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 7 5 96 6 109 21 7 46 37
gene2 1 57 190 97 213 1 74 867 49
gene3 1 11 83 195 2 121 288 10 64
gene4 33 373 126 58 10 58 339 143 72
gene5 17 66 719 4 30 71 1 54 1
gene6 1 4 24 1 1 116 6 17 8
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 120 16 104 194 1 24 18 168
gene2 296 54 62 185 1 233 52 306
gene3 41 4 1 1 157 2 41 72
gene4 6 1 1 3 93 550 55 211
gene5 60 12 548 2 257 118 49 12
gene6 416 27 1 1 46 159 197 116
sample18 sample19 sample20
gene1 20 5 17
gene2 36 40 1
gene3 36 336 805
gene4 1 29 237
gene5 4 27 82
gene6 98 4 616
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 28.65312 -0.8103270 1.98174321 -0.1919243 0
sample2 53.45100 -0.3180619 -0.09926992 -0.2116536 1
sample3 31.35403 -0.2295486 -0.46044418 0.4566301 2
sample4 65.41978 0.2195668 1.54815427 0.8581354 0
sample5 75.81841 0.2897221 -1.20943558 0.4738816 1
sample6 35.60605 0.8436993 -0.32202641 -0.6438498 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 45.2064 1.00008 0.17650904 0.6744367 0.807882 207.764 214.734
gene2 132.3282 1.00008 0.17175108 0.6786206 0.807882 243.256 250.226
gene3 74.6210 1.00025 0.00130449 0.9748719 0.994767 217.664 224.635
gene4 100.3924 1.00008 2.46764143 0.1162332 0.371877 237.495 244.465
gene5 80.6177 1.00010 5.69143342 0.0170548 0.120953 219.484 226.455
gene6 82.2199 1.00010 0.80869480 0.3685670 0.658155 212.160 219.131
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 45.2064 0.5597904 0.418402 1.3379234 0.180921 0.393307 207.764
gene2 132.3282 0.6977581 0.479051 1.4565434 0.145242 0.369934 243.256
gene3 74.6210 -0.7433422 0.472541 -1.5730759 0.115701 0.369934 217.664
gene4 100.3924 -0.7639954 0.497794 -1.5347624 0.124842 0.369934 237.495
gene5 80.6177 -0.0395956 0.458518 -0.0863555 0.931184 0.931184 219.484
gene6 82.2199 -0.8577989 0.535290 -1.6024949 0.109046 0.369934 212.160
BIC
<numeric>
gene1 214.734
gene2 250.226
gene3 224.635
gene4 244.465
gene5 226.455
gene6 219.131
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 45.2064 -0.0187359 0.962016 -0.0194756 0.984462 0.998791 207.764
gene2 132.3282 1.0443612 1.101365 0.9482423 0.343006 0.775683 243.256
gene3 74.6210 0.9340582 1.069404 0.8734377 0.382425 0.775683 217.664
gene4 100.3924 0.4748084 1.141767 0.4158541 0.677517 0.880538 237.495
gene5 80.6177 1.1375227 1.058841 1.0743089 0.282684 0.775683 219.484
gene6 82.2199 0.9920276 1.220882 0.8125503 0.416476 0.775683 212.160
BIC
<numeric>
gene1 214.734
gene2 250.226
gene3 224.635
gene4 244.465
gene5 226.455
gene6 219.131
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene24 69.8719 1.00004 10.01762 0.00155108 0.0274438 210.431 217.401
gene31 89.1033 1.00013 9.96574 0.00159709 0.0274438 229.722 236.693
gene9 62.8589 1.00007 9.90807 0.00164663 0.0274438 209.236 216.206
gene20 115.1506 1.00005 9.13542 0.00250821 0.0313527 222.391 229.361
gene29 95.6909 1.00009 6.40075 0.01141487 0.1021206 222.552 229.522
gene48 124.0337 1.00004 6.27399 0.01225447 0.1021206 225.245 232.215
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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_1.7-3 lifecycle_1.0.4
[16] GenomeInfoDbData_1.2.14 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_1.7.7
[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_4.6.0
[58] png_0.1-8 memoise_2.0.1 evaluate_1.0.3
[61] knitr_1.50 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.