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 473 1 183 27 134 198 609 31 58
gene2 1 1 342 40 5 47 2 1 12
gene3 48 1 2 15 997 22 9 1 12
gene4 178 1 181 1 183 1 6 9 285
gene5 147 29 253 50 3 239 102 25 4
gene6 128 1 45 19 110 4 360 68 49
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 371 120 1 16 84 3 132 1
gene2 86 44 17 1 2 23 160 3
gene3 1 576 97 3 9 1 2 263
gene4 93 1 1 1 358 187 140 2
gene5 45 39 1 13 1 80 6 682
gene6 1 51 1 108 1 12 1 3
sample18 sample19 sample20
gene1 2 8 5
gene2 1 1 122
gene3 184 5 342
gene4 7 20 2
gene5 2 1 3
gene6 10 7 7
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 66.41980 -0.09570406 -2.0176635 -0.6949602 2
sample2 38.70582 -0.41835127 -1.4195692 0.2854073 1
sample3 66.41351 -0.73686886 0.6243587 -1.3613206 0
sample4 77.60001 -1.10360211 0.6327834 -0.5687063 2
sample5 45.05218 -0.57583224 0.4246309 0.5572021 0
sample6 41.02692 -1.02558338 -0.6774509 -0.4957314 0
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 115.2714 1.00017 1.14437 0.28472225 0.4873172 230.244 237.214
gene2 33.4736 1.00006 9.31807 0.00227002 0.0567505 175.295 182.265
gene3 83.2071 1.00005 0.12551 0.72316814 0.8217820 195.006 201.976
gene4 78.3016 1.00011 2.40620 0.12086272 0.3566142 203.704 210.674
gene5 68.9903 1.00009 4.86244 0.02745428 0.2414824 209.284 216.254
gene6 50.9821 1.00007 2.75665 0.09686248 0.3459374 199.111 206.081
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 115.2714 1.066315 0.515773 2.067411 0.03869542 0.2149745 230.244
gene2 33.4736 1.350501 0.476324 2.835257 0.00457888 0.0871452 175.295
gene3 83.2071 0.286147 0.451341 0.633992 0.52608612 0.8397578 195.006
gene4 78.3016 0.243043 0.533967 0.455165 0.64899040 0.8397578 203.704
gene5 68.9903 0.170430 0.494507 0.344647 0.73036010 0.8492559 209.284
gene6 50.9821 0.547279 0.530694 1.031252 0.30242244 0.6474530 199.111
BIC
<numeric>
gene1 237.214
gene2 182.265
gene3 201.976
gene4 210.674
gene5 216.254
gene6 206.081
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 115.2714 -1.1788965 1.003998 -1.1742016 0.24031427 0.546169 230.244
gene2 33.4736 -1.6333736 0.888732 -1.8378691 0.06608170 0.254160 175.295
gene3 83.2071 -1.0314385 0.847781 -1.2166338 0.22374357 0.546169 195.006
gene4 78.3016 -0.0284118 1.036256 -0.0274177 0.97812657 0.981808 203.704
gene5 68.9903 -2.6951364 0.961648 -2.8026212 0.00506892 0.042241 209.284
gene6 50.9821 -0.2447687 1.034223 -0.2366692 0.81291345 0.981808 199.111
BIC
<numeric>
gene1 237.214
gene2 182.265
gene3 201.976
gene4 210.674
gene5 216.254
gene6 206.081
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene24 111.1879 1.00006 10.04466 0.00152897 0.0567505 204.149 211.119
gene2 33.4736 1.00006 9.31807 0.00227002 0.0567505 175.295 182.265
gene26 139.9684 2.08422 12.39541 0.01041899 0.1736498 228.531 236.581
gene31 221.7640 1.00006 5.75978 0.01640255 0.2050318 236.548 243.518
gene5 68.9903 1.00009 4.86244 0.02745428 0.2414824 209.284 216.254
gene18 150.5596 1.00004 4.76919 0.02897789 0.2414824 227.820 234.790
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 Under development (unstable) (2025-03-02 r87868)
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 3.12.0
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_3.5.1 BiocParallel_1.41.2
[3] NBAMSeq_1.23.0 SummarizedExperiment_1.37.0
[5] Biobase_2.67.0 GenomicRanges_1.59.1
[7] GenomeInfoDb_1.43.4 IRanges_2.41.3
[9] S4Vectors_0.45.4 BiocGenerics_0.53.6
[11] generics_0.1.3 MatrixGenerics_1.19.1
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.47.0 gtable_0.3.6 xfun_0.51
[4] bslib_0.9.0 lattice_0.22-6 vctrs_0.6.5
[7] tools_4.5.0 parallel_4.5.0 tibble_3.2.1
[10] AnnotationDbi_1.69.0 RSQLite_2.3.9 blob_1.2.4
[13] pkgconfig_2.0.3 Matrix_1.7-2 lifecycle_1.0.4
[16] GenomeInfoDbData_1.2.13 farver_2.1.2 compiler_4.5.0
[19] Biostrings_2.75.4 munsell_0.5.1 DESeq2_1.47.5
[22] codetools_0.2-20 htmltools_0.5.8.1 sass_0.4.9
[25] yaml_2.3.10 pillar_1.10.1 crayon_1.5.3
[28] jquerylib_0.1.4 DelayedArray_0.33.6 cachem_1.1.0
[31] abind_1.4-8 nlme_3.1-167 genefilter_1.89.0
[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_1.7.6 magrittr_2.0.3
[46] S4Arrays_1.7.3 survival_3.8-3 XML_3.99-0.18
[49] withr_3.0.2 scales_1.3.0 UCSC.utils_1.3.1
[52] bit64_4.6.0-1 rmarkdown_2.29 XVector_0.47.2
[55] httr_1.4.7 bit_4.5.0.1 png_0.1-8
[58] memoise_2.0.1 evaluate_1.0.3 knitr_1.49
[61] mgcv_1.9-1 rlang_1.1.5 Rcpp_1.0.14
[64] xtable_1.8-4 glue_1.8.0 DBI_1.2.3
[67] annotate_1.85.0 jsonlite_1.9.1 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.