NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2023-11-01
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 24 54 113 63 27 2 12
gene2 30 138 99 85 20 3 210 26 3
gene3 157 136 58 4 16 65 16 3 2
gene4 2 12 8 8 1 1 96 208 2
gene5 1 118 20 10 1 6 14 4 15
gene6 61 70 58 132 41 279 48 4 11
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 97 11 59 3 7 60 93 6
gene2 37 79 93 17 55 44 1 10
gene3 19 134 19 1 399 35 84 17
gene4 584 6 9 2 5 126 13 48
gene5 1 50 77 20 1 406 16 1
gene6 10 88 161 82 119 128 5 21
sample18 sample19 sample20
gene1 147 56 27
gene2 1 77 82
gene3 138 313 597
gene4 6 2 30
gene5 11 33 1
gene6 13 84 7colData 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 73.80921 -0.5296293 -0.38644692 0.3314055 0
sample2 62.64547 -1.4221333 0.72979185 -0.7813876 2
sample3 42.21892 -0.1342837 -0.02289044 -0.1576072 1
sample4 41.15586 0.5441802 0.46856961 -0.1227523 1
sample5 32.68910 -0.8832228 1.15048656 -0.5047426 1
sample6 37.19406 -1.1186365 -0.53091742 0.5848132 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 2.5;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 37.9490 1.00007 0.7814047 0.3767691 0.819063 204.296 211.266
gene2 50.5655 1.00006 2.0634587 0.1508802 0.538858 211.916 218.886
gene3 129.5485 1.00007 3.1144645 0.0776163 0.388082 229.087 236.057
gene4 49.0171 1.00003 0.0255126 0.8731673 0.914205 182.852 189.822
gene5 33.1165 1.00011 0.5601260 0.4542135 0.825876 180.221 187.191
gene6 67.1276 1.00009 0.9154465 0.3387066 0.771265 226.631 233.601For 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 37.9490 -0.375223 0.341397 -1.09908 2.71734e-01 0.55241945 204.296
gene2 50.5655 -0.404034 0.318444 -1.26877 2.04522e-01 0.52845201 211.916
gene3 129.5485 -1.399246 0.344755 -4.05867 4.93539e-05 0.00246769 229.087
gene4 49.0171 -0.571546 0.347666 -1.64395 1.00186e-01 0.38533010 182.852
gene5 33.1165 -0.461115 0.368958 -1.24978 2.11381e-01 0.52845201 180.221
gene6 67.1276 -0.264273 0.312682 -0.84518 3.98011e-01 0.62189141 226.631
BIC
<numeric>
gene1 211.266
gene2 218.886
gene3 236.057
gene4 189.822
gene5 187.191
gene6 233.601For 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 37.9490 0.991322 1.15017 0.861891 0.3887474 0.716305 204.296
gene2 50.5655 0.544486 1.07866 0.504782 0.6137122 0.870925 211.916
gene3 129.5485 1.984795 1.15507 1.718328 0.0857368 0.389713 229.087
gene4 49.0171 0.504952 1.19958 0.420939 0.6737996 0.870925 182.852
gene5 33.1165 3.198216 1.25235 2.553770 0.0106564 0.133205 180.221
gene6 67.1276 0.459218 1.05367 0.435827 0.6629623 0.870925 226.631
BIC
<numeric>
gene1 211.266
gene2 218.886
gene3 236.057
gene4 189.822
gene5 187.191
gene6 233.601Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene22 119.0806 1.00005 17.76521 2.57896e-05 0.00128948 204.776 211.747
gene44 94.8223 1.00009 15.66249 7.53275e-05 0.00188319 215.551 222.521
gene32 45.8879 1.00005 10.47680 1.20926e-03 0.02015431 189.474 196.445
gene25 81.1212 1.00006 6.40270 1.13983e-02 0.14247837 202.247 209.218
gene46 107.5987 1.00006 5.49553 1.90712e-02 0.19071162 201.358 208.329
gene26 158.5995 1.00004 4.90149 2.68364e-02 0.22363702 220.513 227.483library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 Under development (unstable) (2023-10-22 r85388)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.3 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.19-bioc/R/lib/libRblas.so
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
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
time zone: America/New_York
tzcode source: system (glibc)
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.4.4 BiocParallel_1.37.0
[3] NBAMSeq_1.19.0 SummarizedExperiment_1.33.0
[5] Biobase_2.63.0 GenomicRanges_1.55.1
[7] GenomeInfoDb_1.39.0 IRanges_2.37.0
[9] S4Vectors_0.41.1 BiocGenerics_0.49.1
[11] MatrixGenerics_1.15.0 matrixStats_1.0.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.43.0 gtable_0.3.4 xfun_0.41
[4] bslib_0.5.1 lattice_0.22-5 vctrs_0.6.4
[7] tools_4.4.0 bitops_1.0-7 generics_0.1.3
[10] parallel_4.4.0 RSQLite_2.3.2 AnnotationDbi_1.65.0
[13] tibble_3.2.1 fansi_1.0.5 highr_0.10
[16] blob_1.2.4 pkgconfig_2.0.3 Matrix_1.6-1.1
[19] lifecycle_1.0.3 GenomeInfoDbData_1.2.11 farver_2.1.1
[22] compiler_4.4.0 Biostrings_2.71.1 munsell_0.5.0
[25] DESeq2_1.43.0 codetools_0.2-19 htmltools_0.5.6.1
[28] sass_0.4.7 RCurl_1.98-1.12 yaml_2.3.7
[31] pillar_1.9.0 crayon_1.5.2 jquerylib_0.1.4
[34] DelayedArray_0.29.0 cachem_1.0.8 abind_1.4-5
[37] nlme_3.1-163 genefilter_1.85.0 tidyselect_1.2.0
[40] locfit_1.5-9.8 digest_0.6.33 dplyr_1.1.3
[43] labeling_0.4.3 splines_4.4.0 fastmap_1.1.1
[46] grid_4.4.0 colorspace_2.1-0 cli_3.6.1
[49] SparseArray_1.3.0 magrittr_2.0.3 S4Arrays_1.3.0
[52] survival_3.5-7 XML_3.99-0.14 utf8_1.2.4
[55] withr_2.5.2 scales_1.2.1 bit64_4.0.5
[58] rmarkdown_2.25 XVector_0.43.0 httr_1.4.7
[61] bit_4.0.5 png_0.1-8 memoise_2.0.1
[64] evaluate_0.23 knitr_1.45 mgcv_1.9-0
[67] rlang_1.1.1 Rcpp_1.0.11 DBI_1.1.3
[70] xtable_1.8-4 glue_1.6.2 annotate_1.81.0
[73] jsonlite_1.8.7 R6_2.5.1 zlibbioc_1.49.0 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.