NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2020-05-06
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 149 54 36 21 181 12 1 2 65
gene2 16 59 191 1 69 238 315 58 90
gene3 223 186 6 1 202 9 248 231 4
gene4 84 503 2 115 1 2 1 33 47
gene5 14 122 108 43 13 1 10 121 118
gene6 29 1 203 2 58 19 485 119 379
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 615 1 46 37 14 161 127
gene2 387 5 205 1 6 1 184 137
gene3 5 79 3 8 85 1 2 2
gene4 132 64 8 42 479 1 19 117
gene5 613 96 5 122 36 2 20 5
gene6 42 162 148 83 281 437 263 54
sample18 sample19 sample20
gene1 5 70 12
gene2 92 274 9
gene3 63 67 54
gene4 48 60 16
gene5 685 3 272
gene6 867 120 330colData 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 52.03148 0.2618515 -0.6656633 0.6129048 2
sample2 22.22902 1.3525567 0.4106865 0.3780545 0
sample3 73.23137 -1.3180993 -0.1906767 -0.7677955 0
sample4 37.00439 0.3475406 0.6929285 -0.4117238 1
sample5 32.27789 0.3885155 -0.1585314 0.8688875 1
sample6 45.55982 0.9917814 0.7774949 0.1518606 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 64.7271 1.00017 0.0483596 0.826015 0.957270 217.404 224.374
gene2 113.6147 1.00004 0.3259410 0.568110 0.957270 238.986 245.956
gene3 75.6826 1.00002 1.6503122 0.198935 0.555999 215.511 222.481
gene4 71.5740 1.00005 1.5626494 0.211280 0.555999 219.600 226.570
gene5 78.5283 1.00006 1.8614700 0.172485 0.555999 217.646 224.616
gene6 178.1046 1.00006 2.1525779 0.142357 0.508416 266.366 273.336For 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 AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 64.7271 0.397008 0.457498 0.867780 0.38551452 0.721486 217.404
gene2 113.6147 -0.241391 0.465337 -0.518744 0.60393908 0.895525 238.986
gene3 75.6826 1.352876 0.488272 2.770740 0.00559291 0.120965 215.511
gene4 71.5740 0.245625 0.460222 0.533711 0.59354182 0.895525 219.600
gene5 78.5283 -0.713184 0.380567 -1.874003 0.06092998 0.328366 217.646
gene6 178.1046 0.178886 0.433886 0.412289 0.68012745 0.959669 266.366
BIC
<numeric>
gene1 224.374
gene2 245.956
gene3 222.481
gene4 226.570
gene5 224.616
gene6 273.336For 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 64.7271 1.531094 0.956190 1.601245 0.10932272 0.3036742 217.404
gene2 113.6147 0.947606 0.973088 0.973813 0.33014962 0.5859518 238.986
gene3 75.6826 -0.320984 1.022575 -0.313898 0.75359844 0.8373316 215.511
gene4 71.5740 0.128533 0.964606 0.133250 0.89399595 0.9312458 219.600
gene5 78.5283 -2.233128 0.809602 -2.758304 0.00581022 0.0515908 217.646
gene6 178.1046 1.103802 0.908037 1.215591 0.22414090 0.5094111 266.366
BIC
<numeric>
gene1 224.374
gene2 245.956
gene3 222.481
gene4 226.570
gene5 224.616
gene6 273.336Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene50 115.9531 1.00004 9.69323 0.00185028 0.0925138 203.056 210.027
gene40 127.2841 1.00004 8.38922 0.00377612 0.0944029 213.087 220.057
gene10 251.0238 1.46594 8.57862 0.00670475 0.0951255 238.576 246.010
gene11 81.0455 1.00008 7.12356 0.00761004 0.0951255 224.182 231.152
gene27 81.2482 1.00006 6.53544 0.01057645 0.1057645 221.921 228.891
gene36 45.3985 1.00005 5.72845 0.01669752 0.1391460 186.652 193.622library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.0.0 (2020-04-24)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.4 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.11-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_3.3.0 BiocParallel_1.22.0
[3] NBAMSeq_1.4.1 SummarizedExperiment_1.18.1
[5] DelayedArray_0.14.0 matrixStats_0.56.0
[7] Biobase_2.48.0 GenomicRanges_1.40.0
[9] GenomeInfoDb_1.24.0 IRanges_2.22.1
[11] S4Vectors_0.26.0 BiocGenerics_0.34.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.4.6 locfit_1.5-9.4 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_1.4.4
[10] zlibbioc_1.34.0 rlang_0.4.6 annotate_1.66.0
[13] blob_1.2.1 Matrix_1.2-18 rmarkdown_2.1
[16] labeling_0.3 splines_4.0.0 geneplotter_1.66.0
[19] stringr_1.4.0 RCurl_1.98-1.2 bit_1.1-15.2
[22] munsell_0.5.0 compiler_4.0.0 xfun_0.13
[25] pkgconfig_2.0.3 mgcv_1.8-31 htmltools_0.4.0
[28] tidyselect_1.0.0 tibble_3.0.1 GenomeInfoDbData_1.2.3
[31] XML_3.99-0.3 withr_2.2.0 crayon_1.3.4
[34] dplyr_0.8.5 bitops_1.0-6 grid_4.0.0
[37] nlme_3.1-147 xtable_1.8-4 gtable_0.3.0
[40] lifecycle_0.2.0 DBI_1.1.0 magrittr_1.5
[43] scales_1.1.0 stringi_1.4.6 farver_2.0.3
[46] XVector_0.28.0 genefilter_1.70.0 ellipsis_0.3.0
[49] vctrs_0.2.4 RColorBrewer_1.1-2 tools_4.0.0
[52] bit64_0.9-7 glue_1.4.0 DESeq2_1.28.0
[55] purrr_0.3.4 survival_3.1-12 yaml_2.2.1
[58] AnnotationDbi_1.50.0 colorspace_1.4-1 memoise_1.1.0
[61] 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). 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.