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       1       1     375     102       1     332      20     141
gene2      71      12       7       3       8     189       1      38     100
gene3      76      16       1      20      46     176      60     176       5
gene4     125      55     324       1      42       2     129     183       2
gene5      20       4     118      19     103      11      46     356      60
gene6       4       2     123       2      23       1      24     199      99
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       19      399       11        7        5      125       51       26
gene2        5        1        1        1       53        4       30      163
gene3        1       19        3       40        1        1        2        1
gene4      419        2       14       10       60       55      509      167
gene5      211        2       83        1      470       98      125      126
gene6      273        5       25        2        1      297       70      155
      sample18 sample19 sample20
gene1        1      149        5
gene2       81      276     1010
gene3      403        1        2
gene4       88        1       61
gene5        9        7       46
gene6       85      267      111

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 66.85296  0.1977064  0.91432247  1.3359741    0
sample2 21.12231  0.7733010 -0.61751034 -0.7682266    0
sample3 38.41918 -1.1293677  0.03642817  1.6802529    2
sample4 33.41475 -1.0303210 -1.30283166  0.3928843    2
sample5 63.25405 -1.0039299 -1.53395832  0.3294808    2
sample6 34.52833  1.6164039 -0.21915569 -0.6614028    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   82.8226   1.00005 0.05828777  0.809261  0.963406   216.531   223.501
gene2   73.7929   1.00007 2.46759252  0.116220  0.605413   213.431   220.401
gene3   54.2551   1.00011 0.47114460  0.492641  0.746426   189.861   196.831
gene4  104.5287   1.00004 1.38887620  0.238601  0.605413   232.412   239.382
gene5   77.1968   1.00004 0.90356660  0.341837  0.681236   227.526   234.496
gene6   83.4661   1.00006 0.00185077  0.965698  0.969067   224.066   231.036

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   82.8226 -0.0560974  0.391026 -0.143462 0.88592532 0.9928059   216.531
gene2   73.7929  0.3003064  0.377588  0.795329 0.42642236 0.8195422   213.431
gene3   54.2551  1.0990539  0.384804  2.856139 0.00428827 0.0357356   189.861
gene4  104.5287 -0.2338392  0.358076 -0.653043 0.51372853 0.8195422   232.412
gene5   77.1968  0.0900283  0.314360  0.286386 0.77458216 0.9682277   227.526
gene6   83.4661  0.2247063  0.362293  0.620233 0.53510408 0.8195422   224.066
            BIC
      <numeric>
gene1   223.501
gene2   220.401
gene3   196.831
gene4   239.382
gene5   234.496
gene6   231.036

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   82.8226 -0.649093  0.955453 -0.679356 0.4969122  0.803186   216.531
gene2   73.7929 -1.066900  0.923389 -1.155417 0.2479196  0.692521   213.431
gene3   54.2551  0.313046  0.934980  0.334815 0.7377645  0.878291   189.861
gene4  104.5287  1.839674  0.875391  2.101546 0.0355931  0.361181   232.412
gene5   77.1968  1.483102  0.769045  1.928498 0.0537932  0.361181   227.526
gene6   83.4661  1.755147  0.885899  1.981205 0.0475683  0.361181   224.066
            BIC
      <numeric>
gene1   223.501
gene2   220.401
gene3   196.831
gene4   239.382
gene5   234.496
gene6   231.036

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat     pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene21   76.6865   1.00024   9.04208 0.00263894  0.131947   206.300   213.270
gene46   96.8958   1.00006   5.87668 0.01534436  0.243961   229.545   236.515
gene13   89.0793   1.00006   5.72448 0.01673363  0.243961   215.708   222.678
gene7    87.8366   1.00016   5.45510 0.01951692  0.243961   223.516   230.486
gene32   67.7956   1.00007   3.96552 0.04644752  0.464475   218.653   225.623
gene40   86.6503   1.00009   3.46852 0.06256151  0.521346   187.709   194.679
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.0.0 (2020-04-24)
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_3.3.0               BiocParallel_1.22.0        
 [3] NBAMSeq_1.4.0               SummarizedExperiment_1.18.0
 [5] DelayedArray_0.14.0         matrixStats_0.56.0         
 [7] Biobase_2.48.0              GenomicRanges_1.40.0       
 [9] GenomeInfoDb_1.24.0         IRanges_2.22.0             
[11] S4Vectors_0.26.0            BiocGenerics_0.34.0        

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.4.6           locfit_1.5-9.4         lattice_0.20-41       
 [4] assertthat_0.2.1       digest_0.6.25          R6_2.4.1              
 [7] RSQLite_2.2.0          evaluate_0.14          pillar_1.4.3          
[10] zlibbioc_1.34.0        rlang_0.4.5            annotate_1.66.0       
[13] blob_1.2.1             Matrix_1.2-18          rmarkdown_2.1         
[16] labeling_0.3           splines_4.0.0          geneplotter_1.66.0    
[19] stringr_1.4.0          RCurl_1.98-1.2         bit_1.1-15.2          
[22] munsell_0.5.0          compiler_4.0.0         xfun_0.13             
[25] pkgconfig_2.0.3        mgcv_1.8-31            htmltools_0.4.0       
[28] tidyselect_1.0.0       tibble_3.0.1           GenomeInfoDbData_1.2.3
[31] XML_3.99-0.3           withr_2.2.0            crayon_1.3.4          
[34] dplyr_0.8.5            bitops_1.0-6           grid_4.0.0            
[37] nlme_3.1-147           xtable_1.8-4           gtable_0.3.0          
[40] lifecycle_0.2.0        DBI_1.1.0              magrittr_1.5          
[43] scales_1.1.0           stringi_1.4.6          farver_2.0.3          
[46] XVector_0.28.0         genefilter_1.70.0      ellipsis_0.3.0        
[49] vctrs_0.2.4            RColorBrewer_1.1-2     tools_4.0.0           
[52] bit64_0.9-7            glue_1.4.0             DESeq2_1.28.0         
[55] purrr_0.3.4            survival_3.1-12        yaml_2.2.1            
[58] AnnotationDbi_1.50.0   colorspace_1.4-1       memoise_1.1.0         
[61] knitr_1.28            

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.