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 67 1008 1 74 291 11 101 20 39
gene2 1 286 71 60 213 261 3 20 92
gene3 1 1 1 4 153 17 19 44 3
gene4 15 8 1246 12 77 166 3 4 4
gene5 116 16 41 7 34 279 107 772 2
gene6 1 142 1 299 10 20 170 1 8
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 153 1 13 1 1 111 165
gene2 2 77 1 1 1 48 183 209
gene3 5 22 1 44 128 1 20 206
gene4 111 354 2 493 65 169 2 6
gene5 122 1 1 1 1 22 1 37
gene6 208 44 1 87 36 22 17 137
sample18 sample19 sample20
gene1 65 124 189
gene2 1 77 30
gene3 6 71 315
gene4 5 398 161
gene5 31 2 38
gene6 38 1 42colData 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 20.16715 0.2184479 0.1793180 0.10342530 2
sample2 28.67469 -0.5348193 -0.2253440 1.96910886 0
sample3 31.76493 -1.3643465 -0.5393728 0.01762547 2
sample4 67.48672 -1.4457682 1.9760324 1.14831552 2
sample5 29.61630 1.2858705 -1.1045828 -1.13049729 0
sample6 29.88034 0.5723151 -0.5904115 1.67435753 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 83.4015 1.00058 6.20576e-05 0.99882756 0.998828 228.837 235.808
gene2 81.4488 1.00008 2.08382e+00 0.14890072 0.553475 217.382 224.353
gene3 40.9799 1.00005 1.00272e+00 0.31671103 0.719798 195.484 202.454
gene4 96.6560 1.00006 8.93141e+00 0.00280399 0.140199 230.531 237.501
gene5 90.4174 1.00004 4.67954e-01 0.49395286 0.873316 204.182 211.152
gene6 51.4623 1.00012 7.37499e+00 0.00661694 0.165424 208.368 215.339For 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 83.4015 0.1077510 0.379196 0.2841563 0.7762906 0.953695 228.837
gene2 81.4488 0.7928548 0.381580 2.0778191 0.0377260 0.188630 217.382
gene3 40.9799 0.3057559 0.363647 0.8408039 0.4004578 0.767597 195.484
gene4 96.6560 0.2340405 0.359351 0.6512867 0.5148614 0.858102 230.531
gene5 90.4174 0.9291528 0.384709 2.4152071 0.0157263 0.112330 204.182
gene6 51.4623 -0.0167848 0.349853 -0.0479769 0.9617346 0.968665 208.368
BIC
<numeric>
gene1 235.808
gene2 224.353
gene3 202.454
gene4 237.501
gene5 211.152
gene6 215.339For 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 83.4015 -0.863572 0.883408 -0.977546 0.3282987 0.820747 228.837
gene2 81.4488 -0.647128 0.885823 -0.730539 0.4650611 0.868908 217.382
gene3 40.9799 -1.483732 0.846367 -1.753061 0.0795916 0.720496 195.484
gene4 96.6560 1.334247 0.837774 1.592609 0.1112479 0.720496 230.531
gene5 90.4174 -0.538872 0.899820 -0.598866 0.5492620 0.868908 204.182
gene6 51.4623 -1.004732 0.818355 -1.227746 0.2195423 0.784080 208.368
BIC
<numeric>
gene1 235.808
gene2 224.353
gene3 202.454
gene4 237.501
gene5 211.152
gene6 215.339Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene4 96.6560 1.00006 8.93141 0.00280399 0.140199 230.531 237.501
gene6 51.4623 1.00012 7.37499 0.00661694 0.165424 208.368 215.339
gene18 67.2896 1.00012 5.47153 0.01933368 0.322228 210.267 217.237
gene26 90.6064 1.00005 4.81565 0.02820648 0.352581 226.111 233.081
gene20 62.5938 1.00011 3.82949 0.05037651 0.479528 203.800 210.770
gene45 185.1473 1.00007 3.60711 0.05754332 0.479528 251.780 258.751library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 (2023-04-18 r84287)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.18-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_1.35.0
[3] NBAMSeq_1.17.0 SummarizedExperiment_1.31.0
[5] Biobase_2.61.0 GenomicRanges_1.53.0
[7] GenomeInfoDb_1.37.0 IRanges_2.35.0
[9] S4Vectors_0.39.0 BiocGenerics_0.47.0
[11] MatrixGenerics_1.13.0 matrixStats_0.63.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.41.0 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_1.63.0 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_2.69.0 munsell_0.5.0
[25] DESeq2_1.41.0 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_0.27.0 cachem_1.0.7 nlme_3.1-162
[37] genefilter_1.83.0 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_0.41.0 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_1.79.0
[70] jsonlite_1.8.4 R6_2.5.1 zlibbioc_1.47.0 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.