NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2019-10-29
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
gene1 8 1 3 127 126 47 37 121
gene2 47 73 21 860 20 10 38 169
gene3 36 25 382 150 74 457 455 372
gene4 10 222 39 1 6 11 1026 85
gene5 1 137 12 153 26 167 2 1
gene6 1 54 17 37 730 7 7 58
sample9 sample10 sample11 sample12 sample13 sample14 sample15
gene1 155 213 62 16 374 1 752
gene2 2 636 6 4 67 105 357
gene3 2 402 1 30 2 25 1
gene4 45 1 133 250 370 143 98
gene5 1 63 2 341 128 1 4
gene6 4 608 4 1262 498 64 112
sample16 sample17 sample18 sample19 sample20
gene1 173 2 2 1 215
gene2 62 1 15 327 1
gene3 25 163 2 160 1
gene4 14 10 194 392 1
gene5 119 198 44 1 588
gene6 356 60 105 7 5colData 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 67.85934 -1.8617370 0.1912061 2.37892508 0
sample2 59.77305 0.1412924 0.4844806 -0.17171879 1
sample3 20.22851 -2.2920789 1.2541955 -0.03143304 2
sample4 76.36915 0.5277706 0.7421966 -2.10155299 0
sample5 31.61560 -0.6002114 0.2913025 -0.33986158 1
sample6 59.20190 -0.5725584 -0.3810616 -0.49112913 1design 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;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 5 columns
baseMean edf stat
<numeric> <numeric> <numeric>
gene1 90.0223445916752 1.00006202023321 0.417989874223938
gene2 99.8447199106719 1.00004146923865 3.08482813260575
gene3 116.603318095633 1.17313756315202 1.91840978954756
gene4 129.620065481309 1.00007983709234 0.12056885931311
gene5 72.0263609716251 1.00012745086756 0.701259411497124
gene6 170.877758873863 1.00007553113959 3.40518981678079
pvalue padj
<numeric> <numeric>
gene1 0.517966982682795 0.742725976693875
gene2 0.0790317301987507 0.3912270673467
gene3 0.172873212566153 0.508450625194567
gene4 0.728400808229941 0.846977683988303
gene5 0.402436600805646 0.71863678715294
gene6 0.0650057990602778 0.3912270673467For 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 6 columns
baseMean coef SE
<numeric> <numeric> <numeric>
gene1 90.0223445916752 0.708462433336299 0.390260334737052
gene2 99.8447199106719 -0.395669230817001 0.365556966182653
gene3 116.603318095633 -1.7566236902356 0.405611108070408
gene4 129.620065481309 0.337320688034654 0.428478622798008
gene5 72.0263609716251 0.991144817749539 0.417783892073528
gene6 170.877758873863 1.21515329226148 0.428474483498771
stat pvalue padj
<numeric> <numeric> <numeric>
gene1 1.81535854473564 0.069468827419237 0.248102955068704
gene2 -1.08237365833511 0.279086528190152 0.498368800339557
gene3 -4.33080765118169 1.48563417093905e-05 0.000742817085469526
gene4 0.787252082337075 0.4311343141514 0.619830976241167
gene5 2.37238638577071 0.0176735976703406 0.0940786487801255
gene6 2.8359991996232 0.00456825604953488 0.0571032006191859For 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 6 columns
baseMean coef SE
<numeric> <numeric> <numeric>
gene1 90.0223445916752 0.0712881217744735 0.891050025315463
gene2 99.8447199106719 -1.78328194518284 0.829949582780345
gene3 116.603318095633 0.0923052717932765 0.916562305528452
gene4 129.620065481309 -0.0360569040117083 0.976593846294209
gene5 72.0263609716251 0.619014307281392 0.956735889968304
gene6 170.877758873863 0.46444006634833 0.97794067199217
stat pvalue padj
<numeric> <numeric> <numeric>
gene1 0.080004623476931 0.93623357875778 0.970547928133608
gene2 -2.14866298168236 0.0316611251622829 0.141069836941244
gene3 0.10070812560861 0.919782160868774 0.970547928133608
gene4 -0.0369210845926688 0.970547928133608 0.970547928133608
gene5 0.647006466227476 0.517627758525079 0.76694156155462
gene6 0.474916403059723 0.634846559417972 0.857900755970232Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 5 columns
baseMean edf stat
<numeric> <numeric> <numeric>
gene11 114.096145981131 1.00009161106674 8.90315658526706
gene15 55.3771483785019 1.00005994731693 6.72535616913074
gene45 107.219726187918 1.0001605021219 6.06083726983454
gene49 39.6521545669267 1.00009383264887 4.31214431501749
gene13 55.503451491174 1.00006114204692 4.02897665640921
gene21 59.1659906642282 1.00012335068253 3.95174603749206
pvalue padj
<numeric> <numeric>
gene11 0.00284763602597408 0.142381801298704
gene15 0.00950640127330121 0.230398483166231
gene45 0.0138239089899739 0.230398483166231
gene49 0.0378584827989891 0.390326288493192
gene13 0.044725009980555 0.390326288493192
gene21 0.046839154619183 0.390326288493192library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.3 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
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
attached base packages:
[1] parallel stats4 stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] ggplot2_3.2.1 NBAMSeq_1.2.0
[3] SummarizedExperiment_1.16.0 DelayedArray_0.12.0
[5] BiocParallel_1.20.0 matrixStats_0.55.0
[7] Biobase_2.46.0 GenomicRanges_1.38.0
[9] GenomeInfoDb_1.22.0 IRanges_2.20.0
[11] S4Vectors_0.24.0 BiocGenerics_0.32.0
loaded via a namespace (and not attached):
[1] bit64_0.9-7 splines_3.6.1 Formula_1.2-3
[4] assertthat_0.2.1 latticeExtra_0.6-28 blob_1.2.0
[7] GenomeInfoDbData_1.2.2 yaml_2.2.0 pillar_1.4.2
[10] RSQLite_2.1.2 backports_1.1.5 lattice_0.20-38
[13] glue_1.3.1 digest_0.6.22 RColorBrewer_1.1-2
[16] XVector_0.26.0 checkmate_1.9.4 colorspace_1.4-1
[19] htmltools_0.4.0 Matrix_1.2-17 DESeq2_1.26.0
[22] XML_3.98-1.20 pkgconfig_2.0.3 genefilter_1.68.0
[25] zlibbioc_1.32.0 purrr_0.3.3 xtable_1.8-4
[28] scales_1.0.0 htmlTable_1.13.2 tibble_2.1.3
[31] annotate_1.64.0 mgcv_1.8-30 withr_2.1.2
[34] nnet_7.3-12 lazyeval_0.2.2 survival_2.44-1.1
[37] magrittr_1.5 crayon_1.3.4 memoise_1.1.0
[40] evaluate_0.14 nlme_3.1-141 foreign_0.8-72
[43] tools_3.6.1 data.table_1.12.6 stringr_1.4.0
[46] locfit_1.5-9.1 munsell_0.5.0 cluster_2.1.0
[49] AnnotationDbi_1.48.0 compiler_3.6.1 rlang_0.4.1
[52] grid_3.6.1 RCurl_1.95-4.12 rstudioapi_0.10
[55] htmlwidgets_1.5.1 labeling_0.3 bitops_1.0-6
[58] base64enc_0.1-3 rmarkdown_1.16 gtable_0.3.0
[61] DBI_1.0.0 R6_2.4.0 gridExtra_2.3
[64] knitr_1.25 dplyr_0.8.3 zeallot_0.1.0
[67] bit_1.1-14 Hmisc_4.2-0 stringi_1.4.3
[70] Rcpp_1.0.2 geneplotter_1.64.0 vctrs_0.2.0
[73] rpart_4.1-15 acepack_1.4.1 tidyselect_0.2.5
[76] xfun_0.10 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). BioMed Central: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). Oxford University Press: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). Oxford University Press:2672–8.