NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2023-04-25
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 314 220 78 26 191 1 119 13 48
gene2 54 2 91 375 1 15 119 15 6
gene3 504 82 3 114 504 4 228 148 23
gene4 560 4 398 1 158 51 74 169 1
gene5 53 184 400 244 2 1 121 221 56
gene6 24 45 62 15 20 80 149 89 2
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 47 15 3 190 540 205 23 1
gene2 5 18 94 1 162 17 1 9
gene3 1 80 1 71 11 7 225 4
gene4 29 799 1 1 280 21 4 1
gene5 13 941 35 207 6 3 188 9
gene6 412 250 1 165 58 26 8 126
sample18 sample19 sample20
gene1 18 44 22
gene2 141 19 1
gene3 138 143 5
gene4 1 31 1
gene5 1 632 1331
gene6 199 2 19colData 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 35.69074 1.7574283 0.35616797 0.6082323 1
sample2 22.38337 -0.1630608 -1.42379609 0.8317170 2
sample3 28.70908 0.3734551 -1.35523249 -0.2085717 1
sample4 41.75098 0.7894484 0.13706945 -1.2922998 1
sample5 34.96640 2.2162639 0.07763842 0.3669172 1
sample6 59.58079 0.1030320 0.58479007 -0.5326034 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 73.7650 1.00004 0.000393897 0.9850251 0.995067 232.351 239.321
gene2 49.9695 1.00005 0.106880717 0.7437918 0.995067 199.867 206.837
gene3 92.0971 1.00013 2.845960441 0.0916208 0.381753 230.677 237.647
gene4 89.7748 1.00007 0.006296591 0.9371847 0.995067 201.874 208.844
gene5 206.1077 1.00007 6.413708698 0.0113297 0.188829 255.317 262.287
gene6 59.5017 1.00005 2.020401125 0.1551896 0.566168 221.385 228.355For 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 73.7650 0.4081456 0.372220 1.096517 0.272853 0.568443 232.351
gene2 49.9695 0.3869508 0.395083 0.979417 0.327374 0.607255 199.867
gene3 92.0971 0.3842441 0.402754 0.954041 0.340063 0.607255 230.677
gene4 89.7748 -0.0483954 0.405281 -0.119412 0.904949 0.961960 201.874
gene5 206.1077 -0.7318945 0.450414 -1.624937 0.104176 0.447010 255.317
gene6 59.5017 -0.5218413 0.333066 -1.566778 0.117167 0.447010 221.385
BIC
<numeric>
gene1 239.321
gene2 206.837
gene3 237.647
gene4 208.844
gene5 262.287
gene6 228.355For 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
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 73.7650 -0.0925709 1.16000 -0.0798026 0.936394276 0.96250870
gene2 49.9695 -2.7321609 1.25342 -2.1797691 0.029274584 0.29274584
gene3 92.0971 -2.0140630 1.25840 -1.6005004 0.109487620 0.46685851
gene4 89.7748 -4.9805070 1.31662 -3.7827932 0.000155078 0.00775391
gene5 206.1077 1.1786030 1.41071 0.8354696 0.403453342 0.74713582
gene6 59.5017 -0.0640978 1.03328 -0.0620336 0.950536043 0.96250870
AIC BIC
<numeric> <numeric>
gene1 232.351 239.321
gene2 199.867 206.837
gene3 230.677 237.647
gene4 201.874 208.844
gene5 255.317 262.287
gene6 221.385 228.355Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene39 53.7132 1.00004 7.13295 0.00756862 0.188829 201.166 208.137
gene12 82.8388 1.00012 6.88767 0.00868050 0.188829 213.152 220.122
gene5 206.1077 1.00007 6.41371 0.01132973 0.188829 255.317 262.287
gene22 83.0278 1.00005 4.78418 0.02872720 0.313714 190.483 197.453
gene40 111.3719 1.00014 4.63275 0.03137138 0.313714 230.209 237.179
gene48 51.3919 1.00006 4.02046 0.04495386 0.329990 204.913 211.883library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.3.0 RC (2023-04-13 r84269)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.17-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_3.4.2 BiocParallel_1.34.0
[3] NBAMSeq_1.16.0 SummarizedExperiment_1.30.0
[5] Biobase_2.60.0 GenomicRanges_1.52.0
[7] GenomeInfoDb_1.36.0 IRanges_2.34.0
[9] S4Vectors_0.38.0 BiocGenerics_0.46.0
[11] MatrixGenerics_1.12.0 matrixStats_0.63.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.40.0 gtable_0.3.3 xfun_0.39
[4] bslib_0.4.2 lattice_0.21-8 vctrs_0.6.2
[7] tools_4.3.0 bitops_1.0-7 generics_0.1.3
[10] parallel_4.3.0 tibble_3.2.1 fansi_1.0.4
[13] AnnotationDbi_1.62.0 RSQLite_2.3.1 highr_0.10
[16] blob_1.2.4 pkgconfig_2.0.3 Matrix_1.5-4
[19] lifecycle_1.0.3 GenomeInfoDbData_1.2.10 farver_2.1.1
[22] compiler_4.3.0 Biostrings_2.68.0 munsell_0.5.0
[25] DESeq2_1.40.0 codetools_0.2-19 htmltools_0.5.5
[28] sass_0.4.5 RCurl_1.98-1.12 yaml_2.3.7
[31] crayon_1.5.2 pillar_1.9.0 jquerylib_0.1.4
[34] DelayedArray_0.26.0 cachem_1.0.7 nlme_3.1-162
[37] genefilter_1.82.0 tidyselect_1.2.0 locfit_1.5-9.7
[40] digest_0.6.31 dplyr_1.1.2 labeling_0.4.2
[43] splines_4.3.0 fastmap_1.1.1 grid_4.3.0
[46] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3
[49] survival_3.5-5 XML_3.99-0.14 utf8_1.2.3
[52] withr_2.5.0 scales_1.2.1 bit64_4.0.5
[55] rmarkdown_2.21 XVector_0.40.0 httr_1.4.5
[58] bit_4.0.5 png_0.1-8 memoise_2.0.1
[61] evaluate_0.20 knitr_1.42 mgcv_1.8-42
[64] rlang_1.1.0 Rcpp_1.0.10 xtable_1.8-4
[67] glue_1.6.2 DBI_1.1.3 annotate_1.78.0
[70] jsonlite_1.8.4 R6_2.5.1 zlibbioc_1.46.0 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.