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     181     124      26      56       1     150      51      41      26
gene2      14     264     104       4      47      30     809     782       5
gene3     130      46      76       2      26       5       1       3      70
gene4      14     112      86     329       1      24       2     243      17
gene5       1      58       1       1       4      23       2      20      31
gene6      62      89      66     215       3     250       1      24       1
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      418       49        2        1       64       37      115        1
gene2       26      172      253      135       17        1      110        1
gene3       39        2      233        5        1       24        5        1
gene4        4       37      251        1        2        3        1       57
gene5      236       21       31        1      373       25       12      140
gene6       45      113      133        1        3        3        1      198
      sample18 sample19 sample20
gene1        2      227       10
gene2       12        1      157
gene3        1       63        6
gene4      661      188        2
gene5        5        6        4
gene6        2        2       19

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 32.59259 -0.2657889  0.87630545 -0.2490041    0
sample2 52.46539 -0.1991162 -0.78586552 -1.5671406    1
sample3 59.18598 -0.9658973  0.65457936 -2.1245159    0
sample4 58.86643  1.2905880  0.06208294  0.3086465    1
sample5 55.62493  0.3164586 -0.02959217  0.1727345    0
sample6 50.27485 -0.6189322  0.67204385 -1.4086403    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   64.0070   1.00015 5.79062e-01 0.4468797  0.709019   220.943   227.913
gene2  135.9113   1.00006 4.91849e+00 0.0265755  0.147642   225.824   232.794
gene3   30.2640   1.00009 1.31078e+00 0.2522620  0.504524   186.494   193.465
gene4   95.3365   1.00032 3.88297e+00 0.0488054  0.187713   215.976   222.946
gene5   34.5089   1.00002 6.80666e-05 0.9934255  0.993425   187.292   194.262
gene6   47.5108   1.00041 5.83530e-03 0.9397012  0.980188   206.009   212.980

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   64.0070  0.928766  0.683896  1.3580521 0.1744471 0.3465837   220.943
gene2  135.9113 -0.404072  0.624429 -0.6471058 0.5175635 0.7321400   225.824
gene3   30.2640  1.763427  0.715015  2.4662782 0.0136525 0.0687635   186.494
gene4   95.3365 -0.056104  0.751092 -0.0746966 0.9404561 0.9992212   215.976
gene5   34.5089 -1.527640  0.665217 -2.2964537 0.0216500 0.0984089   187.292
gene6   47.5108 -0.307646  0.746958 -0.4118655 0.6804380 0.8723564   206.009
            BIC
      <numeric>
gene1   227.913
gene2   232.794
gene3   193.465
gene4   222.946
gene5   194.262
gene6   212.980

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   64.0070  1.989243   1.45286  1.369189 0.1709402  0.427350   220.943
gene2  135.9113  3.246345   1.32419  2.451570 0.0142234  0.101596   225.824
gene3   30.2640  2.238391   1.52067  1.471979 0.1410266  0.419170   186.494
gene4   95.3365  0.677263   1.59065  0.425776 0.6702710  0.823535   215.976
gene5   34.5089 -1.691962   1.39937 -1.209093 0.2266273  0.494493   187.292
gene6   47.5108 -0.468518   1.58324 -0.295923 0.7672892  0.856055   206.009
            BIC
      <numeric>
gene1   227.913
gene2   232.794
gene3   193.465
gene4   222.946
gene5   194.262
gene6   212.980

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$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue       padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric>  <numeric> <numeric> <numeric>
gene8    80.6806   1.00011  14.17418 0.000166812 0.00834058   200.360   207.331
gene16   97.9762   1.00007   9.62293 0.001922368 0.04011843   211.787   218.757
gene18  132.4689   1.00010   9.21091 0.002407106 0.04011843   247.725   254.695
gene41   48.6366   1.00010   7.50130 0.006167421 0.07709277   187.263   194.234
gene11   86.2609   1.00007   6.81324 0.009050762 0.09050762   216.143   223.113
gene26   60.1304   1.00004   6.27541 0.012244079 0.10203399   193.808   200.779
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$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 4.0.0 alpha (2020-04-05 r78150)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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_3.3.0               BiocParallel_1.21.2        
 [3] NBAMSeq_1.3.1               SummarizedExperiment_1.17.5
 [5] DelayedArray_0.13.10        matrixStats_0.56.0         
 [7] Biobase_2.47.3              GenomicRanges_1.39.3       
 [9] GenomeInfoDb_1.23.16        IRanges_2.21.8             
[11] S4Vectors_0.25.15           BiocGenerics_0.33.3        

loaded via a namespace (and not attached):
 [1] locfit_1.5-9.4         Rcpp_1.0.4.6           lattice_0.20-41       
 [4] assertthat_0.2.1       digest_0.6.25          R6_2.4.1              
 [7] RSQLite_2.2.0          evaluate_0.14          pillar_1.4.3          
[10] zlibbioc_1.33.1        rlang_0.4.5            annotate_1.65.1       
[13] blob_1.2.1             Matrix_1.2-18          rmarkdown_2.1         
[16] labeling_0.3           splines_4.0.0          geneplotter_1.65.0    
[19] stringr_1.4.0          RCurl_1.98-1.1         bit_1.1-15.2          
[22] munsell_0.5.0          compiler_4.0.0         xfun_0.12             
[25] pkgconfig_2.0.3        mgcv_1.8-31            htmltools_0.4.0       
[28] tidyselect_1.0.0       tibble_3.0.0           GenomeInfoDbData_1.2.2
[31] XML_3.99-0.3           fansi_0.4.1            withr_2.1.2           
[34] crayon_1.3.4           dplyr_0.8.5            bitops_1.0-6          
[37] grid_4.0.0             nlme_3.1-145           xtable_1.8-4          
[40] gtable_0.3.0           lifecycle_0.2.0        DBI_1.1.0             
[43] magrittr_1.5           scales_1.1.0           cli_2.0.2             
[46] stringi_1.4.6          farver_2.0.3           XVector_0.27.2        
[49] genefilter_1.69.0      ellipsis_0.3.0         vctrs_0.2.4           
[52] RColorBrewer_1.1-2     tools_4.0.0            bit64_0.9-7           
[55] glue_1.4.0             DESeq2_1.27.29         purrr_0.3.3           
[58] survival_3.1-11        yaml_2.2.1             AnnotationDbi_1.49.1  
[61] colorspace_1.4-1       memoise_1.1.0          knitr_1.28            

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.