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 1 253 127 150 77 405 1 1 174
gene2 23 487 11 3 257 1 1 18 1
gene3 1 71 48 36 37 20 2 9 109
gene4 131 214 355 65 30 3 5 424 1
gene5 132 11 18 30 157 122 557 22 151
gene6 8 223 65 36 263 4 108 5 104
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 316 44 4 77 18 1 32
gene2 14 300 780 8 53 40 1 8
gene3 1 32 10 83 20 143 1 77
gene4 405 17 1 16 1 273 1 1
gene5 66 107 105 3 60 43 1136 9
gene6 3 4 1 1 1 97 372 229
sample18 sample19 sample20
gene1 1 10 43
gene2 1 8 52
gene3 24 386 1
gene4 48 1355 184
gene5 303 22 1
gene6 303 1 69
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 36.81531 -0.5683882 1.4185611 -0.5409313 2
sample2 21.17783 -0.8977422 -1.8533758 -1.6161410 2
sample3 45.54073 -0.4470155 1.0136167 -0.3017436 0
sample4 78.48816 -0.6642566 -0.4950269 0.5029641 2
sample5 40.56384 1.3810310 1.2498123 -0.5482465 2
sample6 63.68659 0.6254796 0.3884266 1.3584399 1
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 61.1918 1.00013 0.327782 0.56715505 0.6996128 211.842 218.812
gene2 74.8774 1.00002 9.584033 0.00196352 0.0392788 197.979 204.949
gene3 52.4515 1.00007 1.758163 0.18487417 0.4194704 206.936 213.906
gene4 148.9089 1.00006 3.183950 0.07438376 0.3719188 228.336 235.307
gene5 135.1822 1.00009 5.447494 0.01960392 0.1400280 243.900 250.871
gene6 86.6142 1.00016 0.648823 0.42070505 0.6010072 223.298 230.268
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 61.1918 1.220823 0.491370 2.484529 0.0129723 0.142278 211.842
gene2 74.8774 0.516646 0.457418 1.129485 0.2586932 0.610413 197.979
gene3 52.4515 0.918697 0.468333 1.961630 0.0498056 0.311346 206.936
gene4 148.9089 -0.965681 0.492306 -1.961547 0.0498153 0.311346 228.336
gene5 135.1822 0.766998 0.439320 1.745877 0.0808323 0.359976 243.900
gene6 86.6142 0.466947 0.514991 0.906708 0.3645611 0.628554 223.298
BIC
<numeric>
gene1 218.812
gene2 204.949
gene3 213.906
gene4 235.307
gene5 250.871
gene6 230.268
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 61.1918 -0.244073 1.042865 -0.234041 0.81495329 0.8669716 211.842
gene2 74.8774 1.371764 0.978126 1.402442 0.16078333 0.3227082 197.979
gene3 52.4515 -2.732859 1.006748 -2.714542 0.00663675 0.0414797 206.936
gene4 148.9089 -1.442605 1.061866 -1.358557 0.17428701 0.3227537 228.336
gene5 135.1822 -1.539686 0.951783 -1.617687 0.10573011 0.2517384 243.900
gene6 86.6142 0.575431 1.116210 0.515522 0.60618806 0.7216524 223.298
BIC
<numeric>
gene1 218.812
gene2 204.949
gene3 213.906
gene4 235.307
gene5 250.871
gene6 230.268
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene36 136.8230 1.00007 15.50975 8.28484e-05 0.00414242 204.359 211.330
gene2 74.8774 1.00002 9.58403 1.96352e-03 0.03927884 197.979 204.949
gene13 72.0128 1.00006 9.07464 2.59313e-03 0.03927884 203.497 210.467
gene43 150.5744 1.00006 8.72400 3.14231e-03 0.03927884 225.741 232.711
gene12 51.8926 1.00002 5.95556 1.46720e-02 0.12610134 199.197 206.167
gene19 90.7346 1.00007 5.90183 1.51322e-02 0.12610134 216.078 223.048
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 RC (2025-04-04 r88126)
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_1.42.0
[3] NBAMSeq_1.24.0 SummarizedExperiment_1.38.0
[5] Biobase_2.68.0 GenomicRanges_1.60.0
[7] GenomeInfoDb_1.44.0 IRanges_2.42.0
[9] S4Vectors_0.46.0 BiocGenerics_0.54.0
[11] generics_0.1.3 MatrixGenerics_1.20.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.48.0 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_1.70.0 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_2.76.0 munsell_0.5.1 DESeq2_1.48.0
[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_0.34.0 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-168 genefilter_1.90.0
[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_3.6.4 SparseArray_1.8.0 magrittr_2.0.3
[46] S4Arrays_1.8.0 survival_3.8-3 XML_3.99-0.18
[49] withr_3.0.2 scales_1.3.0 UCSC.utils_1.4.0
[52] bit64_4.6.0-1 rmarkdown_2.29 XVector_0.48.0
[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_1.86.0 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.