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 63 1 49 182 1 119 229 3 1
gene2 165 79 457 1 372 11 82 72 43
gene3 72 238 81 149 78 2 62 17 350
gene4 124 4 45 4 1 25 211 372 126
gene5 179 69 17 9 107 224 1 6 6
gene6 8 24 7 515 62 17 2 397 87
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 81 25 6 38 2 80 1 457
gene2 383 485 7 65 3 14 660 8
gene3 34 141 15 36 5 210 20 4
gene4 3 76 2 85 12 35 164 10
gene5 8 27 1 23 167 1 426 20
gene6 18 413 51 102 24 12 1 115
sample18 sample19 sample20
gene1 49 66 1
gene2 4 253 5
gene3 145 382 18
gene4 7 1 49
gene5 28 1 116
gene6 3 155 529
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 79.08041 -0.3993478 0.9172095 0.1333777 1
sample2 40.53707 1.3645392 -0.2970013 0.4767594 0
sample3 57.76781 0.1044263 0.8023012 0.2832003 0
sample4 33.82920 0.8441772 0.6410707 -1.2560859 0
sample5 66.67510 -0.1217728 -0.7880622 0.2466329 1
sample6 54.30309 -0.7365714 -1.3511212 0.2584657 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 78.2540 1.00003 0.355782 0.5508994 0.810146 212.260 219.231
gene2 182.2583 1.00033 2.739709 0.0979277 0.305704 250.547 257.518
gene3 92.6688 1.00007 0.486304 0.4856130 0.758770 235.198 242.168
gene4 64.5192 1.00003 1.722143 0.1894382 0.430541 212.931 219.901
gene5 91.6361 1.00003 3.145441 0.0761400 0.253800 217.751 224.721
gene6 102.3758 1.00007 3.791063 0.0515417 0.219680 227.028 233.999
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 78.2540 0.9017412 0.629035 1.433530 0.1517065 0.541809 212.260
gene2 182.2583 -0.6071377 0.638470 -0.950926 0.3416418 0.617891 250.547
gene3 92.6688 -0.2177677 0.501251 -0.434448 0.6639628 0.851234 235.198
gene4 64.5192 -1.2291159 0.587317 -2.092763 0.0363703 0.454629 212.931
gene5 91.6361 -0.0814978 0.639349 -0.127470 0.8985685 0.990552 217.751
gene6 102.3758 0.8610738 0.512917 1.678779 0.0931951 0.489732 227.028
BIC
<numeric>
gene1 219.231
gene2 257.518
gene3 242.168
gene4 219.901
gene5 224.721
gene6 233.999
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 78.2540 1.557712 1.246583 1.249585 0.2114511 0.459676 212.260
gene2 182.2583 -1.269328 1.263953 -1.004253 0.3152566 0.569163 250.547
gene3 92.6688 0.178472 0.994575 0.179446 0.8575876 0.912327 235.198
gene4 64.5192 -1.619720 1.165476 -1.389750 0.1646047 0.457235 212.931
gene5 91.6361 -1.225424 1.266665 -0.967441 0.3333236 0.569163 217.751
gene6 102.3758 1.846233 1.017609 1.814286 0.0696337 0.290140 227.028
BIC
<numeric>
gene1 219.231
gene2 257.518
gene3 242.168
gene4 219.901
gene5 224.721
gene6 233.999
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene46 121.9149 1.00008 15.75573 7.18751e-05 0.00359375 208.512 215.483
gene16 139.2076 1.00028 9.93699 1.62335e-03 0.04058372 209.654 216.624
gene10 93.1198 1.00008 8.07722 4.48576e-03 0.06930084 194.311 201.281
gene44 103.1979 1.00008 7.69303 5.54407e-03 0.06930084 213.820 220.791
gene40 118.5934 1.00006 6.40424 1.13888e-02 0.11388815 229.466 236.437
gene17 113.7494 1.00012 5.57733 1.81987e-02 0.15165601 202.401 209.371
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.1.1 Patched (2021-08-22 r80813)
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.0.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] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.3.5 BiocParallel_1.28.0
[3] NBAMSeq_1.10.0 SummarizedExperiment_1.24.0
[5] Biobase_2.54.0 GenomicRanges_1.46.0
[7] GenomeInfoDb_1.30.0 IRanges_2.28.0
[9] S4Vectors_0.32.0 BiocGenerics_0.40.0
[11] MatrixGenerics_1.6.0 matrixStats_0.61.0
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_4.1.1 bslib_0.3.1
[7] assertthat_0.2.1 highr_0.9 blob_1.2.2
[10] GenomeInfoDbData_1.2.7 yaml_2.2.1 pillar_1.6.4
[13] RSQLite_2.2.8 lattice_0.20-45 glue_1.4.2
[16] digest_0.6.28 RColorBrewer_1.1-2 XVector_0.34.0
[19] colorspace_2.0-2 htmltools_0.5.2 Matrix_1.3-4
[22] DESeq2_1.34.0 XML_3.99-0.8 pkgconfig_2.0.3
[25] genefilter_1.76.0 zlibbioc_1.40.0 purrr_0.3.4
[28] xtable_1.8-4 scales_1.1.1 tibble_3.1.5
[31] annotate_1.72.0 mgcv_1.8-38 KEGGREST_1.34.0
[34] farver_2.1.0 generics_0.1.1 ellipsis_0.3.2
[37] withr_2.4.2 cachem_1.0.6 survival_3.2-13
[40] magrittr_2.0.1 crayon_1.4.1 memoise_2.0.0
[43] evaluate_0.14 fansi_0.5.0 nlme_3.1-153
[46] tools_4.1.1 lifecycle_1.0.1 stringr_1.4.0
[49] locfit_1.5-9.4 munsell_0.5.0 DelayedArray_0.20.0
[52] AnnotationDbi_1.56.0 Biostrings_2.62.0 compiler_4.1.1
[55] jquerylib_0.1.4 rlang_0.4.12 grid_4.1.1
[58] RCurl_1.98-1.5 labeling_0.4.2 bitops_1.0-7
[61] rmarkdown_2.11 gtable_0.3.0 DBI_1.1.1
[64] R6_2.5.1 knitr_1.36 dplyr_1.0.7
[67] fastmap_1.1.0 bit_4.0.4 utf8_1.2.2
[70] stringi_1.7.5 parallel_4.1.1 Rcpp_1.0.7
[73] vctrs_0.3.8 geneplotter_1.72.0 png_0.1-7
[76] tidyselect_1.1.1 xfun_0.27
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.