NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data

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:

• Step 1: Data input using NBAMSeqDataSet;

• Step 2: Differential expression (DE) analysis using NBAMSeq function;

• Step 3: Pulling out DE results using results function.

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     198      38     200      10       2     547       1     203      44
gene2     221       5      35      38      57      11       2     503       4
gene3      27      17     562      48       1      37     374       2      16
gene4      11       5       2       8       2     153     110       1     469
gene5     248     214      25       3      35      21      24       2      73
gene6     382       1      24      47      65     189       5      22     115
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1       87       25        1        2       16        2     1177      305
gene2       12       28        1        1        2        1        4       33
gene3        1       70       15        1       27       66        8       38
gene4        7        5       12      214        1      737        1      262
gene5      157        2      503        5      151        1        5       27
gene6      317      109        1        1      233       48      159      315
      sample18 sample19 sample20
gene1        1      129        1
gene2       86      460        5
gene3        1      140       18
gene4       22       35       55
gene5        1       33        7
gene6      323       83       43

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 36.54951  0.04488663 -0.71294090  0.0640629    1
sample2 49.92429  0.83912488  0.13588385  0.1130017    2
sample3 67.91117  0.96257435 -0.74942510 -0.7990847    1
sample4 62.99399 -0.87713156 -0.92663976  0.4771915    1
sample5 41.74307  0.90722197 -0.01735581 -1.5746186    2
sample6 73.50637 -1.17876044 -1.76796116 -1.1692036    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:

• multiple nonlinear covariates are supported, e.g. design = ~ s(pheno) + s(var1) + var2 + var3 + var4;

• the nonlinear covariate cannot be a discrete variable, e.g.  design = ~ s(pheno) + var1 + var2 + var3 + s(var4) as var4 is a factor, and it makes no sense to model a factor as nonlinear;

• at least one nonlinear covariate should be provided in design. If all covariates are assumed to have linear effect on gene count, use DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2010), NBPSeq (Di et al. 2015) or BBSeq (Zhou, Xia, and Wright 2011) instead. e.g.  design = ~ pheno + var1 + var2 + var3 + var4 is not supported in NBAMSeq;

• design matrix is not supported.

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.

• gamma argument can be used to control the smoothness of the nonlinear function. Higher gamma means the nonlinear function will be more smooth. See the gamma argument of gam function in mgcv (Wood and Wood 2015) for details. Default gamma is 2.5;

• fitlin is either TRUE or FALSE indicating whether linear model should be fitted after fitting the nonlinear model;

• parallel is either TRUE or FALSE indicating whether parallel should be used. e.g. Run NBAMSeq with parallel = TRUE:

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  124.8252   1.00041  0.409282 0.5224953  0.761648   222.550   229.521
gene2   78.9734   1.00008  0.907578 0.3407855  0.669120   199.872   206.842
gene3   94.3556   1.00006  1.157500 0.2820112  0.669120   212.541   219.512
gene4   79.2734   1.00005  6.030721 0.0140618  0.100441   206.715   213.685
gene5   57.6009   1.00005  4.540161 0.0331124  0.206952   198.279   205.249
gene6   89.5401   1.00015  0.842993 0.3586933  0.669120   241.729   248.700

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  124.8252  1.3165099  0.554546  2.374031 0.0175951 0.0799776   222.550
gene2   78.9734  1.4065711  0.512671  2.743614 0.0060767 0.0412761   199.872
gene3   94.3556  1.0349204  0.534193  1.937353 0.0527022 0.1756741   212.541
gene4   79.2734 -0.7677040  0.490859 -1.564000 0.1178176 0.3100464   206.715
gene5   57.6009  0.4761483  0.425916  1.117940 0.2635927 0.4881346   198.279
gene6   89.5401 -0.0587845  0.473015 -0.124276 0.9010966 0.9586134   241.729
            BIC
      <numeric>
gene1   229.521
gene2   206.842
gene3   219.512
gene4   213.685
gene5   205.249
gene6   248.700

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  124.8252 -2.023208  1.103220 -1.833911 0.0666672 0.3703733   222.550
gene2   78.9734  1.841593  1.063241  1.732055 0.0832637 0.3784713   199.872
gene3   94.3556  0.965255  1.096824  0.880045 0.3788349 0.7892393   212.541
gene4   79.2734 -3.049029  1.004993 -3.033881 0.0024143 0.0402383   206.715
gene5   57.6009  1.214025  0.877904  1.382867 0.1667055 0.4473678   198.279
gene6   89.5401  0.140884  0.973044  0.144787 0.8848792 0.9351798   241.729
            BIC
      <numeric>
gene1   229.521
gene2   206.842
gene3   219.512
gene4   213.685
gene5   205.249
gene6   248.700

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>
gene45   81.7933   1.00012  12.04693 0.000519048 0.0163565   216.732   223.703
gene46   75.9742   1.00008  11.22271 0.000808667 0.0163565   217.922   224.893
gene50   41.4218   1.00005  10.79412 0.001018701 0.0163565   188.058   195.028
gene7   154.7134   1.00011  10.33237 0.001308517 0.0163565   237.272   244.243
gene31   61.4991   1.00009   6.79512 0.009145027 0.0914503   206.649   213.619
gene13   51.1736   1.00005   6.25324 0.012400312 0.1004411   201.091   208.061

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 Under development (unstable) (2024-10-21 r87258)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.1 LTS

Matrix products: default
BLAS:   /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so 
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_GB              LC_COLLATE=C              
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

time zone: America/New_York
tzcode source: system (glibc)

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

other attached packages:
 [1] ggplot2_3.5.1               BiocParallel_1.41.0        
 [3] NBAMSeq_1.23.0              SummarizedExperiment_1.37.0
 [5] Biobase_2.67.0              GenomicRanges_1.59.0       
 [7] GenomeInfoDb_1.43.0         IRanges_2.41.0             
 [9] S4Vectors_0.45.0            BiocGenerics_0.53.0        
[11] MatrixGenerics_1.19.0       matrixStats_1.4.1          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.47.0         gtable_0.3.6            xfun_0.48              
 [4] bslib_0.8.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.5.0             generics_0.1.3          parallel_4.5.0         
[10] RSQLite_2.3.7           tibble_3.2.1            fansi_1.0.6            
[13] AnnotationDbi_1.69.0    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_4.5.0         
[22] Biostrings_2.75.0       munsell_0.5.1           DESeq2_1.47.0          
[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_0.33.0     cachem_1.1.0           
[34] abind_1.4-8             nlme_3.1-166            genefilter_1.89.0      
[37] tidyselect_1.2.1        locfit_1.5-9.10         digest_0.6.37          
[40] dplyr_1.1.4             labeling_0.4.3          splines_4.5.0          
[43] fastmap_1.2.0           grid_4.5.0              colorspace_2.1-1       
[46] cli_3.6.3               SparseArray_1.7.0       magrittr_2.0.3         
[49] S4Arrays_1.7.0          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_1.3.0        bit64_4.5.2             rmarkdown_2.28         
[58] XVector_0.47.0          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_1.85.0         jsonlite_1.8.9         
[73] R6_2.5.1                zlibbioc_1.53.0        

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): 2672–78.