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      41       2      84     135       1     164      64       9
gene2      31       1       3     245       2     210      51     182      62
gene3     147      33      27       7      81     236      17      18     558
gene4      10      41      26       2      59      48      52       1      63
gene5       8     156       1      31       8       4     177      79     276
gene6       1     133      70      47     602      48       1       2     143
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      110       67        2       85      117       28       35       10
gene2      114       13      417       25      153      220       64       46
gene3      157        4        1       17       20       61       90      248
gene4      121        2      285      175        8      146      122      130
gene5      115       21      233       49        1      360        1      114
gene6      177        9      127        5        2        6       24       23
      sample18 sample19 sample20
gene1       19       51        3
gene2      440        2      370
gene3        1      484       30
gene4      126        1       37
gene5      430      199       13
gene6       30       46        2

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 42.23140 -1.06854777 -1.9148149  2.1622543    1
sample2 41.05865  0.06969265 -0.7117269 -0.6220956    0
sample3 55.72230 -0.18563410  2.7621480 -0.2850841    1
sample4 46.27921  0.72806825  0.9189249 -0.3763677    1
sample5 33.57518  1.05426767  1.0148440 -0.4556817    2
sample6 54.57660  0.56532508  1.4340208  0.6938135    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   37.3776   1.00007 1.0835860 0.2979282  0.677110   207.192   214.162
gene2  116.3574   1.00005 1.4734503 0.2248219  0.672821   244.886   251.856
gene3   85.9155   1.00007 0.0101426 0.9200585  0.959026   234.749   241.719
gene4   61.8265   1.00008 1.1750474 0.2784035  0.675593   220.312   227.283
gene5   95.9509   1.00022 3.0271702 0.0819371  0.533332   231.698   238.669
gene6   65.7465   1.00006 3.3887829 0.0656474  0.533332   205.461   212.431

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   37.3776 -0.451541  0.341495 -1.322248 0.18608557  0.706027   207.192
gene2  116.3574  0.454610  0.384284  1.183004 0.23680745  0.726373   244.886
gene3   85.9155  0.111858  0.383582  0.291613 0.77058225  0.957654   234.749
gene4   61.8265  0.692502  0.356575  1.942097 0.05212536  0.436703   220.312
gene5   95.9509  1.022439  0.384319  2.660390 0.00780503  0.130084   231.698
gene6   65.7465  1.028353  0.364206  2.823548 0.00474953  0.118738   205.461
            BIC
      <numeric>
gene1   214.162
gene2   251.856
gene3   241.719
gene4   227.283
gene5   238.669
gene6   212.431

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   37.3776  0.9647052  0.907750  1.0627436  0.287898  0.712387   207.192
gene2  116.3574  0.0936038  1.022689  0.0915272  0.927074  0.965702   244.886
gene3   85.9155 -1.0997060  1.021815 -1.0762276  0.281825  0.712387   234.749
gene4   61.8265  0.9835362  0.943638  1.0422808  0.297282  0.712387   220.312
gene5   95.9509  0.3212644  1.005216  0.3195975  0.749273  0.936592   231.698
gene6   65.7465 -1.5280669  0.961094 -1.5899237  0.111852  0.632278   205.461
            BIC
      <numeric>
gene1   214.162
gene2   251.856
gene3   241.719
gene4   227.283
gene5   238.669
gene6   212.431

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat    pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene37   51.7417   1.00011   4.44925 0.0349317  0.533332   206.912   213.882
gene40   47.3886   1.00017   4.43987 0.0351192  0.533332   191.171   198.141
gene9    55.5620   1.00006   4.17005 0.0411564  0.533332   202.374   209.344
gene50   77.1378   1.00009   3.71160 0.0540510  0.533332   220.668   227.639
gene6    65.7465   1.00006   3.38878 0.0656474  0.533332   205.461   212.431
gene20   79.3008   1.00100   3.13058 0.0767897  0.533332   234.070   241.041
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.3.1 Patched (2023-06-17 r84564)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.6.5

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] ggplot2_3.4.4               BiocParallel_1.36.0        
 [3] NBAMSeq_1.18.0              SummarizedExperiment_1.32.0
 [5] Biobase_2.62.0              GenomicRanges_1.54.1       
 [7] GenomeInfoDb_1.38.0         IRanges_2.36.0             
 [9] S4Vectors_0.40.1            BiocGenerics_0.48.1        
[11] MatrixGenerics_1.14.0       matrixStats_1.0.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.42.0         gtable_0.3.4            xfun_0.41              
 [4] bslib_0.5.1             lattice_0.22-5          vctrs_0.6.4            
 [7] tools_4.3.1             bitops_1.0-7            generics_0.1.3         
[10] parallel_4.3.1          RSQLite_2.3.2           AnnotationDbi_1.64.0   
[13] tibble_3.2.1            fansi_1.0.5             highr_0.10             
[16] blob_1.2.4              pkgconfig_2.0.3         Matrix_1.6-1.1         
[19] lifecycle_1.0.3         GenomeInfoDbData_1.2.11 farver_2.1.1           
[22] compiler_4.3.1          Biostrings_2.70.1       munsell_0.5.0          
[25] DESeq2_1.42.0           codetools_0.2-19        htmltools_0.5.6.1      
[28] sass_0.4.7              RCurl_1.98-1.12         yaml_2.3.7             
[31] pillar_1.9.0            crayon_1.5.2            jquerylib_0.1.4        
[34] DelayedArray_0.28.0     cachem_1.0.8            abind_1.4-5            
[37] nlme_3.1-163            genefilter_1.84.0       tidyselect_1.2.0       
[40] locfit_1.5-9.8          digest_0.6.33           dplyr_1.1.3            
[43] labeling_0.4.3          splines_4.3.1           fastmap_1.1.1          
[46] grid_4.3.1              colorspace_2.1-0        cli_3.6.1              
[49] SparseArray_1.2.0       magrittr_2.0.3          S4Arrays_1.2.0         
[52] survival_3.5-7          XML_3.99-0.14           utf8_1.2.4             
[55] withr_2.5.2             scales_1.2.1            bit64_4.0.5            
[58] rmarkdown_2.25          XVector_0.42.0          httr_1.4.7             
[61] bit_4.0.5               png_0.1-8               memoise_2.0.1          
[64] evaluate_0.23           knitr_1.45              mgcv_1.9-0             
[67] rlang_1.1.1             Rcpp_1.0.11             DBI_1.1.3              
[70] xtable_1.8-4            glue_1.6.2              annotate_1.80.0        
[73] jsonlite_1.8.7          R6_2.5.1                zlibbioc_1.48.0        

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.