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 2 74 13 46 72 7 105 45 459
gene2 189 215 17 33 724 1 642 278 3
gene3 226 44 1 52 202 267 1 130 64
gene4 728 498 22 1 177 15 3 1 17
gene5 339 55 25 198 3 2 76 43 145
gene6 589 1 22 175 1 4 12 79 147
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 707 6 1 2 38 1 67 114
gene2 40 56 7 1 1 697 43 544
gene3 103 21 548 13 360 444 1 85
gene4 116 194 1 135 8 355 2 111
gene5 9 29 257 1 1 246 12 541
gene6 231 17 56 170 138 6 1081 1
sample18 sample19 sample20
gene1 48 1 5
gene2 44 48 8
gene3 179 25 968
gene4 11 8 105
gene5 67 1 25
gene6 4 22 136
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 63.13188 0.4477818 -0.27312540 0.4139081 0
sample2 78.81099 -1.6380218 -0.31010279 -1.5696608 2
sample3 34.90837 0.2603444 0.63223992 -1.3771187 2
sample4 64.28135 0.1963218 0.61517247 -0.2202156 1
sample5 30.71241 -1.9626649 -0.03298638 -0.6162461 0
sample6 21.87581 -1.1658689 1.31906734 -0.1253764 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 73.2747 1.00003 0.0768108 0.781749 0.897143 218.471 225.441
gene2 128.2247 1.00003 0.0128199 0.909956 0.961245 242.323 249.293
gene3 148.9888 1.00016 0.3797029 0.537802 0.790886 254.258 261.228
gene4 91.7294 1.00006 1.8070581 0.178875 0.508607 223.599 230.569
gene5 70.8992 1.00006 2.0057640 0.156713 0.508607 225.042 232.012
gene6 117.7662 1.00008 0.6081517 0.435491 0.702405 227.222 234.192
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 73.2747 -0.2741298 0.343910 -0.797098 0.42539433 0.6861199 218.471
gene2 128.2247 -0.6776574 0.326704 -2.074223 0.03805858 0.2619053 242.323
gene3 148.9888 0.0868157 0.305268 0.284392 0.77611022 0.8418301 254.258
gene4 91.7294 -0.3800270 0.316189 -1.201897 0.22940359 0.5403049 223.599
gene5 70.8992 0.0987354 0.315541 0.312908 0.75435041 0.8418301 225.042
gene6 117.7662 0.8401965 0.302848 2.774314 0.00553183 0.0612428 227.222
BIC
<numeric>
gene1 225.441
gene2 249.293
gene3 261.228
gene4 230.569
gene5 232.012
gene6 234.192
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 73.2747 -0.723407 1.069139 -0.676626 0.498643 0.709515 218.471
gene2 128.2247 -0.203194 1.015663 -0.200060 0.841433 0.960453 242.323
gene3 148.9888 -0.469363 0.951647 -0.493211 0.621863 0.840356 254.258
gene4 91.7294 -1.000913 0.977330 -1.024129 0.305774 0.709515 223.599
gene5 70.8992 0.450717 0.981468 0.459228 0.646071 0.849384 225.042
gene6 117.7662 -0.953761 0.944179 -1.010148 0.312424 0.709515 227.222
BIC
<numeric>
gene1 225.441
gene2 249.293
gene3 261.228
gene4 230.569
gene5 232.012
gene6 234.192
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene25 150.6752 1.00010 15.94996 6.51374e-05 0.00325687 229.445 236.415
gene47 94.4289 1.00012 8.40062 3.75267e-03 0.09381664 185.108 192.078
gene38 86.3693 1.00016 6.73955 9.43768e-03 0.15729460 220.363 227.333
gene8 127.3620 1.00017 5.65637 1.74025e-02 0.21753169 243.979 250.949
gene35 54.1477 1.00005 3.13197 7.67799e-02 0.50860712 209.227 216.197
gene22 97.5441 1.00014 2.92327 8.73657e-02 0.50860712 219.205 226.175
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.2.1 (2022-06-23 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows Server x64 (build 20348)
Matrix products: default
locale:
[1] LC_COLLATE=C
[2] LC_CTYPE=English_United States.utf8
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.utf8
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.3.6 BiocParallel_1.32.0
[3] NBAMSeq_1.14.0 SummarizedExperiment_1.28.0
[5] Biobase_2.58.0 GenomicRanges_1.50.0
[7] GenomeInfoDb_1.34.0 IRanges_2.32.0
[9] S4Vectors_0.36.0 BiocGenerics_0.44.0
[11] MatrixGenerics_1.10.0 matrixStats_0.62.0
loaded via a namespace (and not attached):
[1] httr_1.4.4 sass_0.4.2 bit64_4.0.5
[4] jsonlite_1.8.3 splines_4.2.1 bslib_0.4.0
[7] assertthat_0.2.1 highr_0.9 blob_1.2.3
[10] GenomeInfoDbData_1.2.9 yaml_2.3.6 pillar_1.8.1
[13] RSQLite_2.2.18 lattice_0.20-45 glue_1.6.2
[16] digest_0.6.30 RColorBrewer_1.1-3 XVector_0.38.0
[19] colorspace_2.0-3 htmltools_0.5.3 Matrix_1.5-1
[22] DESeq2_1.38.0 XML_3.99-0.12 pkgconfig_2.0.3
[25] genefilter_1.80.0 zlibbioc_1.44.0 xtable_1.8-4
[28] snow_0.4-4 scales_1.2.1 tibble_3.1.8
[31] annotate_1.76.0 mgcv_1.8-41 KEGGREST_1.38.0
[34] farver_2.1.1 generics_0.1.3 withr_2.5.0
[37] cachem_1.0.6 cli_3.4.1 survival_3.4-0
[40] magrittr_2.0.3 crayon_1.5.2 memoise_2.0.1
[43] evaluate_0.17 fansi_1.0.3 nlme_3.1-160
[46] tools_4.2.1 lifecycle_1.0.3 stringr_1.4.1
[49] locfit_1.5-9.6 munsell_0.5.0 DelayedArray_0.24.0
[52] AnnotationDbi_1.60.0 Biostrings_2.66.0 compiler_4.2.1
[55] jquerylib_0.1.4 rlang_1.0.6 grid_4.2.1
[58] RCurl_1.98-1.9 labeling_0.4.2 bitops_1.0-7
[61] rmarkdown_2.17 gtable_0.3.1 codetools_0.2-18
[64] DBI_1.1.3 R6_2.5.1 knitr_1.40
[67] dplyr_1.0.10 fastmap_1.1.0 bit_4.0.4
[70] utf8_1.2.2 stringi_1.7.8 parallel_4.2.1
[73] Rcpp_1.0.9 vctrs_0.5.0 geneplotter_1.76.0
[76] png_0.1-7 tidyselect_1.2.0 xfun_0.34
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.