NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2024-05-01
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 23 30 92 6 3 126 12 129 1
gene2 40 65 1 1 19 180 18 70 145
gene3 11 5 63 194 224 20 282 147 799
gene4 512 7 2 3 389 5 134 16 1
gene5 143 20 6 47 20 1 7 272 2
gene6 9 292 1 72 324 2 266 495 9
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 550 3 21 91 4 2 211
gene2 2 6 165 8 23 5 1 117
gene3 8 1491 1 120 12 1 31 132
gene4 1 24 30 82 37 2 2 11
gene5 10 288 223 8 1140 56 512 105
gene6 235 241 168 26 143 59 1 134
sample18 sample19 sample20
gene1 1 104 10
gene2 94 18 9
gene3 9 2 9
gene4 82 3 21
gene5 1 6 37
gene6 1 2 102colData 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 47.80916 -1.2025830 -1.7838450 -0.64103356 1
sample2 60.63673 -1.7494413 0.8675466 -1.85818205 1
sample3 43.73349 1.2382517 -0.2184462 -0.08237318 0
sample4 69.49117 -1.5701106 -1.7502891 -0.32889378 2
sample5 66.04341 -0.2695398 0.1446839 -0.39066974 2
sample6 66.93442 1.3510984 -0.3389946 -1.36065887 0design 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 49.4800 1.00006 3.0550426 0.0805026 0.351480 190.030 197.001
gene2 42.5847 1.00005 0.0999655 0.7519882 0.883283 200.960 207.930
gene3 140.1690 1.00007 0.3445285 0.5572545 0.883283 227.461 234.431
gene4 46.6957 1.00010 0.1057019 0.7451861 0.883283 203.810 210.781
gene5 102.2155 1.00040 5.9903314 0.0143946 0.179933 231.640 238.611
gene6 104.9993 1.00021 1.4346728 0.2310764 0.525174 237.464 244.434For 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 49.4800 0.763569 0.313281 2.437327 0.01479629 0.0882349 190.030
gene2 42.5847 1.121028 0.346958 3.231023 0.00123348 0.0282617 200.960
gene3 140.1690 1.093542 0.359822 3.039122 0.00237269 0.0296586 227.461
gene4 46.6957 -0.578297 0.403091 -1.434658 0.15138467 0.3983807 203.810
gene5 102.2155 -0.769893 0.395222 -1.948000 0.05141499 0.1606719 231.640
gene6 104.9993 -0.179747 0.386673 -0.464855 0.64203543 0.8229957 237.464
BIC
<numeric>
gene1 197.001
gene2 207.930
gene3 234.431
gene4 210.781
gene5 238.611
gene6 244.434For 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 49.4800 -2.88178 0.983146 -2.931186 0.0033767 0.168835 190.030
gene2 42.5847 1.07252 1.073860 0.998756 0.3179131 0.662319 200.960
gene3 140.1690 1.53995 1.119216 1.375919 0.1688467 0.582952 227.461
gene4 46.6957 1.12347 1.266944 0.886759 0.3752089 0.721556 203.810
gene5 102.2155 -2.37423 1.238384 -1.917199 0.0552127 0.552127 231.640
gene6 104.9993 1.42148 1.212236 1.172612 0.2409514 0.582952 237.464
BIC
<numeric>
gene1 197.001
gene2 207.930
gene3 234.431
gene4 210.781
gene5 238.611
gene6 244.434Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene21 78.5311 1.00006 9.78161 0.00176305 0.0881526 221.408 228.379
gene23 64.4750 1.00005 7.03745 0.00798530 0.1799331 209.306 216.276
gene10 32.2968 1.00005 6.19349 0.01282573 0.1799331 184.630 191.600
gene5 102.2155 1.00040 5.99033 0.01439465 0.1799331 231.640 238.611
gene39 121.2724 1.00013 5.45928 0.01947697 0.1947697 232.276 239.246
gene27 59.0689 1.00025 4.73751 0.02954236 0.2103366 217.156 224.127library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.4.0 RC (2024-04-16 r86468)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.4 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.20-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_3.5.1 BiocParallel_1.39.0
[3] NBAMSeq_1.21.0 SummarizedExperiment_1.35.0
[5] Biobase_2.65.0 GenomicRanges_1.57.0
[7] GenomeInfoDb_1.41.0 IRanges_2.39.0
[9] S4Vectors_0.43.0 BiocGenerics_0.51.0
[11] MatrixGenerics_1.17.0 matrixStats_1.3.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.45.0 gtable_0.3.5 xfun_0.43
[4] bslib_0.7.0 lattice_0.22-6 vctrs_0.6.5
[7] tools_4.4.0 generics_0.1.3 parallel_4.4.0
[10] RSQLite_2.3.6 tibble_3.2.1 fansi_1.0.6
[13] AnnotationDbi_1.67.0 highr_0.10 blob_1.2.4
[16] pkgconfig_2.0.3 Matrix_1.7-0 lifecycle_1.0.4
[19] GenomeInfoDbData_1.2.12 farver_2.1.1 compiler_4.4.0
[22] Biostrings_2.73.0 munsell_0.5.1 DESeq2_1.45.0
[25] codetools_0.2-20 htmltools_0.5.8.1 sass_0.4.9
[28] yaml_2.3.8 pillar_1.9.0 crayon_1.5.2
[31] jquerylib_0.1.4 DelayedArray_0.31.0 cachem_1.0.8
[34] abind_1.4-5 nlme_3.1-164 genefilter_1.87.0
[37] tidyselect_1.2.1 locfit_1.5-9.9 digest_0.6.35
[40] dplyr_1.1.4 labeling_0.4.3 splines_4.4.0
[43] fastmap_1.1.1 grid_4.4.0 colorspace_2.1-0
[46] cli_3.6.2 SparseArray_1.5.0 magrittr_2.0.3
[49] S4Arrays_1.5.0 survival_3.6-4 XML_3.99-0.16.1
[52] utf8_1.2.4 withr_3.0.0 scales_1.3.0
[55] UCSC.utils_1.1.0 bit64_4.0.5 rmarkdown_2.26
[58] XVector_0.45.0 httr_1.4.7 bit_4.0.5
[61] png_0.1-8 memoise_2.0.1 evaluate_0.23
[64] knitr_1.46 mgcv_1.9-1 rlang_1.1.3
[67] Rcpp_1.0.12 DBI_1.2.2 xtable_1.8-4
[70] glue_1.7.0 annotate_1.83.0 jsonlite_1.8.8
[73] R6_2.5.1 zlibbioc_1.51.0 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.