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 45 1 220 1 61 30 1 1 387
gene2 83 143 10 186 642 61 31 212 727
gene3 145 1 192 162 1 45 101 15 169
gene4 122 15 3 290 7 249 158 122 1
gene5 3 296 3 72 34 86 1 1 13
gene6 474 34 54 296 46 1 31 49 2
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 174 1 133 8 1 39 859 13
gene2 44 275 1 74 2 790 3 96
gene3 223 44 749 2 7 920 26 298
gene4 28 5 1 16 1 197 610 32
gene5 674 39 151 1 4 2 4 1
gene6 1 87 121 106 2 53 189 72
sample18 sample19 sample20
gene1 2 3 5
gene2 1 26 48
gene3 45 223 15
gene4 1 6 9
gene5 46 2 9
gene6 5 212 27
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 52.32611 -1.0816253 1.7897582 -0.2279812 2
sample2 26.71654 0.2840334 0.7357133 -0.9184919 1
sample3 41.70698 0.2527619 -0.3990051 -1.5988617 2
sample4 36.06898 -0.5359866 0.1256181 -0.2889754 2
sample5 68.87707 -1.0274084 1.4947898 2.2422929 2
sample6 71.59119 0.4194515 -0.3011543 1.7183602 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 64.3026 1.47159 1.961153 0.3244364 0.666099 195.735 203.175
gene2 109.7960 1.00004 0.800297 0.3710159 0.687066 239.903 246.873
gene3 139.5281 1.00011 0.379950 0.5375905 0.770866 248.794 255.765
gene4 54.6754 1.00010 2.558520 0.1097183 0.428936 205.954 212.925
gene5 60.7629 1.00001 6.182734 0.0129013 0.104895 188.366 195.336
gene6 86.4546 1.00026 2.679373 0.1016266 0.428936 223.071 230.042
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 64.3026 1.053961 0.657820 1.602202 0.1091109 0.418607 195.735
gene2 109.7960 -1.248590 0.594812 -2.099134 0.0358051 0.210423 239.903
gene3 139.5281 0.836127 0.650142 1.286070 0.1984188 0.620059 248.794
gene4 54.6754 -0.478043 0.614302 -0.778189 0.4364579 0.727430 205.954
gene5 60.7629 1.001980 0.639592 1.566593 0.1172099 0.418607 188.366
gene6 86.4546 -0.248882 0.574924 -0.432896 0.6650907 0.860347 223.071
BIC
<numeric>
gene1 203.175
gene2 246.873
gene3 255.765
gene4 212.925
gene5 195.336
gene6 230.042
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 64.3026 -1.150748 1.037248 -1.109424 2.67247e-01 0.61686378 195.735
gene2 109.7960 -1.611847 0.952326 -1.692538 9.05435e-02 0.30181159 239.903
gene3 139.5281 0.533674 1.046834 0.509798 6.10193e-01 0.80288517 248.794
gene4 54.6754 -2.999740 0.992400 -3.022714 2.50519e-03 0.03131484 205.954
gene5 60.7629 -1.937264 1.056612 -1.833468 6.67331e-02 0.23833234 188.366
gene6 86.4546 3.956240 0.975214 4.056790 4.97518e-05 0.00248759 223.071
BIC
<numeric>
gene1 203.175
gene2 246.873
gene3 255.765
gene4 212.925
gene5 195.336
gene6 230.042
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene10 69.5151 1.00012 15.02895 0.000105344 0.00526719 202.812 209.782
gene34 109.1564 1.00004 11.76638 0.000603248 0.01508121 226.169 233.139
gene19 55.0658 1.00003 7.52477 0.006086488 0.07675576 207.604 214.574
gene24 92.0654 1.00005 7.50905 0.006140461 0.07675576 202.551 209.521
gene5 60.7629 1.00001 6.18273 0.012901253 0.10489484 188.366 195.336
gene36 65.4285 1.00013 6.17750 0.012940028 0.10489484 192.927 199.897
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.5.0 RC (2025-04-04 r88126 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows Server 2022 x64 (build 20348)
Matrix products: default
LAPACK version 3.12.1
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_3.5.2 BiocParallel_1.42.0
[3] NBAMSeq_1.24.1 SummarizedExperiment_1.38.1
[5] Biobase_2.68.0 GenomicRanges_1.60.0
[7] GenomeInfoDb_1.44.0 IRanges_2.42.0
[9] S4Vectors_0.46.0 BiocGenerics_0.54.0
[11] generics_0.1.3 MatrixGenerics_1.20.0
[13] matrixStats_1.5.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.48.0 gtable_0.3.6 xfun_0.52
[4] bslib_0.9.0 lattice_0.22-7 vctrs_0.6.5
[7] tools_4.5.0 parallel_4.5.0 tibble_3.2.1
[10] AnnotationDbi_1.70.0 RSQLite_2.3.11 blob_1.2.4
[13] pkgconfig_2.0.3 Matrix_1.7-3 RColorBrewer_1.1-3
[16] lifecycle_1.0.4 GenomeInfoDbData_1.2.14 compiler_4.5.0
[19] farver_2.1.2 Biostrings_2.76.0 DESeq2_1.48.1
[22] codetools_0.2-20 snow_0.4-4 htmltools_0.5.8.1
[25] sass_0.4.10 yaml_2.3.10 pillar_1.10.2
[28] crayon_1.5.3 jquerylib_0.1.4 DelayedArray_0.34.1
[31] cachem_1.1.0 abind_1.4-8 nlme_3.1-168
[34] genefilter_1.90.0 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] cli_3.6.5 SparseArray_1.8.0 magrittr_2.0.3
[46] S4Arrays_1.8.0 survival_3.8-3 dichromat_2.0-0.1
[49] XML_3.99-0.18 withr_3.0.2 scales_1.4.0
[52] UCSC.utils_1.4.0 bit64_4.6.0-1 rmarkdown_2.29
[55] XVector_0.48.0 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_1.9-3 rlang_1.1.6
[64] Rcpp_1.0.14 xtable_1.8-4 glue_1.8.0
[67] DBI_1.2.3 annotate_1.86.0 jsonlite_2.0.0
[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.