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 356 1 352 1 3 14 78 83 53
gene2 2 88 13 2 3 23 14 190 54
gene3 28 1 115 57 5 22 96 149 41
gene4 18 1 172 108 1 784 223 3 201
gene5 168 3 144 746 81 12 1 52 245
gene6 1 218 6 47 179 33 78 1 204
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 6 233 405 87 1 1 1 103
gene2 2 2 4 3 214 495 123 4
gene3 21 21 53 62 31 127 62 22
gene4 26 7 12 41 712 723 1 2
gene5 406 9 80 1 129 154 166 14
gene6 7 1 3 48 85 55 85 1
sample18 sample19 sample20
gene1 46 180 50
gene2 1 71 4
gene3 83 25 11
gene4 32 1 52
gene5 200 171 1
gene6 1 19 274
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 25.61004 -1.2327874 -1.1179287 -1.1580542 1
sample2 35.30209 -0.6711554 -0.1106435 -0.2417916 0
sample3 42.30052 1.2168777 1.5992099 -0.4410217 1
sample4 51.85550 -1.2359325 -0.6960942 -0.7816302 0
sample5 59.57958 -1.8242780 -1.4091554 -0.2033634 2
sample6 56.38511 -1.3036284 1.0710648 -0.5117473 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 75.2480 1.00007 0.432404 0.5108561 0.715722 218.960 225.930
gene2 45.6657 1.00005 3.273728 0.0704154 0.352077 191.696 198.666
gene3 38.3879 1.00006 0.019897 0.8879465 0.935294 210.955 217.925
gene4 135.3228 1.00003 0.674892 0.4113666 0.706940 227.510 234.480
gene5 139.8446 1.00004 0.661426 0.4160780 0.706940 247.846 254.816
gene6 55.0088 1.00003 0.286720 0.5923781 0.800511 202.111 209.081
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 75.2480 0.01298663 0.606487 0.0214129 0.982916 0.992163 218.960
gene2 45.6657 0.64361879 0.571305 1.1265763 0.259922 0.618861 191.696
gene3 38.3879 0.00502848 0.448278 0.0112173 0.991050 0.992163 210.955
gene4 135.3228 0.22464124 0.678014 0.3313223 0.740401 0.974212 227.510
gene5 139.8446 0.47037886 0.665285 0.7070335 0.479546 0.773461 247.846
gene6 55.0088 0.12476811 0.561725 0.2221162 0.824223 0.981218 202.111
BIC
<numeric>
gene1 225.930
gene2 198.666
gene3 217.925
gene4 234.480
gene5 254.816
gene6 209.081
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 75.2480 -0.920109 0.966590 -0.951913 0.3411413 0.715663 218.960
gene2 45.6657 1.114578 0.915378 1.217615 0.2233705 0.601426 191.696
gene3 38.3879 -0.323839 0.714045 -0.453527 0.6501693 0.810101 210.955
gene4 135.3228 1.883769 1.079273 1.745406 0.0809142 0.367792 227.510
gene5 139.8446 -0.874070 1.059950 -0.824633 0.4095799 0.729042 247.846
gene6 55.0088 1.573402 0.893412 1.761116 0.0782188 0.367792 202.111
BIC
<numeric>
gene1 225.930
gene2 198.666
gene3 217.925
gene4 234.480
gene5 254.816
gene6 209.081
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene8 107.4649 1.00004 8.11541 0.00439033 0.126907 220.794 227.764
gene10 91.0299 1.00010 7.61008 0.00580716 0.126907 218.334 225.304
gene23 30.7800 1.00005 7.01897 0.00806670 0.126907 189.221 196.191
gene34 68.2838 1.00008 6.51989 0.01066951 0.126907 217.614 224.584
gene45 25.1818 1.00003 5.99319 0.01436468 0.126907 167.253 174.223
gene32 79.2640 1.00011 5.89123 0.01522880 0.126907 213.481 220.451
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.4.1 (2024-06-14 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows Server 2022 x64 (build 20348)
Matrix products: default
locale:
[1] LC_COLLATE=C
[2] LC_CTYPE=English_United States.utf8
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.utf8
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_3.5.1 BiocParallel_1.40.0
[3] NBAMSeq_1.22.0 SummarizedExperiment_1.36.0
[5] Biobase_2.66.0 GenomicRanges_1.58.0
[7] GenomeInfoDb_1.42.0 IRanges_2.40.0
[9] S4Vectors_0.44.0 BiocGenerics_0.52.0
[11] MatrixGenerics_1.18.0 matrixStats_1.4.1
loaded via a namespace (and not attached):
[1] KEGGREST_1.46.0 gtable_0.3.6 xfun_0.48
[4] bslib_0.8.0 lattice_0.22-6 vctrs_0.6.5
[7] tools_4.4.1 generics_0.1.3 parallel_4.4.1
[10] RSQLite_2.3.7 tibble_3.2.1 fansi_1.0.6
[13] AnnotationDbi_1.68.0 highr_0.11 blob_1.2.4
[16] pkgconfig_2.0.3 Matrix_1.7-1 lifecycle_1.0.4
[19] GenomeInfoDbData_1.2.13 farver_2.1.2 compiler_4.4.1
[22] Biostrings_2.74.0 munsell_0.5.1 DESeq2_1.46.0
[25] codetools_0.2-20 snow_0.4-4 htmltools_0.5.8.1
[28] sass_0.4.9 yaml_2.3.10 pillar_1.9.0
[31] crayon_1.5.3 jquerylib_0.1.4 DelayedArray_0.32.0
[34] cachem_1.1.0 abind_1.4-8 nlme_3.1-166
[37] genefilter_1.88.0 tidyselect_1.2.1 locfit_1.5-9.10
[40] digest_0.6.37 dplyr_1.1.4 labeling_0.4.3
[43] splines_4.4.1 fastmap_1.2.0 grid_4.4.1
[46] colorspace_2.1-1 cli_3.6.3 SparseArray_1.6.0
[49] magrittr_2.0.3 S4Arrays_1.6.0 survival_3.7-0
[52] XML_3.99-0.17 utf8_1.2.4 withr_3.0.2
[55] scales_1.3.0 UCSC.utils_1.2.0 bit64_4.5.2
[58] rmarkdown_2.28 XVector_0.46.0 httr_1.4.7
[61] bit_4.5.0 png_0.1-8 memoise_2.0.1
[64] evaluate_1.0.1 knitr_1.48 mgcv_1.9-1
[67] rlang_1.1.4 Rcpp_1.0.13 DBI_1.2.3
[70] xtable_1.8-4 glue_1.8.0 annotate_1.84.0
[73] jsonlite_1.8.9 R6_2.5.1 zlibbioc_1.52.0
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.