227.090
gene6   253.745

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   47.6045  1.300840  0.902112  1.441994  0.149304  0.533229   215.264
gene2  112.3051  0.695493  0.973787  0.714215  0.475095  0.712387   238.963
gene3  131.2139  0.687488  0.778478  0.883118  0.377173  0.712387   236.529
gene4   86.2382 -1.115324  0.975726 -1.143071  0.253009  0.712387   220.545
gene5   79.9994 -1.513357  0.969929 -1.560276  0.118695  0.494562   220.120
gene6  128.6477  0.795117  0.942173  0.843919  0.398715  0.712387   246.775
            BIC
      <numeric>
gene1   222.234
gene2   245.933
gene3   243.499
gene4   227.515
gene5   227.090
gene6   253.745

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene21   87.5658   1.00010   7.86279 0.00505009 0.0926099   214.611   221.581
gene20   33.9079   1.00005   7.18447 0.00735607 0.0926099   202.114   209.084
gene11   88.5419   1.00011   7.10733 0.00767938 0.0926099   223.661   230.632
gene25   63.1237   1.00026   6.87110 0.00876659 0.0926099   206.596   213.566
gene22   58.8182   1.00010   6.77236 0.00926099 0.0926099   207.030   214.000
gene44   48.9418   1.00007   5.71943 0.01678114 0.1395264   183.342   190.312
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] ggplot2_3.3.2               BiocParallel_1.24.0        
 [3] NBAMSeq_1.6.1               SummarizedExperiment_1.20.0
 [5] Biobase_2.50.0              GenomicRanges_1.42.0       
 [7] GenomeInfoDb_1.26.0         IRanges_2.24.0             
 [9] S4Vectors_0.28.0            BiocGenerics_0.36.0        
[11] MatrixGenerics_1.2.0        matrixStats_0.57.0         

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.5             locfit_1.5-9.4         lattice_0.20-41       
 [4] digest_0.6.27          R6_2.5.0               RSQLite_2.2.1         
 [7] evaluate_0.14          httr_1.4.2             pillar_1.4.6          
[10] zlibbioc_1.36.0        rlang_0.4.8            annotate_1.68.0       
[13] blob_1.2.1             Matrix_1.2-18          rmarkdown_2.5         
[16] labeling_0.4.2         splines_4.0.3          geneplotter_1.68.0    
[19] stringr_1.4.0          RCurl_1.98-1.2         bit_4.0.4             
[22] munsell_0.5.0          DelayedArray_0.16.0    compiler_4.0.3        
[25] xfun_0.18              pkgconfig_2.0.3        mgcv_1.8-33           
[28] htmltools_0.5.0        tidyselect_1.1.0       tibble_3.0.4          
[31] GenomeInfoDbData_1.2.4 XML_3.99-0.5           withr_2.3.0           
[34] crayon_1.3.4           dplyr_1.0.2            bitops_1.0-6          
[37] grid_4.0.3             nlme_3.1-150           xtable_1.8-4          
[40] gtable_0.3.0           lifecycle_0.2.0        DBI_1.1.0             
[43] magrittr_1.5           scales_1.1.1           stringi_1.5.3         
[46] farver_2.0.3           XVector_0.30.0         genefilter_1.72.0     
[49] ellipsis_0.3.1         vctrs_0.3.4            generics_0.0.2        
[52] RColorBrewer_1.1-2     tools_4.0.3            bit64_4.0.5           
[55] glue_1.4.2             DESeq2_1.30.0          purrr_0.3.4           
[58] survival_3.2-7         yaml_2.2.1             AnnotationDbi_1.52.0  
[61] colorspace_1.4-1       memoise_1.1.0          knitr_1.30            

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.