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       5       3      53      12       1      56      31      63      63
gene2      11     547      81      57     290     105       1       1       3
gene3      73       4       1      29       1      44      42       1     267
gene4       9       1      22     334      52     487     187      17     214
gene5       5      57      36       2       5      33      17      18     106
gene6     186      33     171      45      34      17     483       9      35
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      194        5       54      136        1      194      131      240
gene2        1       74       80       22       79       36        1       59
gene3        1      193       15       11        2      280      598      183
gene4        1       46       66      138       16      467        3       84
gene5       21      126       56       24       65        1      275       69
gene6       94        4       35      333       79       26       12        7
      sample18 sample19 sample20
gene1       13        1      179
gene2        3      153       38
gene3       12       28        1
gene4       34        1        1
gene5       32       15       88
gene6       60        1        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 57.66254  0.01265036 0.9934029 -1.7142257    1
sample2 34.66720 -0.10435286 0.3137609  0.5980733    0
sample3 56.25247 -0.65644423 1.7424033  1.0073511    1
sample4 78.24353  1.43103207 0.8477051  1.3220032    2
sample5 51.59431 -0.64136458 0.8038664  1.1385558    1
sample6 53.37846  0.08941207 0.6622098  0.3194802    1

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   62.4659   1.00006 0.0493945  0.824246  0.945626   217.952   224.922
gene2   70.1680   1.00017 0.2069966  0.649419  0.942503   209.409   216.380
gene3   86.0899   1.00008 1.5093814  0.219295  0.577093   206.729   213.699
gene4   97.3626   1.00006 1.7793996  0.182247  0.577093   225.370   232.340
gene5   47.8611   1.00011 0.1829719  0.668920  0.942503   211.169   218.139
gene6   63.2627   1.00019 1.6538605  0.198580  0.577093   218.465   225.436

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   62.4659  0.5455755  0.531811  1.025882 3.04947e-01 0.58643716   217.952
gene2   70.1680 -0.6500294  0.506925 -1.282299 1.99738e-01 0.48434398   209.409
gene3   86.0899  2.2221952  0.562946  3.947437 7.89922e-05 0.00394961   206.729
gene4   97.3626  1.4552846  0.566246  2.570059 1.01681e-02 0.08473427   225.370
gene5   47.8611 -0.0738979  0.474452 -0.155754 8.76227e-01 0.94676709   211.169
gene6   63.2627  0.4354026  0.482650  0.902109 3.66999e-01 0.65535566   218.465
            BIC
      <numeric>
gene1   224.922
gene2   216.380
gene3   213.699
gene4   232.340
gene5   218.139
gene6   225.436

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   62.4659 -0.473506  1.055792 -0.448484 0.6538040  0.797322   217.952
gene2   70.1680 -2.186699  0.994064 -2.199756 0.0278242  0.231868   209.409
gene3   86.0899  2.145727  1.141301  1.880072 0.0600983  0.241070   206.729
gene4   97.3626  1.783394  1.143254  1.559929 0.1187767  0.371177   225.370
gene5   47.8611  1.396437  0.943920  1.479401 0.1390331  0.408921   211.169
gene6   63.2627 -0.868513  0.962588 -0.902268 0.3669145  0.611524   218.465
            BIC
      <numeric>
gene1   224.922
gene2   216.380
gene3   213.699
gene4   232.340
gene5   218.139
gene6   225.436

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>
gene19   96.5271   1.00021   9.22165 0.00239504  0.119752   229.806   236.776
gene43   50.9227   1.00007   5.16122 0.02310830  0.345641   206.526   213.496
gene37   49.3237   1.00003   4.90794 0.02673575  0.345641   190.119   197.089
gene35   85.1063   1.00009   4.70989 0.03000369  0.345641   217.393   224.364
gene32   66.0225   1.00241   4.32738 0.03777153  0.345641   197.776   204.749
gene22   52.7951   1.00008   4.11411 0.04253480  0.345641   199.708   206.679

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 4.4.2 (2024-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.1 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        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: Etc/UTC
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_1.59.1       
 [7] GenomeInfoDb_1.43.4         IRanges_2.41.2             
 [9] S4Vectors_0.45.2            BiocGenerics_0.53.5        
[11] generics_0.1.3              MatrixGenerics_1.19.1      
[13] matrixStats_1.5.0           rmarkdown_2.29             

loaded via a namespace (and not attached):
 [1] KEGGREST_1.47.0         gtable_0.3.6            xfun_0.50              
 [4] bslib_0.8.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.4.2             parallel_4.4.2          tibble_3.2.1           
[10] AnnotationDbi_1.69.0    RSQLite_2.3.9           blob_1.2.4             
[13] pkgconfig_2.0.3         Matrix_1.7-2            lifecycle_1.0.4        
[16] GenomeInfoDbData_1.2.13 farver_2.1.2            compiler_4.4.2         
[19] Biostrings_2.75.3       munsell_0.5.1           DESeq2_1.47.1          
[22] codetools_0.2-20        htmltools_0.5.8.1       sys_3.4.3              
[25] buildtools_1.0.0        sass_0.4.9              yaml_2.3.10            
[28] pillar_1.10.1           crayon_1.5.3            jquerylib_0.1.4        
[31] DelayedArray_0.33.4     cachem_1.1.0            abind_1.4-8            
[34] nlme_3.1-167            genefilter_1.89.0       locfit_1.5-9.10        
[37] digest_0.6.37           labeling_0.4.3          splines_4.4.2          
[40] maketools_1.3.1         fastmap_1.2.0           grid_4.4.2             
[43] colorspace_2.1-1        cli_3.6.3               SparseArray_1.7.4      
[46] magrittr_2.0.3          S4Arrays_1.7.1          survival_3.8-3         
[49] XML_3.99-0.18           withr_3.0.2             scales_1.3.0           
[52] UCSC.utils_1.3.1        bit64_4.6.0-1           XVector_0.47.2         
[55] httr_1.4.7              bit_4.5.0.1             png_0.1-8              
[58] memoise_2.0.1           evaluate_1.0.3          knitr_1.49             
[61] mgcv_1.9-1              rlang_1.1.5             Rcpp_1.0.14            
[64] xtable_1.8-4            glue_1.8.0              DBI_1.2.3              
[67] annotate_1.85.0         jsonlite_1.8.9          R6_2.5.1