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 25 40 213 60 1 530 66 143 622
gene2 98 65 29 1 3 159 23 67 294
gene3 61 38 420 81 200 7 129 7 1
gene4 15 2 38 1 14 2 9 193 235
gene5 789 283 1 19 1 127 39 22 78
gene6 12 156 17 84 345 323 116 131 2
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1365 5 1 101 43 1 186 342
gene2 52 1 78 10 212 2 71 14
gene3 204 1 399 16 7 7 71 146
gene4 419 38 103 6 6 332 11 5
gene5 1 4 235 61 8 6 23 8
gene6 326 126 29 15 93 1 6 1
sample18 sample19 sample20
gene1 1 14 457
gene2 393 580 2
gene3 18 7 113
gene4 4 1 1
gene5 183 6 1
gene6 443 154 1
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 62.38993 -0.179919647 -0.104971878 0.7457638 2
sample2 61.96337 -0.011706548 0.834748344 -0.3253055 0
sample3 70.70229 0.004914265 0.002343635 0.7985984 0
sample4 20.77724 2.849819120 -0.208892124 1.1063661 2
sample5 50.67062 -1.927186730 -0.761985950 -2.0688726 1
sample6 43.92942 -0.839516704 0.859811817 -1.5360931 2
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 167.4766 1.00008 0.107563 0.7430686 0.906181 245.212 252.182
gene2 89.8683 1.00009 0.120741 0.7283758 0.906181 225.393 232.364
gene3 88.6469 1.00026 3.295547 0.0694973 0.231658 230.835 237.805
gene4 83.0558 1.00015 5.726640 0.0167304 0.104565 200.221 207.191
gene5 93.0420 1.55155 4.786661 0.0612337 0.231658 217.571 225.091
gene6 95.4173 1.00009 1.689893 0.1936469 0.420972 235.515 242.486
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 167.4766 -0.565053 0.331008 -1.707067 0.087809555 0.3652928 245.212
gene2 89.8683 -0.771655 0.313546 -2.461061 0.013852695 0.1439071 225.393
gene3 88.6469 -0.103488 0.323809 -0.319597 0.749274195 0.8325269 230.835
gene4 83.0558 -1.168333 0.343233 -3.403910 0.000664287 0.0332143 200.221
gene5 93.0420 -0.204255 0.366687 -0.557028 0.577508601 0.7804170 217.571
gene6 95.4173 -0.270921 0.326555 -0.829634 0.406745957 0.7229885 235.515
BIC
<numeric>
gene1 252.182
gene2 232.364
gene3 237.805
gene4 207.191
gene5 225.091
gene6 242.486
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 167.4766 1.0817632 0.879979 1.22930637 0.218957 0.633456 245.212
gene2 89.8683 -0.6840846 0.824085 -0.83011467 0.406474 0.787283 225.393
gene3 88.6469 0.9382077 0.862726 1.08749253 0.276819 0.725849 230.835
gene4 83.0558 -0.3755241 0.891596 -0.42118212 0.673622 0.872964 200.221
gene5 93.0420 -0.3995598 0.962022 -0.41533348 0.677898 0.872964 217.571
gene6 95.4173 0.0075898 0.868061 0.00874339 0.993024 0.993024 235.515
BIC
<numeric>
gene1 252.182
gene2 232.364
gene3 237.805
gene4 207.191
gene5 225.091
gene6 242.486
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene19 76.4506 1.00007 11.21780 0.000810901 0.0234330 213.709 220.679
gene18 35.5800 1.00014 10.95019 0.000937322 0.0234330 170.105 177.075
gene26 85.4089 1.00006 7.67440 0.005604715 0.0827091 218.953 225.924
gene24 98.9852 1.00013 7.26666 0.007030268 0.0827091 206.003 212.973
gene49 56.0795 1.00004 6.85068 0.008862841 0.0827091 199.813 206.783
gene43 78.7780 1.00011 6.64949 0.009925093 0.0827091 219.029 225.999
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.2.0 RC (2022-04-19 r82224)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/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] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.3.5 BiocParallel_1.30.0
[3] NBAMSeq_1.12.0 SummarizedExperiment_1.26.0
[5] Biobase_2.56.0 GenomicRanges_1.48.0
[7] GenomeInfoDb_1.32.0 IRanges_2.30.0
[9] S4Vectors_0.34.0 BiocGenerics_0.42.0
[11] MatrixGenerics_1.8.0 matrixStats_0.62.0
loaded via a namespace (and not attached):
[1] httr_1.4.2 sass_0.4.1 bit64_4.0.5
[4] jsonlite_1.8.0 splines_4.2.0 bslib_0.3.1
[7] assertthat_0.2.1 highr_0.9 blob_1.2.3
[10] GenomeInfoDbData_1.2.8 yaml_2.3.5 pillar_1.7.0
[13] RSQLite_2.2.12 lattice_0.20-45 glue_1.6.2
[16] digest_0.6.29 RColorBrewer_1.1-3 XVector_0.36.0
[19] colorspace_2.0-3 htmltools_0.5.2 Matrix_1.4-1
[22] DESeq2_1.36.0 XML_3.99-0.9 pkgconfig_2.0.3
[25] genefilter_1.78.0 zlibbioc_1.42.0 purrr_0.3.4
[28] xtable_1.8-4 scales_1.2.0 tibble_3.1.6
[31] annotate_1.74.0 mgcv_1.8-40 KEGGREST_1.36.0
[34] farver_2.1.0 generics_0.1.2 ellipsis_0.3.2
[37] withr_2.5.0 cachem_1.0.6 cli_3.3.0
[40] survival_3.3-1 magrittr_2.0.3 crayon_1.5.1
[43] memoise_2.0.1 evaluate_0.15 fansi_1.0.3
[46] nlme_3.1-157 tools_4.2.0 lifecycle_1.0.1
[49] stringr_1.4.0 locfit_1.5-9.5 munsell_0.5.0
[52] DelayedArray_0.22.0 AnnotationDbi_1.58.0 Biostrings_2.64.0
[55] compiler_4.2.0 jquerylib_0.1.4 rlang_1.0.2
[58] grid_4.2.0 RCurl_1.98-1.6 labeling_0.4.2
[61] bitops_1.0-7 rmarkdown_2.14 gtable_0.3.0
[64] DBI_1.1.2 R6_2.5.1 knitr_1.38
[67] dplyr_1.0.8 fastmap_1.1.0 bit_4.0.4
[70] utf8_1.2.2 stringi_1.7.6 parallel_4.2.0
[73] Rcpp_1.0.8.3 vctrs_0.4.1 geneplotter_1.74.0
[76] png_0.1-7 tidyselect_1.1.2 xfun_0.30
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.