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 53 26 10 1 3 24 36 9 717
gene2 15 1 24 1 3 87 4 165 114
gene3 1 144 86 61 8 1 1 102 23
gene4 63 1 89 1 4 1 15 26 7
gene5 1 2 5 73 14 79 1 11 159
gene6 493 16 227 53 13 2 1 73 29
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 144 148 1 230 14 29 6 5
gene2 3 23 50 13 271 6 880 13
gene3 275 4 14 408 1 1 11 673
gene4 4 132 56 9 8 25 12 153
gene5 611 6 7 5 53 1 63 73
gene6 153 308 144 19 109 54 125 256
sample18 sample19 sample20
gene1 1 1 142
gene2 3 118 75
gene3 16 2 209
gene4 126 21 63
gene5 320 70 35
gene6 1 2 40colData 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 76.51054 -0.6496998 0.2927702 -1.5273647 0
sample2 26.37295 -0.9217091 -0.9537890 1.5869146 0
sample3 60.35212 -2.3911142 -0.2198217 -0.2261561 1
sample4 48.53997 -0.3861458 0.2509984 -0.4601455 0
sample5 54.50890 0.4179040 -0.3389644 -1.1644001 2
sample6 24.44823 1.6967647 0.7766880 -0.1418359 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
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 64.1040 1.34270 1.17354e+00 5.50273e-01 0.70547827 202.708
gene2 82.5379 1.00020 4.21507e-01 5.16361e-01 0.68572125 213.991
gene3 92.6232 1.00006 1.02758e+00 3.10793e-01 0.51798758 211.195
gene4 40.2564 1.00007 1.85418e+00 1.73322e-01 0.33331126 200.916
gene5 78.0204 1.00009 1.30103e-05 9.99348e-01 0.99934824 212.934
gene6 116.8766 1.00006 1.75100e+01 2.92882e-05 0.00146441 219.870
BIC
<numeric>
gene1 210.019
gene2 220.962
gene3 218.165
gene4 207.886
gene5 219.905
gene6 226.840For 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 64.1040 -0.0910321 0.478085 -0.1904100 0.8489879 0.943320 202.708
gene2 82.5379 0.8700025 0.498938 1.7437102 0.0812096 0.290034 213.991
gene3 92.6232 0.2917115 0.520528 0.5604150 0.5751964 0.835619 211.195
gene4 40.2564 0.2587779 0.473784 0.5461934 0.5849330 0.835619 200.916
gene5 78.0204 0.9774854 0.520471 1.8780800 0.0603702 0.251543 212.934
gene6 116.8766 -0.0167402 0.398504 -0.0420075 0.9664927 0.982245 219.870
BIC
<numeric>
gene1 210.019
gene2 220.962
gene3 218.165
gene4 207.886
gene5 219.905
gene6 226.840For 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 64.1040 -2.90309267 1.185422 -2.44899533 0.0143255 0.160638 202.708
gene2 82.5379 -0.00798848 1.207086 -0.00661798 0.9947197 0.994720 213.991
gene3 92.6232 -0.71786831 1.281608 -0.56013088 0.5753902 0.799153 211.195
gene4 40.2564 0.29066022 1.149747 0.25280360 0.8004200 0.889356 200.916
gene5 78.0204 1.03388791 1.242819 0.83188931 0.4054714 0.652694 212.934
gene6 116.8766 -2.34348371 0.973425 -2.40746276 0.0160638 0.160638 219.870
BIC
<numeric>
gene1 210.019
gene2 220.962
gene3 218.165
gene4 207.886
gene5 219.905
gene6 226.840Visualization
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene6 116.8766 1.00006 17.51001 2.92882e-05 0.00146441 219.870 226.840
gene36 72.3637 2.09155 18.84096 4.98531e-04 0.01246327 186.942 194.999
gene45 58.9811 1.00005 8.55268 3.45180e-03 0.05752997 200.370 207.340
gene37 86.2045 1.00006 7.76642 5.32574e-03 0.06389474 218.340 225.310
gene30 117.5830 1.00010 7.22448 7.19852e-03 0.06389474 226.923 233.893
gene47 117.4313 1.00005 7.11031 7.66737e-03 0.06389474 236.993 243.963library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.3.1 (2023-06-16)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.3 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_3.4.4 BiocParallel_1.36.0
[3] NBAMSeq_1.18.0 SummarizedExperiment_1.32.0
[5] Biobase_2.62.0 GenomicRanges_1.54.1
[7] GenomeInfoDb_1.38.0 IRanges_2.36.0
[9] S4Vectors_0.40.1 BiocGenerics_0.48.1
[11] MatrixGenerics_1.14.0 matrixStats_1.0.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.42.0 gtable_0.3.4 xfun_0.41
[4] bslib_0.5.1 lattice_0.22-5 vctrs_0.6.4
[7] tools_4.3.1 bitops_1.0-7 generics_0.1.3
[10] parallel_4.3.1 RSQLite_2.3.2 AnnotationDbi_1.64.0
[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_4.3.1 Biostrings_2.70.1 munsell_0.5.0
[25] DESeq2_1.42.0 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_0.28.0 cachem_1.0.8 abind_1.4-5
[37] nlme_3.1-163 genefilter_1.84.0 tidyselect_1.2.0
[40] locfit_1.5-9.8 digest_0.6.33 dplyr_1.1.3
[43] labeling_0.4.3 splines_4.3.1 fastmap_1.1.1
[46] grid_4.3.1 colorspace_2.1-0 cli_3.6.1
[49] SparseArray_1.2.0 magrittr_2.0.3 S4Arrays_1.2.0
[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_0.42.0 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_1.80.0
[73] jsonlite_1.8.7 R6_2.5.1 zlibbioc_1.48.0 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.