NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2021-05-19
Installation
To install and load 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
NBAMSeqfunction;Step 3: Pulling out DE results using
resultsfunction.
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 530 15 94 248 1 37 126 67 77
gene2 11 12 3 201 52 4 4 110 17
gene3 9 7 1 1 32 220 337 91 422
gene4 3 3 5 151 206 2 1 262 3
gene5 3 53 180 64 314 12 2 1 91
gene6 83 2 19 1 1 97 1298 1 26
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 20 2 363 29 1 38 174
gene2 54 586 17 9 199 35 1 127
gene3 1 1 5 126 3 9 106 2
gene4 16 404 57 10 212 38 1 79
gene5 149 294 622 2 11 1 280 239
gene6 135 127 1 5 135 93 51 138
sample18 sample19 sample20
gene1 242 60 701
gene2 227 46 89
gene3 435 2 1
gene4 1 6 1
gene5 66 45 12
gene6 77 30 266colData 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 68.02791 -0.6161603 -0.1301888 1.3166746 2
sample2 75.51706 -0.7063917 0.8411168 -0.1783757 0
sample3 61.63397 -0.3797644 0.9230199 1.4793823 2
sample4 25.85360 0.3205278 0.1807490 -0.5231973 1
sample5 32.68332 -0.3750781 0.8562689 0.9641655 2
sample6 45.64452 1.7378885 0.3242683 0.7408498 2design 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:
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)asvar4is 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 + var4is not supported in NBAMSeq;design matrix is not supported.
We then construct the NBAMSeqDataSet using countData, colData, and design:
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 var4Differential expression analysis
Differential expression analysis can be performed by NBAMSeq function:
Several other arguments in NBAMSeq function are available for users to customize the analysis.
gammaargument can be used to control the smoothness of the nonlinear function. Highergammameans the nonlinear function will be more smooth. See thegammaargument of gam function in mgcv (Wood and Wood 2015) for details. Defaultgammais 2.5;fitlinis eitherTRUEorFALSEindicating whether linear model should be fitted after fitting the nonlinear model;parallelis eitherTRUEorFALSEindicating whether parallel should be used. e.g. RunNBAMSeqwithparallel = 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.
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 150.1351 1.00010 0.294831937 0.58722738 0.863570 241.187 248.157
gene2 73.9266 1.00010 1.509395927 0.21928369 0.580796 221.000 227.970
gene3 60.6195 1.00010 2.073674804 0.14990659 0.499689 205.165 212.135
gene4 53.5216 1.00011 0.829544740 0.36251367 0.697570 205.482 212.452
gene5 109.4553 1.00038 0.000360007 0.99164934 0.991649 234.712 241.682
gene6 103.9510 1.00006 6.687226291 0.00971908 0.161985 227.629 234.599For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 150.1351 0.491522029 0.457555 1.074237102 0.282716 0.579238
gene2 73.9266 0.645825550 0.403676 1.599863035 0.109629 0.416217
gene3 60.6195 0.000119174 0.514245 0.000231746 0.999815 0.999815
gene4 53.5216 -0.197023397 0.506856 -0.388717073 0.697485 0.830340
gene5 109.4553 0.022854550 0.469582 0.048669998 0.961182 0.999815
gene6 103.9510 0.201451690 0.468924 0.429604134 0.667484 0.814004
AIC BIC
<numeric> <numeric>
gene1 241.187 248.157
gene2 221.000 227.970
gene3 205.165 212.135
gene4 205.482 212.452
gene5 234.712 241.682
gene6 227.629 234.599For discrete covariates, the contrast argument should be specified. e.g. contrast = c("var4", "2", "0") means comparing level 2 vs. level 0 in var4.
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 150.1351 1.316918 1.089958 1.2082284 0.2269594 0.667528 241.187
gene2 73.9266 0.526804 0.961311 0.5480056 0.5836881 0.775198 221.000
gene3 60.6195 -0.905719 1.217645 -0.7438287 0.4569801 0.771474 205.165
gene4 53.5216 0.080167 1.209217 0.0662967 0.9471416 0.986606 205.482
gene5 109.4553 -2.501405 1.119020 -2.2353536 0.0253941 0.211618 234.712
gene6 103.9510 1.223695 1.116206 1.0962988 0.2729480 0.682370 227.629
BIC
<numeric>
gene1 248.157
gene2 227.970
gene3 212.135
gene4 212.452
gene5 241.682
gene6 234.599Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene50 21.2811 1.00003 8.66888 0.00323827 0.161914 168.367 175.338
gene47 163.6726 1.00018 6.97203 0.00829817 0.161985 250.624 257.595
gene6 103.9510 1.00006 6.68723 0.00971908 0.161985 227.629 234.599
gene15 131.0714 1.00006 4.82839 0.02801147 0.238817 206.091 213.061
gene34 107.1092 1.00011 4.74397 0.02942056 0.238817 214.321 221.291
gene16 101.9969 1.00006 4.53552 0.03321386 0.238817 220.562 227.532library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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
R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.2 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.13-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.13-bioc/R/lib/libRlapack.so
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
attached base packages:
[1] parallel stats4 stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] ggplot2_3.3.3 BiocParallel_1.26.0
[3] NBAMSeq_1.8.0 SummarizedExperiment_1.22.0
[5] Biobase_2.52.0 GenomicRanges_1.44.0
[7] GenomeInfoDb_1.28.0 IRanges_2.26.0
[9] S4Vectors_0.30.0 BiocGenerics_0.38.0
[11] MatrixGenerics_1.4.0 matrixStats_0.58.0
loaded via a namespace (and not attached):
[1] httr_1.4.2 sass_0.4.0 bit64_4.0.5
[4] jsonlite_1.7.2 splines_4.1.0 bslib_0.2.5.1
[7] assertthat_0.2.1 highr_0.9 blob_1.2.1
[10] GenomeInfoDbData_1.2.6 yaml_2.2.1 pillar_1.6.1
[13] RSQLite_2.2.7 lattice_0.20-44 glue_1.4.2
[16] digest_0.6.27 RColorBrewer_1.1-2 XVector_0.32.0
[19] colorspace_2.0-1 htmltools_0.5.1.1 Matrix_1.3-3
[22] DESeq2_1.32.0 XML_3.99-0.6 pkgconfig_2.0.3
[25] genefilter_1.74.0 zlibbioc_1.38.0 purrr_0.3.4
[28] xtable_1.8-4 scales_1.1.1 tibble_3.1.2
[31] annotate_1.70.0 mgcv_1.8-35 KEGGREST_1.32.0
[34] farver_2.1.0 generics_0.1.0 ellipsis_0.3.2
[37] withr_2.4.2 cachem_1.0.5 survival_3.2-11
[40] magrittr_2.0.1 crayon_1.4.1 memoise_2.0.0
[43] evaluate_0.14 fansi_0.4.2 nlme_3.1-152
[46] tools_4.1.0 lifecycle_1.0.0 stringr_1.4.0
[49] locfit_1.5-9.4 munsell_0.5.0 DelayedArray_0.18.0
[52] AnnotationDbi_1.54.0 Biostrings_2.60.0 compiler_4.1.0
[55] jquerylib_0.1.4 rlang_0.4.11 grid_4.1.0
[58] RCurl_1.98-1.3 labeling_0.4.2 bitops_1.0-7
[61] rmarkdown_2.8 gtable_0.3.0 DBI_1.1.1
[64] R6_2.5.0 knitr_1.33 dplyr_1.0.6
[67] fastmap_1.1.0 bit_4.0.4 utf8_1.2.1
[70] stringi_1.6.2 Rcpp_1.0.6 vctrs_0.3.8
[73] geneplotter_1.70.0 png_0.1-7 tidyselect_1.1.1
[76] xfun_0.23 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.