To install and load NBAMSeq
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 NBAMSeq
function;
Step 3: Pulling out DE results using results
function.
Here we illustrate each of these steps respectively.
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 1 622 3 1 55 480 5 123 107
gene2 44 105 73 1 22 297 431 1 443
gene3 40 377 172 30 25 8 5 23 135
gene4 2 137 20 96 8 3 145 1 9
gene5 29 36 93 44 149 1 54 146 1
gene6 5 1 265 12 21 275 1 1 33
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 612 38 21 2 3 80 108 89
gene2 14 27 83 43 4 13 50 1
gene3 1 831 35 9 173 5 164 5
gene4 2 104 294 114 85 120 260 1
gene5 19 14 24 54 28 25 12 54
gene6 99 1 412 10 74 1 51 80
sample18 sample19 sample20
gene1 41 6 324
gene2 4 132 213
gene3 46 343 193
gene4 6 1 4
gene5 31 70 2
gene6 8 39 53
colData
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 23.46853 -0.8107729 1.1672727 -0.9758171 2
sample2 30.11858 -0.1677050 -0.8317767 -0.9979414 1
sample3 75.40656 0.5406788 -0.5764541 -0.1479813 1
sample4 41.90524 -0.1856598 -0.9826310 2.0318533 2
sample5 76.04125 2.0879219 1.7203353 -0.3404363 1
sample6 42.80713 -0.8261199 0.8607129 -0.4904841 2
design
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)
as var4
is 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 + var4
is 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 var4
Differential expression analysis can be performed by NBAMSeq
function:
Several other arguments in NBAMSeq
function are available for users to customize the analysis.
gamma
argument can be used to control the smoothness of the nonlinear function. Higher gamma
means the nonlinear function will be more smooth. See the gamma
argument of gam function in mgcv (Wood and Wood 2015) for details. Default gamma
is 2.5;
fitlin
is either TRUE
or FALSE
indicating whether linear model should be fitted after fitting the nonlinear model;
parallel
is either TRUE
or FALSE
indicating whether parallel should be used. e.g. Run NBAMSeq
with parallel = TRUE
:
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 108.0045 1.00006 0.543868 0.4609310 0.746769 234.980 241.950
gene2 86.8759 1.00006 0.272677 0.6015919 0.791378 229.024 235.995
gene3 123.5539 1.00007 0.249200 0.6176760 0.791378 235.126 242.096
gene4 49.9436 1.00018 0.865087 0.3522740 0.715972 206.312 213.282
gene5 40.6054 1.00004 1.491237 0.2220338 0.580245 206.313 213.284
gene6 59.9212 1.00004 2.728438 0.0985781 0.410742 210.434 217.404
For 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 108.0045 -0.3618531 0.436487 -0.8290125 0.407097 0.709718 234.980
gene2 86.8759 -0.2633533 0.412891 -0.6378281 0.523586 0.805055 229.024
gene3 123.5539 0.2043466 0.378848 0.5393888 0.589619 0.805055 235.126
gene4 49.9436 -0.5430207 0.391187 -1.3881369 0.165095 0.405787 206.312
gene5 40.6054 0.4888901 0.330508 1.4792065 0.139085 0.386348 206.313
gene6 59.9212 -0.0410265 0.415154 -0.0988223 0.921279 0.980084 210.434
BIC
<numeric>
gene1 241.950
gene2 235.995
gene3 242.096
gene4 213.282
gene5 213.284
gene6 217.404
For 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 108.0045 0.697545 1.122008 0.621693 0.53414365 0.763516 234.980
gene2 86.8759 -0.690297 1.059487 -0.651539 0.51469874 0.763516 229.024
gene3 123.5539 -2.543048 0.973513 -2.612238 0.00899515 0.112439 235.126
gene4 49.9436 -0.222265 1.000601 -0.222131 0.82421154 0.925469 206.312
gene5 40.6054 0.731280 0.853571 0.856731 0.39159370 0.716784 206.313
gene6 59.9212 1.491542 1.066900 1.398014 0.16210879 0.470570 210.434
BIC
<numeric>
gene1 241.950
gene2 235.995
gene3 242.096
gene4 213.282
gene5 213.284
gene6 217.404
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene38 104.8909 1.00010 6.82526 0.00899020 0.223544 219.327 226.298
gene30 55.8566 1.00006 6.77117 0.00926886 0.223544 209.464 216.434
gene28 105.8213 1.00007 5.64262 0.01753244 0.223544 215.458 222.428
gene40 23.3175 1.00009 5.60820 0.01788352 0.223544 171.626 178.596
gene49 66.8204 1.00006 4.05882 0.04395746 0.375988 203.090 210.060
gene29 57.4066 1.00008 4.01471 0.04511861 0.375988 215.849 222.819
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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))
R version 4.5.0 Patched (2025-04-21 r88169)
Platform: x86_64-apple-darwin20
Running under: macOS Monterey 12.7.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/New_York
tzcode source: internal
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.5.2 BiocParallel_1.43.0
[3] NBAMSeq_1.25.0 SummarizedExperiment_1.39.0
[5] Biobase_2.69.0 GenomicRanges_1.61.0
[7] GenomeInfoDb_1.45.0 IRanges_2.43.0
[9] S4Vectors_0.47.0 BiocGenerics_0.55.0
[11] generics_0.1.3 MatrixGenerics_1.21.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.49.0 gtable_0.3.6 xfun_0.52
[4] bslib_0.9.0 lattice_0.22-7 vctrs_0.6.5
[7] tools_4.5.0 parallel_4.5.0 tibble_3.2.1
[10] AnnotationDbi_1.71.0 RSQLite_2.3.9 blob_1.2.4
[13] pkgconfig_2.0.3 Matrix_1.7-3 lifecycle_1.0.4
[16] GenomeInfoDbData_1.2.14 farver_2.1.2 compiler_4.5.0
[19] Biostrings_2.77.0 munsell_0.5.1 DESeq2_1.49.0
[22] codetools_0.2-20 htmltools_0.5.8.1 sass_0.4.10
[25] yaml_2.3.10 pillar_1.10.2 crayon_1.5.3
[28] jquerylib_0.1.4 DelayedArray_0.35.1 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-168 genefilter_1.91.0
[34] tidyselect_1.2.1 locfit_1.5-9.12 digest_0.6.37
[37] dplyr_1.1.4 labeling_0.4.3 splines_4.5.0
[40] fastmap_1.2.0 grid_4.5.0 colorspace_2.1-1
[43] cli_3.6.5 SparseArray_1.9.0 magrittr_2.0.3
[46] S4Arrays_1.9.0 survival_3.8-3 XML_3.99-0.18
[49] withr_3.0.2 scales_1.3.0 UCSC.utils_1.5.0
[52] bit64_4.6.0-1 rmarkdown_2.29 XVector_0.49.0
[55] httr_1.4.7 bit_4.6.0 png_0.1-8
[58] memoise_2.0.1 evaluate_1.0.3 knitr_1.50
[61] mgcv_1.9-3 rlang_1.1.6 Rcpp_1.0.14
[64] xtable_1.8-4 glue_1.8.0 DBI_1.2.3
[67] annotate_1.87.0 jsonlite_2.0.0 R6_2.6.1
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.