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 88 59 29 76 5 1 5 316 52
gene2 104 374 6 23 1 7 1 3 104
gene3 231 243 1 151 75 93 1 51 1
gene4 85 6 1 238 393 50 7 45 1
gene5 95 1 8 7 8 11 52 332 82
gene6 1 27 4 88 1 140 10 47 1
sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1 173 14 496 356 53 71 2 195
gene2 5 97 1 181 98 139 11 35
gene3 2 11 1 68 352 63 11 13
gene4 2 24 83 9 14 55 322 3
gene5 3 19 237 278 1 3 98 66
gene6 336 85 2 16 105 388 96 257
sample18 sample19 sample20
gene1 38 9 102
gene2 741 46 332
gene3 209 83 24
gene4 245 29 2
gene5 224 3 5
gene6 166 277 74
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 20.43057 -0.1724116788 0.87827995 0.5001326 2
sample2 46.03175 0.0243048940 -0.13275538 -1.3997528 2
sample3 50.23663 -0.0001535236 -0.66098183 -0.4139497 2
sample4 43.58145 -0.4691252360 -0.07641307 -0.9515732 0
sample5 79.56687 -2.6383135539 -0.21832630 -0.1268177 1
sample6 52.78352 1.0867948512 -0.39693743 -0.5377321 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 116.1983 1.00005 0.1758578 0.674973 0.888122 238.698 245.669
gene2 93.9918 1.00011 0.0443517 0.833449 0.905923 230.774 237.744
gene3 71.5139 1.00006 0.0593034 0.807703 0.905923 217.063 224.033
gene4 71.5176 1.00006 0.3407305 0.559454 0.847658 205.150 212.120
gene5 83.4670 1.00006 0.0584695 0.809055 0.905923 221.815 228.785
gene6 108.0406 1.00018 0.5959644 0.440142 0.720443 235.606 242.576
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 116.1983 0.507738 0.375361 1.352664 0.17616290 0.5554333 238.698
gene2 93.9918 -0.428628 0.409724 -1.046138 0.29549742 0.6543103 230.774
gene3 71.5139 -0.803994 0.362808 -2.216030 0.02668946 0.1906390 217.063
gene4 71.5176 -1.002984 0.352478 -2.845524 0.00443385 0.0554231 205.150
gene5 83.4670 -0.427596 0.424741 -1.006721 0.31406895 0.6543103 221.815
gene6 108.0406 0.202912 0.398469 0.509228 0.61059238 0.8208329 235.606
BIC
<numeric>
gene1 245.669
gene2 237.744
gene3 224.033
gene4 212.120
gene5 228.785
gene6 242.576
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 116.1983 -1.146756 0.836543 -1.3708270 0.170429 0.655496 238.698
gene2 93.9918 0.647494 0.912663 0.7094556 0.478042 0.839010 230.774
gene3 71.5139 -0.069360 0.796764 -0.0870522 0.930630 0.997733 217.063
gene4 71.5176 -0.695986 0.742880 -0.9368760 0.348822 0.824082 205.150
gene5 83.4670 -0.353683 0.944703 -0.3743852 0.708118 0.973802 221.815
gene6 108.0406 0.800512 0.888494 0.9009767 0.367601 0.824082 235.606
BIC
<numeric>
gene1 245.669
gene2 237.744
gene3 224.033
gene4 212.120
gene5 228.785
gene6 242.576
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$pvalue),]
topgene = rownames(res1)[1]
sf = getsf(gsd) ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf)
head(res1)
DataFrame with 6 rows and 7 columns
baseMean edf stat pvalue padj AIC BIC
<numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene41 120.8680 1.00012 11.15473 0.000839531 0.0419766 224.955 231.925
gene37 52.8471 1.00007 8.85421 0.002926677 0.0646522 177.585 184.555
gene48 73.8833 1.00007 8.22877 0.004125567 0.0646522 210.047 217.018
gene40 95.9986 1.00005 7.81871 0.005172174 0.0646522 202.359 209.329
gene10 206.4794 1.00013 7.12030 0.007625829 0.0762583 231.206 238.176
gene45 157.5003 1.00004 6.29149 0.012135047 0.1011254 241.130 248.100
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
annotate("text", x = max(df$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 4.3.0 RC (2023-04-13 r84266)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.6.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
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_3.4.2 BiocParallel_1.34.1
[3] NBAMSeq_1.16.0 SummarizedExperiment_1.30.1
[5] Biobase_2.60.0 GenomicRanges_1.52.0
[7] GenomeInfoDb_1.36.0 IRanges_2.34.0
[9] S4Vectors_0.38.1 BiocGenerics_0.46.0
[11] MatrixGenerics_1.12.0 matrixStats_0.63.0
loaded via a namespace (and not attached):
[1] KEGGREST_1.40.0 gtable_0.3.3 xfun_0.38
[4] bslib_0.4.2 lattice_0.21-8 vctrs_0.6.1
[7] tools_4.3.0 bitops_1.0-7 generics_0.1.3
[10] parallel_4.3.0 RSQLite_2.3.1 AnnotationDbi_1.62.1
[13] tibble_3.2.1 fansi_1.0.4 highr_0.10
[16] blob_1.2.4 pkgconfig_2.0.3 Matrix_1.5-4
[19] lifecycle_1.0.3 GenomeInfoDbData_1.2.10 farver_2.1.1
[22] compiler_4.3.0 Biostrings_2.68.0 munsell_0.5.0
[25] DESeq2_1.40.1 codetools_0.2-19 htmltools_0.5.5
[28] sass_0.4.5 RCurl_1.98-1.12 yaml_2.3.7
[31] pillar_1.9.0 crayon_1.5.2 jquerylib_0.1.4
[34] DelayedArray_0.26.2 cachem_1.0.7 nlme_3.1-162
[37] genefilter_1.82.1 tidyselect_1.2.0 locfit_1.5-9.7
[40] digest_0.6.31 dplyr_1.1.1 labeling_0.4.2
[43] splines_4.3.0 fastmap_1.1.1 grid_4.3.0
[46] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3
[49] S4Arrays_1.0.1 survival_3.5-5 XML_3.99-0.14
[52] utf8_1.2.3 withr_2.5.0 scales_1.2.1
[55] bit64_4.0.5 rmarkdown_2.21 XVector_0.40.0
[58] httr_1.4.5 bit_4.0.5 png_0.1-8
[61] memoise_2.0.1 evaluate_0.20 knitr_1.42
[64] mgcv_1.8-42 rlang_1.1.0 Rcpp_1.0.10
[67] DBI_1.1.3 xtable_1.8-4 glue_1.6.2
[70] annotate_1.78.0 jsonlite_1.8.4 R6_2.5.1
[73] zlibbioc_1.46.0