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      66       1       3     142       1       1       3      41       7
gene2       3     162      44      95       5       2     116      18       2
gene3      48      11       6      15       2       2     278       1      27
gene4     163      48     178     354     144    1172      93       9      20
gene5       8       8       1       3     257      11     407       8     331
gene6      56     105      48      12      75       2      38      88       5
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       20       43       68      465      216       27       97      440
gene2      164        1      116        2       26       22      161       38
gene3      500        4       75      260      137       38      205        6
gene4       36      572       37       38        6        3       78       31
gene5        1       15      270        8      103       22      295      225
gene6        6       18      234       22       54        1        1        2
      sample18 sample19 sample20
gene1       11      710      317
gene2        1        1       96
gene3        1        1        9
gene4        2      137      169
gene5      155       13      160
gene6        7        6       22

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 39.32583 -1.466817457  0.253565457 -0.4836906    0
sample2 64.96879  0.009883497 -0.005491285  0.3062376    2
sample3 48.43803 -1.379046346  0.245591511 -1.1989460    0
sample4 72.23607  0.091576885 -2.368038614  1.5361869    0
sample5 58.18745 -0.581581836 -0.183409295  1.2285452    2
sample6 68.01419 -0.710004188  0.553171134 -0.7510875    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   83.4950   1.00004 2.85330461 0.09119168 0.3039723   230.078   237.048
gene2   40.7426   1.00013 0.00143641 0.97128357 0.9896601   202.512   209.482
gene3   50.4769   1.00014 1.01512994 0.31365235 0.7025948   204.952   211.922
gene4  244.9670   1.00011 7.85478951 0.00507215 0.0634018   250.354   257.324
gene5   78.4993   1.00017 0.30093433 0.58329219 0.7495266   229.711   236.681
gene6   30.8898   1.00008 3.29121405 0.06966618 0.2631689   192.840   199.810

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   83.4950 -0.5531634  0.359970 -1.536692 0.12436883  0.518203   230.078
gene2   40.7426  0.1824976  0.346935  0.526028 0.59886894  0.893616   202.512
gene3   50.4769  0.0480085  0.351486  0.136587 0.89135712  0.938854   204.952
gene4  244.9670 -0.9428239  0.343721 -2.742996 0.00608815  0.101469   250.354
gene5   78.4993 -0.1652298  0.350587 -0.471295 0.63743019  0.893616   229.711
gene6   30.8898  0.1267646  0.310087  0.408803 0.68268420  0.893616   192.840
            BIC
      <numeric>
gene1   237.048
gene2   209.482
gene3   211.922
gene4   257.324
gene5   236.681
gene6   199.810

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   83.4950 -0.281249  0.902434 -0.311656 0.7553023  0.939681   230.078
gene2   40.7426  1.359620  0.868752  1.565026 0.1175769  0.576695   202.512
gene3   50.4769  1.165995  0.878958  1.326564 0.1846528  0.576695   204.952
gene4  244.9670 -1.211238  0.860779 -1.407141 0.1593857  0.576695   250.354
gene5   78.4993 -0.189416  0.881924 -0.214776 0.8299417  0.953234   229.711
gene6   30.8898  1.670768  0.779445  2.143536 0.0320701  0.446951   192.840
            BIC
      <numeric>
gene1   237.048
gene2   209.482
gene3   211.922
gene4   257.324
gene5   236.681
gene6   199.810

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene16   70.9235   1.00010  14.17082 0.000166878 0.00494364   203.322   210.292
gene7    60.5208   1.00007  13.85170 0.000197746 0.00494364   206.712   213.682
gene32  115.5726   1.00007   9.83554 0.001712764 0.02854607   240.093   247.063
gene4   244.9670   1.00011   7.85479 0.005072146 0.06340182   250.354   257.324
gene10  110.1209   1.00006   6.93856 0.008438374 0.08438374   217.894   224.864
gene50   80.7912   1.00005   6.53371 0.010587286 0.08754528   216.427   223.397
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.4.1 (2024-06-14)
Platform: x86_64-apple-darwin20
Running under: macOS Monterey 12.7.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

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_3.5.1               BiocParallel_1.40.0        
 [3] NBAMSeq_1.22.0              SummarizedExperiment_1.36.0
 [5] Biobase_2.66.0              GenomicRanges_1.58.0       
 [7] GenomeInfoDb_1.42.0         IRanges_2.40.0             
 [9] S4Vectors_0.44.0            BiocGenerics_0.52.0        
[11] MatrixGenerics_1.18.0       matrixStats_1.4.1          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.46.0         gtable_0.3.6            xfun_0.48              
 [4] bslib_0.8.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.4.1             generics_0.1.3          parallel_4.4.1         
[10] RSQLite_2.3.7           tibble_3.2.1            fansi_1.0.6            
[13] AnnotationDbi_1.68.0    highr_0.11              blob_1.2.4             
[16] pkgconfig_2.0.3         Matrix_1.7-1            lifecycle_1.0.4        
[19] GenomeInfoDbData_1.2.13 farver_2.1.2            compiler_4.4.1         
[22] Biostrings_2.74.0       munsell_0.5.1           DESeq2_1.46.0          
[25] codetools_0.2-20        htmltools_0.5.8.1       sass_0.4.9             
[28] yaml_2.3.10             pillar_1.9.0            crayon_1.5.3           
[31] jquerylib_0.1.4         DelayedArray_0.32.0     cachem_1.1.0           
[34] abind_1.4-8             nlme_3.1-166            genefilter_1.88.0      
[37] tidyselect_1.2.1        locfit_1.5-9.10         digest_0.6.37          
[40] dplyr_1.1.4             labeling_0.4.3          splines_4.4.1          
[43] fastmap_1.2.0           grid_4.4.1              colorspace_2.1-1       
[46] cli_3.6.3               SparseArray_1.6.0       magrittr_2.0.3         
[49] S4Arrays_1.6.0          survival_3.7-0          XML_3.99-0.17          
[52] utf8_1.2.4              withr_3.0.2             scales_1.3.0           
[55] UCSC.utils_1.2.0        bit64_4.5.2             rmarkdown_2.28         
[58] XVector_0.46.0          httr_1.4.7              bit_4.5.0              
[61] png_0.1-8               memoise_2.0.1           evaluate_1.0.1         
[64] knitr_1.48              mgcv_1.9-1              rlang_1.1.4            
[67] Rcpp_1.0.13             DBI_1.2.3               xtable_1.8-4           
[70] glue_1.8.0              annotate_1.84.0         jsonlite_1.8.9         
[73] R6_2.5.1                zlibbioc_1.52.0        

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.