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 9 209 166 309 1 64 63 1 30
gene2 6 1 329 319 9 17 256 722 126
gene3 15 274 7 21 3 2 62 57 12
gene4 11 28 912 98 2 32 295 7 211
gene5 176 13 172 328 359 1 216 23 364
gene6 7 645 9 5 43 3 34 36 1
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 847 130 79 136 9 42 3 19
gene2 99 67 1 108 141 9 166 48
gene3 19 174 1 5 23 115 2 22
gene4 4 244 1 15 386 84 12 80
gene5 188 2 6 153 173 6 368 15
gene6 459 2 13 509 1 100 6 4
sample18 sample19 sample20
gene1 4 33 308
gene2 92 11 176
gene3 876 1 488
gene4 1 65 3
gene5 119 406 10
gene6 49 37 108
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 52.83477 -0.80213662 2.0417279 0.78715949 2
sample2 77.28252 -0.05196036 -0.1352802 -0.01054929 1
sample3 41.54699 -0.31173715 -0.9224491 1.24921362 1
sample4 53.17015 0.57616514 -0.3935760 0.38090169 1
sample5 55.28492 -1.12731817 1.0873633 -0.37820532 0
sample6 37.35198 -0.64955508 0.3338783 -0.75570594 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 89.6698 1.00005 0.5237387 0.4692780 0.7305072 231.385 238.355
gene2 105.0001 1.00006 0.8779267 0.3488040 0.6551071 240.505 247.475
gene3 104.2485 1.00016 0.1126638 0.7371822 0.8824308 211.976 218.947
gene4 124.9324 1.00005 0.0613833 0.8044041 0.8824308 232.449 239.419
gene5 167.9805 1.00022 2.8759754 0.0900224 0.3462400 256.617 263.588
gene6 70.6001 1.00014 6.5745285 0.0103518 0.0862646 214.617 221.587
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 89.6698 0.06561384 0.382124 0.171708 0.863667 0.912787 231.385
gene2 105.0001 0.21138565 0.371712 0.568682 0.569572 0.808937 240.505
gene3 104.2485 0.25375663 0.400859 0.633033 0.526712 0.808937 211.976
gene4 124.9324 0.54125412 0.442660 1.222730 0.221432 0.607415 232.449
gene5 167.9805 -0.00629937 0.425663 -0.014799 0.988193 0.988193 256.617
gene6 70.6001 -0.15226341 0.421126 -0.361563 0.717679 0.875218 214.617
BIC
<numeric>
gene1 238.355
gene2 247.475
gene3 218.947
gene4 239.419
gene5 263.588
gene6 221.587
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 89.6698 -0.9924955 0.878626 -1.1295995 0.258645 0.553176 231.385
gene2 105.0001 0.2065561 0.853790 0.2419286 0.808836 0.941782 240.505
gene3 104.2485 1.3301748 0.924014 1.4395616 0.149991 0.543406 211.976
gene4 124.9324 -0.4007816 1.016548 -0.3942575 0.693391 0.912357 232.449
gene5 167.9805 -0.7609564 0.977115 -0.7787787 0.436110 0.736491 256.617
gene6 70.6001 0.0403743 0.968328 0.0416949 0.966742 0.966742 214.617
BIC
<numeric>
gene1 238.355
gene2 247.475
gene3 218.947
gene4 239.419
gene5 263.588
gene6 221.587
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene16 97.8351 1.00007 16.29587 5.46549e-05 0.00273275 205.016 211.987
gene27 104.8707 1.00005 8.67384 3.22863e-03 0.08071563 222.246 229.216
gene33 35.9451 1.00004 7.36471 6.65304e-03 0.08626461 176.881 183.851
gene48 39.2942 1.00005 7.01054 8.10622e-03 0.08626461 175.587 182.557
gene12 187.7381 1.00008 6.77530 9.24514e-03 0.08626461 223.632 230.602
gene6 70.6001 1.00014 6.57453 1.03518e-02 0.08626461 214.617 221.587
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 Under development (unstable) (2025-03-01 r87860 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows Server 2022 x64 (build 20348)
Matrix products: default
LAPACK version 3.12.0
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_1.41.2
[3] NBAMSeq_1.23.0 SummarizedExperiment_1.37.0
[5] Biobase_2.67.0 GenomicRanges_1.59.1
[7] GenomeInfoDb_1.43.4 IRanges_2.41.3
[9] S4Vectors_0.45.4 BiocGenerics_0.53.6
[11] generics_0.1.3 MatrixGenerics_1.19.1
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.47.0 gtable_0.3.6 xfun_0.51
[4] bslib_0.9.0 lattice_0.22-6 vctrs_0.6.5
[7] tools_4.5.0 parallel_4.5.0 tibble_3.2.1
[10] AnnotationDbi_1.69.0 RSQLite_2.3.9 blob_1.2.4
[13] pkgconfig_2.0.3 Matrix_1.7-2 lifecycle_1.0.4
[16] GenomeInfoDbData_1.2.13 farver_2.1.2 compiler_4.5.0
[19] Biostrings_2.75.4 munsell_0.5.1 DESeq2_1.47.5
[22] codetools_0.2-20 snow_0.4-4 htmltools_0.5.8.1
[25] sass_0.4.9 yaml_2.3.10 pillar_1.10.1
[28] crayon_1.5.3 jquerylib_0.1.4 DelayedArray_0.33.6
[31] cachem_1.1.0 abind_1.4-8 nlme_3.1-167
[34] genefilter_1.89.0 tidyselect_1.2.1 locfit_1.5-9.12
[37] digest_0.6.37 dplyr_1.1.4 labeling_0.4.3
[40] splines_4.5.0 fastmap_1.2.0 grid_4.5.0
[43] colorspace_2.1-1 cli_3.6.4 SparseArray_1.7.6
[46] magrittr_2.0.3 S4Arrays_1.7.3 survival_3.8-3
[49] XML_3.99-0.18 withr_3.0.2 scales_1.3.0
[52] UCSC.utils_1.3.1 bit64_4.6.0-1 rmarkdown_2.29
[55] XVector_0.47.2 httr_1.4.7 bit_4.5.0.1
[58] png_0.1-8 memoise_2.0.1 evaluate_1.0.3
[61] knitr_1.49 mgcv_1.9-1 rlang_1.1.5
[64] Rcpp_1.0.14 xtable_1.8-4 glue_1.8.0
[67] DBI_1.2.3 annotate_1.85.0 jsonlite_1.9.1
[70] R6_2.6.1
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.