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 165 158 3 1 47 5 47 43 11
gene2 50 15 168 42 28 2 1 1 27
gene3 38 485 945 130 128 471 46 160 3
gene4 85 152 41 152 136 295 2 209 4
gene5 107 32 1 3 320 1 508 325 1
gene6 2 738 37 3 1 434 1 18 518
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 235 107 336 2 146 6 2 7
gene2 27 83 182 22 89 4 1067 10
gene3 277 14 10 63 1 312 118 1
gene4 180 1 5 103 1 17 93 39
gene5 1 19 5 24 264 51 15 2
gene6 3 40 36 67 30 5 21 1
sample18 sample19 sample20
gene1 31 4 163
gene2 38 1 140
gene3 413 3 134
gene4 41 17 1
gene5 1 101 1
gene6 6 8 2
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 33.60814 -0.1611642 -0.80979948 -2.0400091 0
sample2 25.90787 0.2359096 0.23376247 -0.5595276 1
sample3 21.03667 -0.1910845 -0.45812649 -0.6949608 1
sample4 26.26290 0.3897112 -1.03781937 -0.4809042 2
sample5 63.07196 0.2442023 0.91481319 0.3887636 0
sample6 30.85611 0.4390571 0.05824031 0.1351116 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 63.3195 1.00008 1.0092614 0.315121873 0.53568148 213.047 220.017
gene2 73.4118 1.00003 0.0636229 0.800923392 0.91014022 214.527 221.497
gene3 150.6450 1.00006 14.4048867 0.000147803 0.00739015 236.446 243.416
gene4 62.5279 1.00012 1.4009098 0.236629326 0.50060858 222.969 229.939
gene5 78.0680 1.00024 1.2599253 0.261704291 0.50060858 203.980 210.951
gene6 88.8574 1.00013 10.0229349 0.001547982 0.02779178 194.182 201.153
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 63.3195 0.687066 0.518838 1.324239 0.1854238 0.461410 213.047
gene2 73.4118 0.332254 0.527712 0.629613 0.5289478 0.678138 214.527
gene3 150.6450 1.121019 0.478497 2.342793 0.0191400 0.206668 236.446
gene4 62.5279 0.267556 0.550919 0.485653 0.6272132 0.729585 222.969
gene5 78.0680 -1.142323 0.622864 -1.833984 0.0666564 0.333282 203.980
gene6 88.8574 -0.539335 0.539076 -1.000481 0.3170780 0.609765 194.182
BIC
<numeric>
gene1 220.017
gene2 221.497
gene3 243.416
gene4 229.939
gene5 210.951
gene6 201.153
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 63.3195 -1.074082 0.839010 -1.280179 0.20048233 0.5941217 213.047
gene2 73.4118 0.927933 0.857791 1.081771 0.27935419 0.6124693 214.527
gene3 150.6450 -1.579379 0.758888 -2.081175 0.03741790 0.2672707 236.446
gene4 62.5279 -0.480400 0.890642 -0.539386 0.58962045 0.7967844 222.969
gene5 78.0680 -2.839493 0.975634 -2.910407 0.00360958 0.0451198 203.980
gene6 88.8574 2.911130 0.886285 3.284642 0.00102112 0.0203060 194.182
BIC
<numeric>
gene1 220.017
gene2 221.497
gene3 243.416
gene4 229.939
gene5 210.951
gene6 201.153
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene3 150.6450 1.00006 14.40489 0.000147803 0.00739015 236.446 243.416
gene6 88.8574 1.00013 10.02293 0.001547982 0.02779178 194.182 201.153
gene16 59.6816 1.00003 9.88442 0.001667507 0.02779178 204.873 211.843
gene13 86.9408 1.00008 7.44741 0.006355485 0.06755652 227.454 234.424
gene35 45.3740 1.00005 7.33760 0.006755652 0.06755652 199.444 206.414
gene48 76.6157 1.00007 6.72508 0.009511253 0.06931729 224.710 231.680
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.3.0 RC (2023-04-13 r84257)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.6.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/New_York
tzcode source: internal
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggplot2_3.4.2 BiocParallel_1.34.1
[3] NBAMSeq_1.16.0 SummarizedExperiment_1.30.1
[5] Biobase_2.60.0 GenomicRanges_1.52.0
[7] GenomeInfoDb_1.36.0 IRanges_2.34.0
[9] S4Vectors_0.38.1 BiocGenerics_0.46.0
[11] MatrixGenerics_1.12.0 matrixStats_0.63.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.40.0 gtable_0.3.3 xfun_0.39
[4] bslib_0.4.2 lattice_0.21-8 vctrs_0.6.2
[7] tools_4.3.0 bitops_1.0-7 generics_0.1.3
[10] parallel_4.3.0 RSQLite_2.3.1 AnnotationDbi_1.62.1
[13] tibble_3.2.1 fansi_1.0.4 highr_0.10
[16] blob_1.2.4 pkgconfig_2.0.3 Matrix_1.5-4
[19] lifecycle_1.0.3 GenomeInfoDbData_1.2.10 farver_2.1.1
[22] compiler_4.3.0 Biostrings_2.68.0 munsell_0.5.0
[25] DESeq2_1.40.1 codetools_0.2-19 htmltools_0.5.5
[28] sass_0.4.6 RCurl_1.98-1.12 yaml_2.3.7
[31] pillar_1.9.0 crayon_1.5.2 jquerylib_0.1.4
[34] DelayedArray_0.26.2 cachem_1.0.8 nlme_3.1-162
[37] genefilter_1.82.1 tidyselect_1.2.0 locfit_1.5-9.7
[40] digest_0.6.31 dplyr_1.1.2 labeling_0.4.2
[43] splines_4.3.0 fastmap_1.1.1 grid_4.3.0
[46] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3
[49] S4Arrays_1.0.1 survival_3.5-5 XML_3.99-0.14
[52] utf8_1.2.3 withr_2.5.0 scales_1.2.1
[55] bit64_4.0.5 rmarkdown_2.21 XVector_0.40.0
[58] httr_1.4.6 bit_4.0.5 png_0.1-8
[61] memoise_2.0.1 evaluate_0.21 knitr_1.42
[64] mgcv_1.8-42 rlang_1.1.1 Rcpp_1.0.10
[67] DBI_1.1.3 xtable_1.8-4 glue_1.6.2
[70] annotate_1.78.0 jsonlite_1.8.4 R6_2.5.1
[73] zlibbioc_1.46.0
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.