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 164 78 104 5 1 1 6 1 8
gene2 22 1 28 3 7 55 403 46 179
gene3 19 1 3 7 235 202 466 186 1
gene4 15 9 251 159 300 9 3 122 1
gene5 1 131 149 125 55 380 186 4 1
gene6 14 27 128 14 3 382 413 4 162
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 1 60 44 89 8 57 70 1
gene2 24 486 66 492 7 6 369 1
gene3 301 2 121 472 98 59 360 1
gene4 147 263 266 70 2 237 60 9
gene5 63 51 11 18 195 39 25 1
gene6 16 751 34 2 25 83 184 5
sample18 sample19 sample20
gene1 28 84 30
gene2 1 159 141
gene3 303 69 2
gene4 42 1 281
gene5 7 102 154
gene6 12 3 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 31.65458 -0.1699300 -0.2868070 -1.1233824 1
sample2 40.85614 0.9186161 1.4822072 -0.4300385 0
sample3 55.20760 0.2069261 -1.1843105 -0.6091992 1
sample4 65.15571 -1.0138770 -0.6949176 0.8366814 2
sample5 61.31593 0.6011855 -0.9866629 0.4540759 1
sample6 26.88190 1.5008849 0.1690043 -0.1783239 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 30.7518 1.00005 0.0482581 0.8262010 0.918001 193.457 200.427
gene2 105.9935 1.00009 5.8326377 0.0157387 0.157387 227.127 234.097
gene3 125.3798 1.00006 0.8592767 0.3539785 0.573654 237.859 244.829
gene4 91.3419 1.00013 5.9158227 0.0150067 0.157387 227.586 234.556
gene5 82.3314 1.00018 1.7341189 0.1879657 0.469914 230.672 237.643
gene6 105.8434 1.00011 0.1156068 0.7339973 0.853485 228.587 235.557
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 30.7518 0.0825266 0.394580 0.209151 0.834331 0.834331 193.457
gene2 105.9935 0.3476968 0.439385 0.791327 0.428753 0.612505 227.127
gene3 125.3798 0.6716173 0.466004 1.441228 0.149520 0.442273 237.859
gene4 91.3419 -0.2638111 0.397832 -0.663122 0.507252 0.679190 227.586
gene5 82.3314 0.3891930 0.445956 0.872716 0.382818 0.589418 230.672
gene6 105.8434 0.1652133 0.486316 0.339724 0.734064 0.815627 228.587
BIC
<numeric>
gene1 200.427
gene2 234.097
gene3 244.829
gene4 234.556
gene5 237.643
gene6 235.557
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 30.7518 1.284028 1.14855 1.117958 0.263585 0.536587 193.457
gene2 105.9935 -0.476629 1.25355 -0.380225 0.703778 0.818347 227.127
gene3 125.3798 -1.747926 1.33165 -1.312606 0.189316 0.526634 237.859
gene4 91.3419 -0.467842 1.14068 -0.410142 0.681702 0.811550 227.586
gene5 82.3314 -0.347003 1.27611 -0.271923 0.785681 0.868714 230.672
gene6 105.8434 0.324240 1.39511 0.232412 0.816218 0.868714 228.587
BIC
<numeric>
gene1 200.427
gene2 234.097
gene3 244.829
gene4 234.556
gene5 237.643
gene6 235.557
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene22 54.6599 1.00004 22.67270 1.59771e-06 7.98857e-05 185.963
gene20 37.7694 1.00009 8.12414 4.37213e-03 1.09303e-01 188.420
gene23 86.4547 1.00007 7.19452 7.31643e-03 1.21941e-01 214.975
gene4 91.3419 1.00013 5.91582 1.50067e-02 1.57387e-01 227.586
gene2 105.9935 1.00009 5.83264 1.57387e-02 1.57387e-01 227.127
gene41 145.2649 1.00007 5.17348 2.29415e-02 1.71771e-01 231.465
BIC
<numeric>
gene22 192.933
gene20 195.390
gene23 221.945
gene4 234.556
gene2 234.097
gene41 238.435
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 (2021-05-10 r80283)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows Server x64 (build 17763)
Matrix products: default
locale:
[1] LC_COLLATE=C
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] parallel stats4 stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] ggplot2_3.3.3 BiocParallel_1.26.0
[3] NBAMSeq_1.8.0 SummarizedExperiment_1.22.0
[5] Biobase_2.52.0 GenomicRanges_1.44.0
[7] GenomeInfoDb_1.28.0 IRanges_2.26.0
[9] S4Vectors_0.30.0 BiocGenerics_0.38.0
[11] MatrixGenerics_1.4.0 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_0.32.0
[19] colorspace_2.0-1 htmltools_0.5.1.1 Matrix_1.3-3
[22] DESeq2_1.32.0 XML_3.99-0.6 pkgconfig_2.0.3
[25] genefilter_1.74.0 zlibbioc_1.38.0 purrr_0.3.4
[28] xtable_1.8-4 snow_0.4-3 scales_1.1.1
[31] tibble_3.1.2 annotate_1.70.0 mgcv_1.8-35
[34] KEGGREST_1.32.0 farver_2.1.0 generics_0.1.0
[37] ellipsis_0.3.2 withr_2.4.2 cachem_1.0.5
[40] survival_3.2-11 magrittr_2.0.1 crayon_1.4.1
[43] memoise_2.0.0 evaluate_0.14 fansi_0.4.2
[46] nlme_3.1-152 tools_4.1.0 lifecycle_1.0.0
[49] stringr_1.4.0 locfit_1.5-9.4 munsell_0.5.0
[52] DelayedArray_0.18.0 AnnotationDbi_1.54.0 Biostrings_2.60.0
[55] compiler_4.1.0 jquerylib_0.1.4 rlang_0.4.11
[58] grid_4.1.0 RCurl_1.98-1.3 labeling_0.4.2
[61] bitops_1.0-7 rmarkdown_2.8 gtable_0.3.0
[64] DBI_1.1.1 R6_2.5.0 knitr_1.33
[67] dplyr_1.0.6 fastmap_1.1.0 bit_4.0.4
[70] utf8_1.2.1 stringi_1.6.2 Rcpp_1.0.6
[73] vctrs_0.3.8 geneplotter_1.70.0 png_0.1-7
[76] tidyselect_1.1.1 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.