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 1 1 2 9 291 421 453 39 89
gene2 26 420 7 106 60 2 189 208 1
gene3 1 174 340 1 8 5 2 119 2
gene4 11 132 54 7 79 46 80 3 6
gene5 126 929 19 124 11 359 8 85 3
gene6 1 328 3 1119 12 24 10 4 42
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 3 1 17 11 1 40 230 1
gene2 1 63 2 595 52 142 3 19
gene3 1 9 80 12 1 40 201 1
gene4 1 1 89 32 1 18 14 1161
gene5 1 12 1 146 47 159 93 444
gene6 19 1 1 358 144 1 46 10
sample18 sample19 sample20
gene1 11 18 2
gene2 126 76 148
gene3 71 31 26
gene4 24 1 184
gene5 114 162 27
gene6 46 403 23colData 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 41.73174 0.9468455 -0.1231153 -0.50320534 1
sample2 61.79489 -1.2978668 0.5838662 -0.08850541 1
sample3 78.25007 1.6509330 1.5847842 -0.00786075 0
sample4 64.72470 0.5327862 -0.8553626 0.39325437 2
sample5 65.15181 0.8759616 0.7456919 0.84867099 0
sample6 67.79239 -0.7312094 0.0374443 -1.29698795 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 65.0314 1.00013 0.0349426 0.851836 0.913758 196.873 203.843
gene2 83.1839 1.00017 0.0242483 0.876462 0.913758 230.356 237.326
gene3 54.4536 1.00011 0.3665395 0.545028 0.801651 187.975 194.945
gene4 70.8177 1.00008 0.3034318 0.581806 0.801651 207.397 214.367
gene5 103.1989 1.00012 0.6178096 0.431978 0.799959 237.420 244.391
gene6 93.4488 1.00011 0.0615414 0.804217 0.913758 215.271 222.241For 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 65.0314 0.1583023 0.439083 0.3605290 0.718452 0.846646 196.873
gene2 83.1839 0.0207493 0.410970 0.0504887 0.959733 0.988504 230.356
gene3 54.4536 -0.1106871 0.397565 -0.2784126 0.780696 0.867440 187.975
gene4 70.8177 -0.6378196 0.415525 -1.5349721 0.124791 0.311977 207.397
gene5 103.1989 -0.2115241 0.384776 -0.5497328 0.582503 0.824217 237.420
gene6 93.4488 0.1388827 0.434182 0.3198723 0.749065 0.851210 215.271
BIC
<numeric>
gene1 203.843
gene2 237.326
gene3 194.945
gene4 214.367
gene5 244.391
gene6 222.241For 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 65.0314 -0.454763 1.40160 -0.324460 0.745590016 0.93478332 196.873
gene2 83.1839 0.322964 1.32707 0.243367 0.807721368 0.94650109 230.356
gene3 54.4536 -4.902645 1.29185 -3.795045 0.000147616 0.00738082 187.975
gene4 70.8177 -0.431718 1.34280 -0.321506 0.747826655 0.93478332 207.397
gene5 103.1989 0.241940 1.24408 0.194472 0.845806080 0.94650109 237.420
gene6 93.4488 4.054993 1.41788 2.859907 0.004237657 0.04556218 215.271
BIC
<numeric>
gene1 203.843
gene2 237.326
gene3 194.945
gene4 214.367
gene5 244.391
gene6 222.241Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene27 55.3069 1.00007 15.3250 9.05769e-05 0.00448350 208.320 215.290
gene21 152.5731 1.00009 14.0376 1.79340e-04 0.00448350 227.492 234.462
gene43 86.3873 1.00008 12.3738 4.35538e-04 0.00725896 190.809 197.779
gene38 116.6806 1.00012 11.3185 7.68016e-04 0.00954241 223.442 230.412
gene31 103.8317 1.00005 10.9150 9.54241e-04 0.00954241 231.098 238.068
gene33 41.7787 1.00010 10.0025 1.56356e-03 0.01302969 188.655 195.625library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 RC (2020-04-19 r78255)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 18.04.4 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
LAPACK: /home/biocbuild/bbs-3.12-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_1.23.0
[3] NBAMSeq_1.5.1 SummarizedExperiment_1.19.2
[5] DelayedArray_0.15.1 matrixStats_0.56.0
[7] Biobase_2.49.0 GenomicRanges_1.41.1
[9] GenomeInfoDb_1.25.0 IRanges_2.23.4
[11] S4Vectors_0.27.5 BiocGenerics_0.35.2
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_1.35.0 rlang_0.4.6 annotate_1.67.0
[13] blob_1.2.1 Matrix_1.2-18 rmarkdown_2.1
[16] labeling_0.3 splines_4.0.0 geneplotter_1.67.0
[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_0.29.0 genefilter_1.71.0 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_1.29.0
[55] purrr_0.3.4 survival_3.1-12 yaml_2.2.1
[58] AnnotationDbi_1.51.0 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.