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       6     383     105       1      13       2     269      30       2
gene2      21       1     107      42      62     590      33       6       3
gene3       5       1     224      54     348      93      48       3     106
gene4      40       3      88       2      84       1      10      43       1
gene5       7       1       1      32     264     495       1     313      25
gene6      18     187     429      54     113      10      71     259     329
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1      829       90       25       26      190        1       29
gene2       14        1        4       81        5       11        7      240
gene3        1       18      113      116        6       24       47      519
gene4      142        1       89      254       18       54       51      165
gene5       38      244        2       22      584       38       19       11
gene6      166       20        8       18      409        1      333        1
      sample18 sample19 sample20
gene1      362      555       87
gene2        1       19       71
gene3       11       32        1
gene4        1      237       15
gene5      129       54       88
gene6       57      256        4

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 52.55769  0.4057805  0.6013479  0.2075753    2
sample2 23.30403 -0.9993752 -1.3777764 -0.5602620    0
sample3 51.68711  0.2635050  1.1771741  0.1922988    1
sample4 61.19599 -0.2998339 -0.1286972  0.8450080    1
sample5 29.01202 -0.1791292  0.6729535  1.2452066    0
sample6 28.43087 -0.1542338  0.4686567  0.3787563    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  139.5799   1.00011 1.91730054 0.16617764 0.3381527   235.366   242.337
gene2   48.4910   1.00007 4.30997779 0.03790077 0.1579199   202.808   209.778
gene3   71.3969   1.00005 1.46381633 0.22635648 0.4191787   222.196   229.166
gene4   48.3398   1.00003 0.00192697 0.96532379 0.9653238   210.856   217.826
gene5  110.4328   1.00045 1.16933654 0.27941004 0.4989465   227.762   234.732
gene6  135.3996   1.00005 7.01952648 0.00806541 0.0685061   239.698   246.669

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  139.5799 -1.009102  0.581583 -1.735095 0.0827240  0.335890   235.366
gene2   48.4910 -0.914815  0.532511 -1.717927 0.0858098  0.335890   202.808
gene3   71.3969  0.229234  0.542713  0.422385 0.6727439  0.814590   222.196
gene4   48.3398  0.209226  0.525609  0.398065 0.6905823  0.814590   210.856
gene5  110.4328  0.558515  0.533348  1.047186 0.2950140  0.702414   227.762
gene6  135.3996  0.877554  0.495197  1.772130 0.0763731  0.335890   239.698
            BIC
      <numeric>
gene1   242.337
gene2   209.778
gene3   229.166
gene4   217.826
gene5   234.732
gene6   246.669

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  139.5799  0.00271884  0.939435  0.00289412  0.997691  0.997691   235.366
gene2   48.4910  0.26728609  0.854884  0.31265789  0.754541  0.852870   202.808
gene3   71.3969 -0.15873737  0.877887 -0.18081751  0.856511  0.892199   222.196
gene4   48.3398  0.40327761  0.847841  0.47565231  0.634322  0.834929   210.856
gene5  110.4328 -0.66411027  0.865337 -0.76745872  0.442809  0.763463   227.762
gene6  135.3996 -0.82391355  0.802511 -1.02666949  0.304576  0.722251   239.698
            BIC
      <numeric>
gene1   242.337
gene2   209.778
gene3   229.166
gene4   217.826
gene5   234.732
gene6   246.669

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric> <numeric> <numeric> <numeric>
gene48  124.6309   1.00015  11.80001 0.000592563 0.0296282   208.393   215.364
gene42   81.2981   1.00016  10.10974 0.001475949 0.0368987   205.221   212.191
gene40  142.2276   1.00006   8.97884 0.002732339 0.0455390   232.839   239.809
gene44   97.6084   1.00004   7.17318 0.007401462 0.0685061   214.788   221.759
gene6   135.3996   1.00005   7.01953 0.008065414 0.0685061   239.698   246.669
gene12  149.3512   1.00018   6.94023 0.008432862 0.0685061   232.933   239.903
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 (2021-05-10 r80283)
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_1.26.0        
 [3] NBAMSeq_1.8.0               SummarizedExperiment_1.22.0
 [5] Biobase_2.52.0              GenomicRanges_1.44.0       
 [7] GenomeInfoDb_1.28.0         IRanges_2.26.0             
 [9] S4Vectors_0.30.0            BiocGenerics_0.38.0        
[11] MatrixGenerics_1.4.0        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_0.32.0        
[19] colorspace_2.0-1       htmltools_0.5.1.1      Matrix_1.3-3          
[22] DESeq2_1.32.0          XML_3.99-0.6           pkgconfig_2.0.3       
[25] genefilter_1.74.0      zlibbioc_1.38.0        purrr_0.3.4           
[28] xtable_1.8-4           scales_1.1.1           tibble_3.1.2          
[31] annotate_1.70.0        mgcv_1.8-35            KEGGREST_1.32.0       
[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_0.18.0   
[52] AnnotationDbi_1.54.0   Biostrings_2.60.0      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_1.70.0     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.