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      22       1     110      25     496      15       9      30       1
gene2      25      11       1       4     303      13     136       1     182
gene3       2       6      45      12      15     279      62      10      85
gene4       8      23      48     139      21      40      58     248      15
gene5      15     186     174      14       8      32     403       4     126
gene6      14      20      10     139       1       3      14      60      37
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      263        1        5       90        1        8       14        7
gene2       46       20       86        7      261        5       11        4
gene3       23        9        9      104        4      266      136        3
gene4      135       22       59       39      417       22        2      464
gene5        1       10       12      190        3      206        1        1
gene6       17        1       15      273        4      406       25       10
      sample18 sample19 sample20
gene1        1        1       97
gene2       93        2       47
gene3        1       73       32
gene4      124      243       73
gene5      113      118       14
gene6       68       91      243

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 64.77751 -0.01786747 -0.2158260 0.8455936    1
sample2 23.13641 -0.65015821  0.5520884 1.2248022    2
sample3 35.87109  1.42192469 -1.5658659 0.3892501    0
sample4 46.13160  0.38520581  0.2284249 0.9802081    0
sample5 51.27738 -1.77963158  2.2299165 0.3287545    2
sample6 39.62400 -1.41437028 -0.8344269 0.8472873    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   46.4759   1.00035  1.693718 0.1933743  0.508880   197.565   204.536
gene2   55.1668   1.00006  0.838292 0.3599303  0.749855   210.234   217.204
gene3   61.4953   1.00005  0.023307 0.8787783  0.971141   212.998   219.968
gene4  121.1870   1.00020  0.115022 0.7347070  0.895984   244.334   251.305
gene5   71.3971   1.00020  1.584382 0.2080788  0.520197   213.216   220.186
gene6   65.7973   1.00007  6.034145 0.0140328  0.175411   208.255   215.226

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   46.4759  0.309811  0.506923  0.6111599 0.5410937  0.877446   197.565
gene2   55.1668  0.035383  0.460184  0.0768889 0.9387120  0.939397   210.234
gene3   61.4953  0.173693  0.450252  0.3857675 0.6996689  0.929572   212.998
gene4  121.1870 -0.445956  0.420115 -1.0615083 0.2884590  0.627085   244.334
gene5   71.3971  0.694289  0.435905  1.5927528 0.1112156  0.327105   213.216
gene6   65.7973  0.991281  0.404050  2.4533602 0.0141529  0.117940   208.255
            BIC
      <numeric>
gene1   204.536
gene2   217.204
gene3   219.968
gene4   251.305
gene5   220.186
gene6   215.226

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   46.4759  2.780283   1.33829  2.077483 0.0377570 0.1784528   197.565
gene2   55.1668  0.544549   1.21386  0.448608 0.6537142 0.7972124   210.234
gene3   61.4953 -2.975896   1.20781 -2.463880 0.0137442 0.0763567   212.998
gene4  121.1870 -1.896866   1.11144 -1.706679 0.0878818 0.2584758   244.334
gene5   71.3971 -0.304525   1.15217 -0.264305 0.7915450 0.8991422   213.216
gene6   65.7973 -0.796894   1.07516 -0.741189 0.4585787 0.6369148   208.255
            BIC
      <numeric>
gene1   204.536
gene2   217.204
gene3   219.968
gene4   251.305
gene5   220.186
gene6   215.226

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue        padj       AIC
       <numeric> <numeric> <numeric>   <numeric>   <numeric> <numeric>
gene24  149.5841   1.00031  20.90242 5.51951e-06 0.000275975   196.473
gene12   74.6923   1.00010   9.84994 1.69956e-03 0.042489058   216.690
gene26  111.0369   1.00036   6.54394 1.05245e-02 0.175407914   212.109
gene6    65.7973   1.00007   6.03415 1.40328e-02 0.175410613   208.255
gene46   56.8009   2.29215   8.83707 3.04569e-02 0.240854828   201.704
gene18   83.9014   1.40378   5.17996 3.08674e-02 0.240854828   184.044
             BIC
       <numeric>
gene24   203.444
gene12   223.660
gene26   219.080
gene6    215.226
gene46   209.961
gene18   191.417
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.1.0 RC (2021-05-16 r80304)
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.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] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] ggplot2_3.3.3               BiocParallel_1.27.0        
 [3] NBAMSeq_1.9.0               SummarizedExperiment_1.23.0
 [5] Biobase_2.53.0              GenomicRanges_1.45.0       
 [7] GenomeInfoDb_1.29.0         IRanges_2.27.0             
 [9] S4Vectors_0.31.0            BiocGenerics_0.39.0        
[11] MatrixGenerics_1.5.0        matrixStats_0.58.0         

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_4.1.0          bslib_0.2.5.1         
 [7] assertthat_0.2.1       highr_0.9              blob_1.2.1            
[10] GenomeInfoDbData_1.2.6 yaml_2.2.1             pillar_1.6.1          
[13] RSQLite_2.2.7          lattice_0.20-44        glue_1.4.2            
[16] digest_0.6.27          RColorBrewer_1.1-2     XVector_0.33.0        
[19] colorspace_2.0-1       htmltools_0.5.1.1      Matrix_1.3-3          
[22] DESeq2_1.33.0          XML_3.99-0.6           pkgconfig_2.0.3       
[25] genefilter_1.75.0      zlibbioc_1.39.0        purrr_0.3.4           
[28] xtable_1.8-4           scales_1.1.1           tibble_3.1.2          
[31] annotate_1.71.0        mgcv_1.8-35            KEGGREST_1.33.0       
[34] farver_2.1.0           generics_0.1.0         ellipsis_0.3.2        
[37] withr_2.4.2            cachem_1.0.5           survival_3.2-11       
[40] magrittr_2.0.1         crayon_1.4.1           memoise_2.0.0         
[43] evaluate_0.14          fansi_0.4.2            nlme_3.1-152          
[46] tools_4.1.0            lifecycle_1.0.0        stringr_1.4.0         
[49] locfit_1.5-9.4         munsell_0.5.0          DelayedArray_0.19.0   
[52] AnnotationDbi_1.55.0   Biostrings_2.61.0      compiler_4.1.0        
[55] jquerylib_0.1.4        rlang_0.4.11           grid_4.1.0            
[58] RCurl_1.98-1.3         labeling_0.4.2         bitops_1.0-7          
[61] rmarkdown_2.8          gtable_0.3.0           DBI_1.1.1             
[64] R6_2.5.0               knitr_1.33             dplyr_1.0.6           
[67] fastmap_1.1.0          bit_4.0.4              utf8_1.2.1            
[70] stringi_1.6.2          Rcpp_1.0.6             vctrs_0.3.8           
[73] geneplotter_1.71.0     png_0.1-7              tidyselect_1.1.1      
[76] xfun_0.23             

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.