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 41 557 18 14 6 34 1 993 169
gene2 1 119 59 55 1 16 1 2 17
gene3 9 3 7 3 104 6 6 226 496
gene4 306 16 51 5 2 132 2 7 2
gene5 23 343 1 130 37 450 1 86 67
gene6 3 144 263 34 103 1 45 408 3
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 15 262 142 79 96 9 92 53
gene2 177 43 9 1 38 14 1 6
gene3 3 240 24 63 380 65 286 1
gene4 502 1 75 63 80 1 528 108
gene5 1560 38 454 2 2 11 1 221
gene6 287 2 1 9 455 73 1 184
sample18 sample19 sample20
gene1 30 204 19
gene2 1 95 30
gene3 1 20 264
gene4 212 54 302
gene5 3 1 44
gene6 3 9 35
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 79.71063 1.0323115 0.09477607 0.2343479 0
sample2 77.36460 1.3468202 -0.03951843 -1.5117014 1
sample3 45.87374 0.5597939 1.50724898 2.4349669 0
sample4 73.89417 -0.3049792 -0.66059218 0.9008444 0
sample5 61.70722 0.3883174 -0.45387197 0.7146592 1
sample6 22.78496 -0.3740537 -0.91291343 -1.5444831 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 110.2078 1.00006 0.315578 0.5743190 0.766513 236.828 243.798
gene2 23.2179 1.00012 0.991417 0.3193967 0.591475 184.448 191.419
gene3 79.2017 1.00004 2.367909 0.1238594 0.329530 215.541 222.512
gene4 90.8124 1.00004 1.864554 0.1721250 0.409822 224.525 231.495
gene5 102.3511 1.00027 2.792619 0.0947501 0.329530 229.662 236.633
gene6 74.0875 1.00009 0.183001 0.6688220 0.807061 211.684 218.654
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 110.2078 0.4414852 0.460024 0.959701 0.3372057 0.565192 236.828
gene2 23.2179 -0.6490583 0.512037 -1.267600 0.2049408 0.565192 184.448
gene3 79.2017 -0.0655163 0.499119 -0.131264 0.8955666 0.920619 215.541
gene4 90.8124 0.4859443 0.501346 0.969278 0.3324063 0.565192 224.525
gene5 102.3511 1.0214008 0.603638 1.692076 0.0906315 0.453158 229.662
gene6 74.0875 0.0613949 0.497726 0.123351 0.9018293 0.920619 211.684
BIC
<numeric>
gene1 243.798
gene2 191.419
gene3 222.512
gene4 231.495
gene5 236.633
gene6 218.654
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 110.2078 0.520359 0.99603 0.522433 0.6013691 0.887700 236.828
gene2 23.2179 -1.015113 1.12031 -0.906100 0.3648827 0.887700 184.448
gene3 79.2017 -2.447532 1.13399 -2.158342 0.0309012 0.220723 215.541
gene4 90.8124 -0.562141 1.07859 -0.521182 0.6022401 0.887700 224.525
gene5 102.3511 -0.439348 1.30342 -0.337074 0.7360608 0.898613 229.662
gene6 74.0875 0.975552 1.07511 0.907397 0.3641969 0.887700 211.684
BIC
<numeric>
gene1 243.798
gene2 191.419
gene3 222.512
gene4 231.495
gene5 236.633
gene6 218.654
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene22 70.5105 1.00007 11.33913 0.000758956 0.0379478 210.709 217.679
gene32 53.0644 1.00005 7.43202 0.006410054 0.1602513 212.283 219.253
gene48 88.3198 1.00007 6.19187 0.012835336 0.1773691 219.424 226.394
gene45 138.1574 1.00006 6.01448 0.014189526 0.1773691 241.017 247.987
gene50 75.0694 1.00007 5.35981 0.020609638 0.1983969 207.493 214.463
gene21 54.9851 1.00005 5.10890 0.023807629 0.1983969 216.168 223.138
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.0.0 (2020-04-24)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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_3.3.0 BiocParallel_1.22.0
[3] NBAMSeq_1.4.1 SummarizedExperiment_1.18.1
[5] DelayedArray_0.14.0 matrixStats_0.56.0
[7] Biobase_2.48.0 GenomicRanges_1.40.0
[9] GenomeInfoDb_1.24.0 IRanges_2.22.1
[11] S4Vectors_0.26.0 BiocGenerics_0.34.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.4.6 locfit_1.5-9.4 lattice_0.20-41
[4] assertthat_0.2.1 digest_0.6.25 R6_2.4.1
[7] RSQLite_2.2.0 evaluate_0.14 pillar_1.4.4
[10] zlibbioc_1.34.0 rlang_0.4.6 annotate_1.66.0
[13] blob_1.2.1 Matrix_1.2-18 rmarkdown_2.1
[16] labeling_0.3 splines_4.0.0 geneplotter_1.66.0
[19] stringr_1.4.0 RCurl_1.98-1.2 bit_1.1-15.2
[22] munsell_0.5.0 compiler_4.0.0 xfun_0.13
[25] pkgconfig_2.0.3 mgcv_1.8-31 htmltools_0.4.0
[28] tidyselect_1.0.0 tibble_3.0.1 GenomeInfoDbData_1.2.3
[31] XML_3.99-0.3 withr_2.2.0 crayon_1.3.4
[34] dplyr_0.8.5 bitops_1.0-6 grid_4.0.0
[37] nlme_3.1-147 xtable_1.8-4 gtable_0.3.0
[40] lifecycle_0.2.0 DBI_1.1.0 magrittr_1.5
[43] scales_1.1.0 stringi_1.4.6 farver_2.0.3
[46] XVector_0.28.0 genefilter_1.70.0 ellipsis_0.3.0
[49] vctrs_0.2.4 RColorBrewer_1.1-2 tools_4.0.0
[52] bit64_0.9-7 glue_1.4.0 DESeq2_1.28.0
[55] purrr_0.3.4 survival_3.1-12 yaml_2.2.1
[58] AnnotationDbi_1.50.0 colorspace_1.4-1 memoise_1.1.0
[61] knitr_1.28
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.