To install and load NBAMSeq
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
::install("NBAMSeq") BiocManager
library(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
= 50 ## n stands for number of genes
n = 20 ## m stands for sample size
m = matrix(rnbinom(n*m, mu=100, size=1/3), ncol = m) + 1
countData 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 150 4 9 219 180 2 14 13 118
gene2 1091 486 1008 35 97 27 246 1 1
gene3 219 62 11 5 1 1 424 245 73
gene4 7 3 1 1 189 2 23 9 66
gene5 6 73 2 468 275 60 74 491 123
gene6 7 1084 97 4 35 39 8 282 5
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 6 5 219 33 21 135 19 2
gene2 44 28 1 244 47 1 52 278
gene3 275 3 650 13 1 2 188 7
gene4 1 6 8 25 5 121 55 13
gene5 75 1 130 4 204 2 24 127
gene6 1 398 2 107 1 1 70 22
sample18 sample19 sample20
gene1 3 3 5
gene2 37 78 348
gene3 17 1 22
gene4 3 68 64
gene5 21 666 17
gene6 106 238 70
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
= runif(m, 20, 80)
pheno = rnorm(m)
var1 = rnorm(m)
var2 = rnorm(m)
var3 = as.factor(sample(c(0,1,2), m, replace = TRUE))
var4 = data.frame(pheno = pheno, var1 = var1, var2 = var2,
colData var3 = var3, var4 = var4)
rownames(colData) = paste0("sample", 1:m)
head(colData)
pheno var1 var2 var3 var4
sample1 26.31145 0.5619716 0.7018006 -1.0332727 0
sample2 32.65385 -1.5831876 -1.3020107 -0.4120632 0
sample3 36.35482 0.3354885 1.5923540 0.7890664 0
sample4 63.09763 1.8712693 -0.4193318 0.1665577 0
sample5 52.04506 0.4440052 0.4032179 -2.5101022 0
sample6 79.47380 -0.6617745 -0.7963773 -0.1440922 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:
= ~ s(pheno) + var1 + var2 + var3 + var4 design
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
:
= NBAMSeqDataSet(countData = countData, colData = colData, design = design)
gsd gsd
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:
= NBAMSeq(gsd) gsd
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
:
library(BiocParallel)
= NBAMSeq(gsd, parallel = TRUE) gsd
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.
= results(gsd, name = "pheno")
res1 head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 42.1177 1.00007 0.704822 0.4011572 0.866849 204.918 211.888
gene2 190.3664 1.00006 0.167499 0.6824645 0.866849 250.985 257.955
gene3 86.3021 1.00003 5.736975 0.0166168 0.166168 213.627 220.597
gene4 24.9000 1.00006 0.577917 0.4471980 0.866849 173.331 180.301
gene5 116.8376 1.00007 0.223324 0.6365618 0.866849 244.170 251.140
gene6 101.9065 1.00022 0.296017 0.5864264 0.866849 227.354 234.325
For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.
= results(gsd, name = "var1")
res2 head(res2)
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 42.1177 0.682894 0.347605 1.964571 0.04946395 0.2248361 204.918
gene2 190.3664 0.186876 0.387345 0.482454 0.62948331 0.7726939 250.985
gene3 86.3021 -0.541995 0.378282 -1.432782 0.15192026 0.3798006 213.627
gene4 24.9000 0.405423 0.280748 1.444085 0.14871508 0.3798006 173.331
gene5 116.8376 0.176978 0.371293 0.476653 0.63360896 0.7726939 244.170
gene6 101.9065 -1.198137 0.390713 -3.066541 0.00216551 0.0360919 227.354
BIC
<numeric>
gene1 211.888
gene2 257.955
gene3 220.597
gene4 180.301
gene5 251.140
gene6 234.325
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
.
= results(gsd, contrast = c("var4", "2", "0"))
res3 head(res3)
DataFrame with 6 rows and 8 columns
baseMean coef SE stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1 42.1177 2.472889 1.063383 2.325493 0.02004561 0.1670467 204.918
gene2 190.3664 -2.333386 1.184841 -1.969367 0.04891100 0.2717278 250.985
gene3 86.3021 0.928979 1.156933 0.802967 0.42199406 0.7903945 213.627
gene4 24.9000 2.603689 0.865194 3.009369 0.00261791 0.0357933 173.331
gene5 116.8376 -0.334079 1.134194 -0.294552 0.76833633 0.9870746 244.170
gene6 101.9065 0.952467 1.190479 0.800071 0.42366991 0.7903945 227.354
BIC
<numeric>
gene1 211.888
gene2 257.955
gene3 220.597
gene4 180.301
gene5 251.140
gene6 234.325
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[order(res1$pvalue),]
res1 = rownames(res1)[1]
topgene = getsf(gsd) ## get the estimated size factors
sf ## divide raw count by size factors to obtain normalized counts
= t(t(countData)/sf)
countnorm head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene47 151.7339 1.00009 21.13499 4.69291e-06 0.000234645 225.501
gene24 64.1522 1.00005 7.34558 6.72497e-03 0.142823093 211.686
gene28 76.2668 1.00004 6.74958 9.37973e-03 0.142823093 209.340
gene21 68.8090 1.00007 6.39823 1.14258e-02 0.142823093 217.279
gene3 86.3021 1.00003 5.73698 1.66168e-02 0.166168096 213.627
gene26 41.6453 1.00011 4.70073 3.01494e-02 0.232673590 186.669
BIC
<numeric>
gene47 232.471
gene24 218.656
gene28 216.310
gene21 224.249
gene3 220.597
gene26 193.639
library(ggplot2)
= topgene
setTitle = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
df ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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))
sessionInfo()
R version 4.2.1 Patched (2022-07-09 r82577)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur ... 10.16
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_GB/en_US.UTF-8
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.3.6 BiocParallel_1.32.0
[3] NBAMSeq_1.14.0 SummarizedExperiment_1.28.0
[5] Biobase_2.58.0 GenomicRanges_1.50.0
[7] GenomeInfoDb_1.34.0 IRanges_2.32.0
[9] S4Vectors_0.36.0 BiocGenerics_0.44.0
[11] MatrixGenerics_1.10.0 matrixStats_0.62.0
loaded via a namespace (and not attached):
[1] httr_1.4.4 sass_0.4.2 bit64_4.0.5
[4] jsonlite_1.8.3 splines_4.2.1 bslib_0.4.0
[7] assertthat_0.2.1 highr_0.9 blob_1.2.3
[10] GenomeInfoDbData_1.2.9 yaml_2.3.6 pillar_1.8.1
[13] RSQLite_2.2.18 lattice_0.20-45 glue_1.6.2
[16] digest_0.6.30 RColorBrewer_1.1-3 XVector_0.38.0
[19] colorspace_2.0-3 htmltools_0.5.3 Matrix_1.5-1
[22] DESeq2_1.38.0 XML_3.99-0.12 pkgconfig_2.0.3
[25] genefilter_1.80.0 zlibbioc_1.44.0 xtable_1.8-4
[28] scales_1.2.1 tibble_3.1.8 annotate_1.76.0
[31] mgcv_1.8-41 KEGGREST_1.38.0 farver_2.1.1
[34] generics_0.1.3 withr_2.5.0 cachem_1.0.6
[37] cli_3.4.1 survival_3.4-0 magrittr_2.0.3
[40] crayon_1.5.2 memoise_2.0.1 evaluate_0.17
[43] fansi_1.0.3 nlme_3.1-160 tools_4.2.1
[46] lifecycle_1.0.3 stringr_1.4.1 locfit_1.5-9.6
[49] munsell_0.5.0 DelayedArray_0.24.0 AnnotationDbi_1.60.0
[52] Biostrings_2.66.0 compiler_4.2.1 jquerylib_0.1.4
[55] rlang_1.0.6 grid_4.2.1 RCurl_1.98-1.9
[58] labeling_0.4.2 bitops_1.0-7 rmarkdown_2.17
[61] gtable_0.3.1 codetools_0.2-18 DBI_1.1.3
[64] R6_2.5.1 knitr_1.40 dplyr_1.0.10
[67] fastmap_1.1.0 bit_4.0.4 utf8_1.2.2
[70] stringi_1.7.8 parallel_4.2.1 Rcpp_1.0.9
[73] vctrs_0.5.0 geneplotter_1.76.0 png_0.1-7
[76] tidyselect_1.2.0 xfun_0.34