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
gene1 11 2 13 1 1 1 182 37
gene2 4 215 1 1 22 2 102 251
gene3 1 1 755 22 771 80 100 11
gene4 206 33 1 14 27 47 100 27
gene5 74 3 1 46 1 2 367 948
gene6 359 218 86 12 2 74 80 1
sample9 sample10 sample11 sample12 sample13 sample14 sample15
gene1 1 39 1 33 260 1 60
gene2 1 730 103 1 22 10 248
gene3 33 13 60 29 18 155 1
gene4 1 1 1 4 80 198 1
gene5 74 1 11 450 62 38 1
gene6 2 12 155 16 34 1 2
sample16 sample17 sample18 sample19 sample20
gene1 41 1 366 58 125
gene2 20 31 6 80 382
gene3 234 64 39 330 1
gene4 99 1 26 1 35
gene5 44 1 301 48 1
gene6 310 35 31 10 25
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 56.71001 -0.9252505 2.5510666 -0.04407704 1
sample2 42.82190 -0.4743782 0.1186176 0.69148752 0
sample3 56.39007 -1.0110220 1.8915161 -0.65682697 1
sample4 61.96079 0.4861810 -0.6827808 -1.06145104 1
sample5 78.65690 -1.5942347 0.1678182 -0.09032828 1
sample6 50.10764 0.3402041 -0.4617337 0.40869536 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;
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 5 columns
baseMean edf stat
<numeric> <numeric> <numeric>
gene1 40.3810146240061 1.00017302129931 1.12044733145051
gene2 96.7401711174761 1.00039281978881 0.171517325979447
gene3 149.573397066495 1.00006351214147 13.8061182285047
gene4 47.235216463515 1.0000945107179 1.43635576975853
gene5 95.9107080475714 1.0001624639408 4.90521198796358
gene6 84.1219859462146 1.00021586944167 4.57684858147298
pvalue padj
<numeric> <numeric>
gene1 0.289915767979256 NA
gene2 0.678943874202626 0.754382082447362
gene3 0.000202849778211936 0.00811399112847742
gene4 0.230820684901683 NA
gene5 0.0267854835391625 0.0989579098302048
gene6 0.0324248504278656 0.0989579098302048
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 6 columns
baseMean coef SE
<numeric> <numeric> <numeric>
gene1 40.3810146240061 0.353433740196638 0.414016182003223
gene2 96.7401711174761 0.0871144252319114 0.441707871041739
gene3 149.573397066495 -0.00154839879570697 0.390158033656235
gene4 47.235216463515 1.05830851716423 0.392288278246941
gene5 95.9107080475714 1.29107549206216 0.406902766883482
gene6 84.1219859462146 0.370196602672857 0.394083646878235
stat pvalue padj
<numeric> <numeric> <numeric>
gene1 0.853671319044932 0.393287129912476 0.6832066370896
gene2 0.197221808672908 0.843653964919896 0.938686985438606
gene3 -0.00396864516974487 0.996833487603929 0.996833487603929
gene4 2.69778266608834 0.00698029956400901 0.0707383696245858
gene5 3.17293367639316 0.00150906993629059 0.0289491930302151
gene6 0.939385852738114 0.34753267389232 0.643579025726519
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 6 columns
baseMean coef SE
<numeric> <numeric> <numeric>
gene1 40.3810146240061 -0.855860329793421 1.03260925066148
gene2 96.7401711174761 -1.25067920649459 1.10070173899278
gene3 149.573397066495 3.54281601766681 1.00302321903271
gene4 47.235216463515 -0.556913273859132 0.990916453627581
gene5 95.9107080475714 2.81210596534219 1.04488357762558
gene6 84.1219859462146 0.894420466004872 0.987885983814718
stat pvalue padj
<numeric> <numeric> <numeric>
gene1 -0.828832716000915 0.407199072804799 NA
gene2 -1.13625622835761 0.25584934415566 0.513377986070939
gene3 3.53213759207231 0.000412214814169106 0.0161082737828756
gene4 -0.562018394003213 0.574103486848939 0.748074240439526
gene5 2.69131032926415 0.00711719558427978 0.0612078820248061
gene6 0.905388355193653 0.365259682672914 0.604083321343666
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 5 columns
baseMean edf stat
<numeric> <numeric> <numeric>
gene3 149.573397066495 1.00006351214147 13.8061182285047
gene49 66.0854645089602 1.00005373188331 10.2593467301833
gene17 77.4485801604086 1.00010374540359 8.9558005471839
gene13 97.5065784092174 1.00020404133988 8.77140103140255
gene15 76.8324894578036 1.00009577334564 8.2674782977527
gene28 139.360992342529 1.00016414887239 7.59776763363783
pvalue padj
<numeric> <numeric>
gene3 0.000202849778211936 0.00811399112847742
gene49 0.00136015516538303 0.0272031033076607
gene17 0.0027688630648992 0.0306634012293218
gene13 0.00306634012293218 0.0306634012293218
gene15 0.00403866918625302 0.0323093534900242
gene28 0.00584860568825095 0.0389907045883397
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: OS X El Capitan 10.11.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] parallel stats4 stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] ggplot2_3.2.1 NBAMSeq_1.0.1
[3] SummarizedExperiment_1.14.1 DelayedArray_0.10.0
[5] BiocParallel_1.18.1 matrixStats_0.54.0
[7] Biobase_2.44.0 GenomicRanges_1.36.0
[9] GenomeInfoDb_1.20.0 IRanges_2.18.1
[11] S4Vectors_0.22.0 BiocGenerics_0.30.0
loaded via a namespace (and not attached):
[1] bit64_0.9-7 splines_3.6.1 Formula_1.2-3
[4] assertthat_0.2.1 latticeExtra_0.6-28 blob_1.2.0
[7] GenomeInfoDbData_1.2.1 yaml_2.2.0 pillar_1.4.2
[10] RSQLite_2.1.2 backports_1.1.4 lattice_0.20-38
[13] glue_1.3.1 digest_0.6.20 RColorBrewer_1.1-2
[16] XVector_0.24.0 checkmate_1.9.4 colorspace_1.4-1
[19] htmltools_0.3.6 Matrix_1.2-17 DESeq2_1.24.0
[22] XML_3.98-1.20 pkgconfig_2.0.2 genefilter_1.66.0
[25] zlibbioc_1.30.0 purrr_0.3.2 xtable_1.8-4
[28] scales_1.0.0 htmlTable_1.13.1 tibble_2.1.3
[31] annotate_1.62.0 mgcv_1.8-28 withr_2.1.2
[34] nnet_7.3-12 lazyeval_0.2.2 survival_2.44-1.1
[37] magrittr_1.5 crayon_1.3.4 memoise_1.1.0
[40] evaluate_0.14 nlme_3.1-141 foreign_0.8-72
[43] tools_3.6.1 data.table_1.12.2 stringr_1.4.0
[46] locfit_1.5-9.1 munsell_0.5.0 cluster_2.1.0
[49] AnnotationDbi_1.46.0 compiler_3.6.1 rlang_0.4.0
[52] grid_3.6.1 RCurl_1.95-4.12 rstudioapi_0.10
[55] htmlwidgets_1.3 labeling_0.3 bitops_1.0-6
[58] base64enc_0.1-3 rmarkdown_1.14 gtable_0.3.0
[61] DBI_1.0.0 R6_2.4.0 gridExtra_2.3
[64] knitr_1.24 dplyr_0.8.3 zeallot_0.1.0
[67] bit_1.1-14 Hmisc_4.2-0 stringi_1.4.3
[70] Rcpp_1.0.2 geneplotter_1.62.0 vctrs_0.2.0
[73] rpart_4.1-15 acepack_1.4.1 tidyselect_0.2.5
[76] xfun_0.8
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.