NBAMSeq: Negative Binomial Additive Model for RNA-Seq Data
Xu Ren and Pei Fen Kuan
2024-04-21
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 447 6 189 173 660 6 57 14 59
gene2 1 1 13 19 2 57 171 39 16
gene3 83 2 3 26 4 70 94 203 166
gene4 188 63 108 3 317 174 2 10 190
gene5 46 1 10 82 2 2 11 1 2
gene6 64 66 852 151 78 88 4 1 30
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 511 123 181 1 4 308 67 121
gene2 8 50 101 25 51 284 13 121
gene3 114 553 261 41 9 82 49 398
gene4 106 129 279 56 250 466 39 3
gene5 119 34 2 48 1 547 8 5
gene6 33 1 376 2 1 204 8 509
sample18 sample19 sample20
gene1 5 9 174
gene2 31 27 1
gene3 45 106 103
gene4 399 204 17
gene5 26 141 132
gene6 16 3 1103colData 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 30.66316 0.9197954 -0.67261583 -1.223635570 2
sample2 69.57554 1.5787574 -1.66481889 0.221199611 1
sample3 34.17805 -0.3004315 1.19648809 0.003652822 0
sample4 67.37383 -1.2610021 -0.84742589 0.871489633 1
sample5 34.64948 -2.1675244 -1.30741001 -0.288487532 2
sample6 47.88003 -0.5407355 0.07943524 -0.185664564 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 128.4559 1.00035 1.7873865 0.18124213 0.4491028 246.360 253.330
gene2 39.1156 1.00007 0.3961528 0.52910008 0.7585839 203.051 210.021
gene3 89.9361 1.00005 0.0826494 0.77384184 0.8657102 239.651 246.621
gene4 129.6968 1.00008 3.5926601 0.05804429 0.3040951 253.006 259.976
gene5 38.5948 1.00004 1.1605420 0.28138026 0.5210746 182.995 189.965
gene6 111.6350 1.00014 7.9796805 0.00473321 0.0788868 230.549 237.519For 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 128.4559 -0.2811095 0.287376 -0.978195 0.327978 0.729785 246.360
gene2 39.1156 -0.1891584 0.266038 -0.711020 0.477072 0.822538 203.051
gene3 89.9361 0.4073337 0.253912 1.604229 0.108664 0.417937 239.651
gene4 129.6968 -0.2213903 0.271676 -0.814907 0.415126 0.741296 253.006
gene5 38.5948 0.3153874 0.263116 1.198664 0.230658 0.576646 182.995
gene6 111.6350 0.0736847 0.307060 0.239968 0.810355 0.920858 230.549
BIC
<numeric>
gene1 253.330
gene2 210.021
gene3 246.621
gene4 259.976
gene5 189.965
gene6 237.519For 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 128.4559 0.287457 0.846404 0.339621 0.73414176 0.872092 246.360
gene2 39.1156 -0.779832 0.784121 -0.994530 0.31996506 0.734333 203.051
gene3 89.9361 -0.781760 0.746888 -1.046689 0.29524299 0.734333 239.651
gene4 129.6968 0.776996 0.801765 0.969106 0.33249217 0.734333 253.006
gene5 38.5948 2.462611 0.806275 3.054306 0.00225582 0.112791 182.995
gene6 111.6350 -2.040184 0.903882 -2.257134 0.02399970 0.194605 230.549
BIC
<numeric>
gene1 253.330
gene2 210.021
gene3 246.621
gene4 259.976
gene5 189.965
gene6 237.519Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene46 85.9535 1.00006 11.80775 0.000590149 0.0295075 212.849 219.819
gene19 100.8409 1.00005 8.42182 0.003708768 0.0788868 225.344 232.315
gene6 111.6350 1.00014 7.97968 0.004733210 0.0788868 230.549 237.519
gene10 99.5487 1.00006 7.05229 0.007919015 0.0796559 220.348 227.318
gene43 104.3044 1.00016 7.04252 0.007965585 0.0796559 216.586 223.557
gene22 62.2711 1.00003 6.23009 0.012563784 0.1046982 205.659 212.629library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 beta (2024-04-15 r86425)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.4 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_3.5.0 BiocParallel_1.37.1
[3] NBAMSeq_1.19.0 SummarizedExperiment_1.33.3
[5] Biobase_2.63.1 GenomicRanges_1.55.4
[7] GenomeInfoDb_1.39.14 IRanges_2.37.1
[9] S4Vectors_0.41.6 BiocGenerics_0.49.1
[11] MatrixGenerics_1.15.1 matrixStats_1.3.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.43.0 gtable_0.3.4 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_1.65.2 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_2.71.5 munsell_0.5.1 DESeq2_1.43.5
[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_0.29.9 cachem_1.0.8
[34] abind_1.4-5 nlme_3.1-164 genefilter_1.85.1
[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_1.3.5 magrittr_2.0.3
[49] S4Arrays_1.3.7 survival_3.5-8 XML_3.99-0.16.1
[52] utf8_1.2.4 withr_3.0.0 scales_1.3.0
[55] UCSC.utils_0.99.7 bit64_4.0.5 rmarkdown_2.26
[58] XVector_0.43.1 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_1.81.2 jsonlite_1.8.8
[73] R6_2.5.1 zlibbioc_1.49.3 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.