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 22 1 110 25 496 15 9 30 1
gene2 25 11 1 4 303 13 136 1 182
gene3 2 6 45 12 15 279 62 10 85
gene4 8 23 48 139 21 40 58 248 15
gene5 15 186 174 14 8 32 403 4 126
gene6 14 20 10 139 1 3 14 60 37
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 263 1 5 90 1 8 14 7
gene2 46 20 86 7 261 5 11 4
gene3 23 9 9 104 4 266 136 3
gene4 135 22 59 39 417 22 2 464
gene5 1 10 12 190 3 206 1 1
gene6 17 1 15 273 4 406 25 10
sample18 sample19 sample20
gene1 1 1 97
gene2 93 2 47
gene3 1 73 32
gene4 124 243 73
gene5 113 118 14
gene6 68 91 243
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 64.77751 -0.01786747 -0.2158260 0.8455936 1
sample2 23.13641 -0.65015821 0.5520884 1.2248022 2
sample3 35.87109 1.42192469 -1.5658659 0.3892501 0
sample4 46.13160 0.38520581 0.2284249 0.9802081 0
sample5 51.27738 -1.77963158 2.2299165 0.3287545 2
sample6 39.62400 -1.41437028 -0.8344269 0.8472873 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 46.4759 1.00035 1.693718 0.1933743 0.508880 197.565 204.536
gene2 55.1668 1.00006 0.838292 0.3599303 0.749855 210.234 217.204
gene3 61.4953 1.00005 0.023307 0.8787783 0.971141 212.998 219.968
gene4 121.1870 1.00020 0.115022 0.7347070 0.895984 244.334 251.305
gene5 71.3971 1.00020 1.584382 0.2080788 0.520197 213.216 220.186
gene6 65.7973 1.00007 6.034145 0.0140328 0.175411 208.255 215.226
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 46.4759 0.309811 0.506923 0.6111599 0.5410937 0.877446 197.565
gene2 55.1668 0.035383 0.460184 0.0768889 0.9387120 0.939397 210.234
gene3 61.4953 0.173693 0.450252 0.3857675 0.6996689 0.929572 212.998
gene4 121.1870 -0.445956 0.420115 -1.0615083 0.2884590 0.627085 244.334
gene5 71.3971 0.694289 0.435905 1.5927528 0.1112156 0.327105 213.216
gene6 65.7973 0.991281 0.404050 2.4533602 0.0141529 0.117940 208.255
BIC
<numeric>
gene1 204.536
gene2 217.204
gene3 219.968
gene4 251.305
gene5 220.186
gene6 215.226
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 46.4759 2.780283 1.33829 2.077483 0.0377570 0.1784528 197.565
gene2 55.1668 0.544549 1.21386 0.448608 0.6537142 0.7972124 210.234
gene3 61.4953 -2.975896 1.20781 -2.463880 0.0137442 0.0763567 212.998
gene4 121.1870 -1.896866 1.11144 -1.706679 0.0878818 0.2584758 244.334
gene5 71.3971 -0.304525 1.15217 -0.264305 0.7915450 0.8991422 213.216
gene6 65.7973 -0.796894 1.07516 -0.741189 0.4585787 0.6369148 208.255
BIC
<numeric>
gene1 204.536
gene2 217.204
gene3 219.968
gene4 251.305
gene5 220.186
gene6 215.226
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene24 149.5841 1.00031 20.90242 5.51951e-06 0.000275975 196.473
gene12 74.6923 1.00010 9.84994 1.69956e-03 0.042489058 216.690
gene26 111.0369 1.00036 6.54394 1.05245e-02 0.175407914 212.109
gene6 65.7973 1.00007 6.03415 1.40328e-02 0.175410613 208.255
gene46 56.8009 2.29215 8.83707 3.04569e-02 0.240854828 201.704
gene18 83.9014 1.40378 5.17996 3.08674e-02 0.240854828 184.044
BIC
<numeric>
gene24 203.444
gene12 223.660
gene26 219.080
gene6 215.226
gene46 209.961
gene18 191.417
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.1.0 RC (2021-05-16 r80304)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/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_3.3.3 BiocParallel_1.27.0
[3] NBAMSeq_1.9.0 SummarizedExperiment_1.23.0
[5] Biobase_2.53.0 GenomicRanges_1.45.0
[7] GenomeInfoDb_1.29.0 IRanges_2.27.0
[9] S4Vectors_0.31.0 BiocGenerics_0.39.0
[11] MatrixGenerics_1.5.0 matrixStats_0.58.0
loaded via a namespace (and not attached):
[1] httr_1.4.2 sass_0.4.0 bit64_4.0.5
[4] jsonlite_1.7.2 splines_4.1.0 bslib_0.2.5.1
[7] assertthat_0.2.1 highr_0.9 blob_1.2.1
[10] GenomeInfoDbData_1.2.6 yaml_2.2.1 pillar_1.6.1
[13] RSQLite_2.2.7 lattice_0.20-44 glue_1.4.2
[16] digest_0.6.27 RColorBrewer_1.1-2 XVector_0.33.0
[19] colorspace_2.0-1 htmltools_0.5.1.1 Matrix_1.3-3
[22] DESeq2_1.33.0 XML_3.99-0.6 pkgconfig_2.0.3
[25] genefilter_1.75.0 zlibbioc_1.39.0 purrr_0.3.4
[28] xtable_1.8-4 scales_1.1.1 tibble_3.1.2
[31] annotate_1.71.0 mgcv_1.8-35 KEGGREST_1.33.0
[34] farver_2.1.0 generics_0.1.0 ellipsis_0.3.2
[37] withr_2.4.2 cachem_1.0.5 survival_3.2-11
[40] magrittr_2.0.1 crayon_1.4.1 memoise_2.0.0
[43] evaluate_0.14 fansi_0.4.2 nlme_3.1-152
[46] tools_4.1.0 lifecycle_1.0.0 stringr_1.4.0
[49] locfit_1.5-9.4 munsell_0.5.0 DelayedArray_0.19.0
[52] AnnotationDbi_1.55.0 Biostrings_2.61.0 compiler_4.1.0
[55] jquerylib_0.1.4 rlang_0.4.11 grid_4.1.0
[58] RCurl_1.98-1.3 labeling_0.4.2 bitops_1.0-7
[61] rmarkdown_2.8 gtable_0.3.0 DBI_1.1.1
[64] R6_2.5.0 knitr_1.33 dplyr_1.0.6
[67] fastmap_1.1.0 bit_4.0.4 utf8_1.2.1
[70] stringi_1.6.2 Rcpp_1.0.6 vctrs_0.3.8
[73] geneplotter_1.71.0 png_0.1-7 tidyselect_1.1.1
[76] xfun_0.23
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.