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 5 195 16 38 1 258 1 81 52
gene2 574 119 26 52 1 24 8 175 204
gene3 2 78 199 2 43 1 48 1 1
gene4 1 320 3 2 70 5 96 1 163
gene5 352 209 277 13 274 28 118 54 23
gene6 113 211 96 116 42 2 24 36 2
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 180 119 45 40 100 170 5 10
gene2 23 74 17 133 20 8 78 1
gene3 227 8 7 7 6 109 48 419
gene4 21 1 60 49 209 101 4 3
gene5 9 8 11 1 7 130 269 9
gene6 485 34 8 4 1 8 32 8
sample18 sample19 sample20
gene1 1 533 12
gene2 36 35 9
gene3 1 8 111
gene4 132 11 191
gene5 228 159 1
gene6 277 25 4
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 27.58401 0.6501462 -1.4634808 0.2495924 2
sample2 52.96869 -1.1945369 -0.4601252 0.1985181 0
sample3 77.50772 -1.1041742 -1.5669763 -1.9828937 0
sample4 25.84204 0.5408499 0.9292463 -0.4723164 1
sample5 76.86154 -0.6434235 -0.7285971 1.4055751 0
sample6 22.98632 -0.6297166 0.7319863 -0.6933401 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:
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 79.3411 1.00006 3.481707 0.06206167 0.2216488 215.490 222.461
gene2 65.4688 1.00005 4.086654 0.04323461 0.1712771 217.997 224.968
gene3 53.3500 1.00006 8.953142 0.00277099 0.0435694 198.590 205.561
gene4 53.0708 1.00003 2.013322 0.15592877 0.4331355 204.645 211.615
gene5 77.4277 1.00003 0.120025 0.72906045 0.8477447 231.593 238.563
gene6 62.1240 1.00016 0.327752 0.56725582 0.7509692 217.823 224.794
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 79.3411 0.2558010 0.385711 0.6631927 0.507207 0.845345 215.490
gene2 65.4688 -0.2975635 0.384450 -0.7739980 0.438932 0.783807 217.997
gene3 53.3500 0.0433835 0.444812 0.0975321 0.922304 0.944133 198.590
gene4 53.0708 -0.3643095 0.410775 -0.8868825 0.375142 0.755291 204.645
gene5 77.4277 -0.3457732 0.417767 -0.8276708 0.407857 0.755291 231.593
gene6 62.1240 -0.6820386 0.447316 -1.5247347 0.127325 0.432541 217.823
BIC
<numeric>
gene1 222.461
gene2 224.968
gene3 205.561
gene4 211.615
gene5 238.563
gene6 224.794
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 79.3411 -3.6295911 1.10358 -3.2889143 0.00100575 0.0251437 215.490
gene2 65.4688 0.7374638 1.08279 0.6810789 0.49582155 0.7753749 217.997
gene3 53.3500 2.3222829 1.23593 1.8789762 0.06024775 0.3347097 198.590
gene4 53.0708 -1.8110701 1.19411 -1.5166721 0.12934950 0.4974981 204.645
gene5 77.4277 0.6393265 1.17726 0.5430625 0.58708674 0.8260584 231.593
gene6 62.1240 -0.0287999 1.26000 -0.0228571 0.98176424 0.9817642 217.823
BIC
<numeric>
gene1 222.461
gene2 224.968
gene3 205.561
gene4 211.615
gene5 238.563
gene6 224.794
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene43 62.5764 1.00011 12.21163 0.000475519 0.0215939 196.188 203.159
gene34 38.0694 1.00002 11.09945 0.000863755 0.0215939 185.753 192.723
gene3 53.3500 1.00006 8.95314 0.002770992 0.0435694 198.590 205.561
gene23 38.6098 1.00003 8.53465 0.003485553 0.0435694 183.161 190.131
gene11 88.4396 1.00003 7.30672 0.006870682 0.0613455 213.484 220.454
gene30 96.0069 1.00007 7.18312 0.007361460 0.0613455 210.314 217.284
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.4.0 beta (2024-04-15 r86425 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_1.38.0
[3] NBAMSeq_1.20.0 SummarizedExperiment_1.34.0
[5] Biobase_2.64.0 GenomicRanges_1.56.0
[7] GenomeInfoDb_1.40.0 IRanges_2.38.0
[9] S4Vectors_0.42.0 BiocGenerics_0.50.0
[11] MatrixGenerics_1.16.0 matrixStats_1.3.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.44.0 gtable_0.3.5 xfun_0.43
[4] bslib_0.7.0 lattice_0.22-6 vctrs_0.6.5
[7] tools_4.4.0 generics_0.1.3 parallel_4.4.0
[10] RSQLite_2.3.6 tibble_3.2.1 fansi_1.0.6
[13] AnnotationDbi_1.66.0 highr_0.10 blob_1.2.4
[16] pkgconfig_2.0.3 Matrix_1.7-0 lifecycle_1.0.4
[19] GenomeInfoDbData_1.2.12 farver_2.1.1 compiler_4.4.0
[22] Biostrings_2.72.0 munsell_0.5.1 DESeq2_1.44.0
[25] codetools_0.2-20 snow_0.4-4 htmltools_0.5.8.1
[28] sass_0.4.9 yaml_2.3.8 pillar_1.9.0
[31] crayon_1.5.2 jquerylib_0.1.4 DelayedArray_0.30.0
[34] cachem_1.0.8 abind_1.4-5 nlme_3.1-164
[37] genefilter_1.86.0 tidyselect_1.2.1 locfit_1.5-9.9
[40] digest_0.6.35 dplyr_1.1.4 labeling_0.4.3
[43] splines_4.4.0 fastmap_1.1.1 grid_4.4.0
[46] colorspace_2.1-0 cli_3.6.2 SparseArray_1.4.0
[49] magrittr_2.0.3 S4Arrays_1.4.0 survival_3.6-4
[52] XML_3.99-0.16.1 utf8_1.2.4 withr_3.0.0
[55] scales_1.3.0 UCSC.utils_1.0.0 bit64_4.0.5
[58] rmarkdown_2.26 XVector_0.44.0 httr_1.4.7
[61] bit_4.0.5 png_0.1-8 memoise_2.0.1
[64] evaluate_0.23 knitr_1.46 mgcv_1.9-1
[67] rlang_1.1.3 Rcpp_1.0.12 DBI_1.2.2
[70] xtable_1.8-4 glue_1.7.0 annotate_1.82.0
[73] jsonlite_1.8.8 R6_2.5.1 zlibbioc_1.50.0
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.