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     195      19       2      61       8       4     804     329       1
gene2      77     122       4      87      10       9       3     458      31
gene3     199      96     146     155      43      49     424     257      10
gene4     411      20      72     380     218      28     389      67     331
gene5       1       2      10      60      11       4     163       1     588
gene6      42     284      35       1       2      70       1       2     745
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      105      115       15       21       53       77       13       22
gene2      188        2      687      292       51       10       21       44
gene3       36       65        1       22      180      142        8      148
gene4        6        1       21        1        2      118      912        2
gene5       34       59       68      163       49       16        1       21
gene6        1        1      105      197     1091       45       44       60
      sample18 sample19 sample20
gene1       75       28        1
gene2      167        3        1
gene3        1       60       46
gene4        6       27        6
gene5       46        1       63
gene6      182        1      244

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 60.03657  0.1735732  1.952116e-01 -1.62958401    2
sample2 75.54840 -0.3448225  1.358539e-07 -0.90582229    2
sample3 43.67510  0.5759888 -2.417837e-01  0.36415755    0
sample4 54.91128  0.2746436 -1.425638e-01 -0.05653739    0
sample5 77.04134  0.1616370  1.235222e+00  0.15572026    2
sample6 73.97851  1.8351914 -4.850546e-02  1.11533887    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   88.7336   1.00007  0.147293 0.70124657 0.8551787   220.328   227.299
gene2  118.1393   1.00007  1.747603 0.18618820 0.4822348   218.672   225.642
gene3   91.6939   1.00009  0.341405 0.55911736 0.7765519   236.531   243.501
gene4  114.8791   1.00006  1.497269 0.22109540 0.5024895   232.374   239.344
gene5   61.6824   1.00006  8.406867 0.00373971 0.0389551   200.715   207.685
gene6  127.5728   1.00097  1.713240 0.19131154 0.4822348   228.915   235.886

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   88.7336 -0.630657  0.473103 -1.333022 0.18252468 0.5350987   220.328
gene2  118.1393  1.285774  0.451041  2.850682 0.00436256 0.0436256   218.672
gene3   91.6939 -0.576917  0.431077 -1.338316 0.18079358 0.5350987   236.531
gene4  114.8791 -0.151883  0.518596 -0.292874 0.76961867 0.8700008   232.374
gene5   61.6824 -1.036167  0.460892 -2.248180 0.02456472 0.1649465   200.715
gene6  127.5728 -0.473169  0.549416 -0.861221 0.38911610 0.5895698   228.915
            BIC
      <numeric>
gene1   227.299
gene2   225.642
gene3   243.501
gene4   239.344
gene5   207.685
gene6   235.886

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   88.7336  1.252631  0.871536  1.437268 0.1506417  0.538006   220.328
gene2  118.1393  0.660543  0.826117  0.799575 0.4239571  0.860247   218.672
gene3   91.6939 -0.196345  0.790023 -0.248531 0.8037234  0.999692   236.531
gene4  114.8791 -0.373967  0.948155 -0.394415 0.6932746  0.999692   232.374
gene5   61.6824  1.456765  0.846881  1.720154 0.0854045  0.427022   200.715
gene6  127.5728  0.737587  1.008007  0.731729 0.4643342  0.860247   228.915
            BIC
      <numeric>
gene1   227.299
gene2   225.642
gene3   243.501
gene4   239.344
gene5   207.685
gene6   235.886

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric> <numeric> <numeric> <numeric>
gene23  101.2455   1.00009  11.95961 0.000544027 0.0272014   224.142   231.112
gene33   52.2875   1.00009   8.88980 0.002868356 0.0389551   205.592   212.563
gene46   40.8649   1.00004   8.73020 0.003130496 0.0389551   189.330   196.300
gene5    61.6824   1.00006   8.40687 0.003739709 0.0389551   200.715   207.685
gene49   98.5282   1.00007   8.33279 0.003895513 0.0389551   218.656   225.626
gene47   68.7150   1.00050   6.77471 0.009290820 0.0774235   209.791   216.762
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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-w64-mingw32/x64 (64-bit)
Running under: Windows Server 2012 R2 x64 (build 9600)

Matrix products: default

locale:
[1] LC_COLLATE=C                          
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

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_1.4.1               SummarizedExperiment_1.18.1
 [5] DelayedArray_0.14.0         matrixStats_0.56.0         
 [7] Biobase_2.48.0              GenomicRanges_1.40.0       
 [9] GenomeInfoDb_1.24.0         IRanges_2.22.1             
[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] snow_0.4-3             assertthat_0.2.1       digest_0.6.25         
 [7] R6_2.4.1               RSQLite_2.2.0          evaluate_0.14         
[10] pillar_1.4.4           zlibbioc_1.34.0        rlang_0.4.6           
[13] annotate_1.66.0        blob_1.2.1             Matrix_1.2-18         
[16] rmarkdown_2.1          labeling_0.3           splines_4.0.0         
[19] geneplotter_1.66.0     stringr_1.4.0          RCurl_1.98-1.2        
[22] bit_1.1-15.2           munsell_0.5.0          compiler_4.0.0        
[25] xfun_0.13              pkgconfig_2.0.3        mgcv_1.8-31           
[28] htmltools_0.4.0        tidyselect_1.0.0       tibble_3.0.1          
[31] GenomeInfoDbData_1.2.3 XML_3.99-0.3           withr_2.2.0           
[34] crayon_1.3.4           dplyr_0.8.5            bitops_1.0-6          
[37] grid_4.0.0             nlme_3.1-147           xtable_1.8-4          
[40] gtable_0.3.0           lifecycle_0.2.0        DBI_1.1.0             
[43] magrittr_1.5           scales_1.1.0           stringi_1.4.6         
[46] farver_2.0.3           XVector_0.28.0         genefilter_1.70.0     
[49] ellipsis_0.3.0         vctrs_0.2.4            RColorBrewer_1.1-2    
[52] tools_4.0.0            bit64_0.9-7            glue_1.4.0            
[55] DESeq2_1.28.0          purrr_0.3.4            survival_3.1-12       
[58] yaml_2.2.1             AnnotationDbi_1.50.0   colorspace_1.4-1      
[61] memoise_1.1.0          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.