Elastic-Net models with additional regularization based on network centrality metrics
glmSparseNet is a R package that generalizes sparse
regression models when the features (e.g. genes) have a graph
structure (e.g. protein-protein interactions), by including
network-based regularizers. glmSparseNet uses the
glmnet R-package, by including centrality measures of the
network as penalty weights in the regularization. The current version
implements regularization based on node degree, i.e. the strength and/or
number of its associated edges, either by promoting hubs in the solution
or orphan genes in the solution. All the glmnet
distribution families are supported, namely “gaussian”,
“poisson”, “binomial”, “multinomial”,
“cox”, and “mgaussian”.
It adds two new main functions called glmSparseNet and
cv.glmSparseNet that extend both model inference and model
selection via cross-validation with network-based regularization. These
functions are very flexible and allow to transform the penalty weights
after the centrality metric is calculated, thus allowing to change how
it affects the regularization. To facilitate users, we made available a
function that will penalize low connected nodes in the network -
glmHub or glmDegree - and another that will
penalize hubs - glmOrphan.
Below, we provide one example for survival analysis using transcriptomic data from the TCGA Adrenocortical Carcinoma project. More information and Rmd files are available in the vignettes folder where more extensive and complete examples are provided for logistic regresson and Cox’s regression for different types of cancer data.
Veríssimo, A., Carrasquinha E., Lopes, M.B., Oliveira, A.L., Sagot, M.-F. & Vinga, S. (2018), Sparse network-based regularization for the analysis of patientomics high-dimensional survival data. bioRxiv 403402; doi: https://doi.org/10.1101/403402
Veríssimo, A., Oliveira, A.L., Sagot, M.-F., & Vinga, S. (2016). DegreeCox – a network-based regularization method for survival analysis. BMC Bioinformatics. 17(16): 449. https://doi.org/10.1186/s12859-016-1310-4
This package was developed by André Veríssimo, Eunice Carrasquinha, Marta B. Lopes and Susana Vinga under the project SOUND, funded from the European Union Horizon 2020 research and innovation program under grant agreement No. 633974.
Bioconductor is necessary for the installation of this package.
if (!require("BiocManager")) {
install.packages("BiocManager")
}
BiocManager::install("glmSparseNet")This package extends the glmnet r-package with
network-based regularization based on features relations. This network
can be calculated from the data itself or using external networks to
enrich the model.
There are 2 methods available to use data-dependant methods to generate the network:
Alternatively, the network can be passed as an adjancency matrix or an already calculate metric for each node.
The main functions from this packages are the
glmSparseNet and cv.glmSparseNet and the
arguments for the functions are defined as:
xdata: A MultiAssayExperiment object or an input matrix
of dimension Observations x Featuresydata: Response object that can take different forms
depending on the model family that is usedfamily: Model type that can take: “gaussian”,
“poisson”, “binomial”, “multinomial”,
“cox”, and “mgaussian”network: Network to use in penalization, it can take as
input: “correlation”, “covariance”, a matrix object with p.vars x p.vars
representing the network, a weighted vector of penaltiesexperiment.name: Optional parameter used with a
“MultiAssayExperiment” object as inputnetwork.options: Optional parameter defining the
options to process the network, such as:
cutoff: A real number to use to remove edges from the
networkminDegree: Minimum value that the weight should have,
this is useful as when the weight is 0, there is no regularization on
that feature, which may lead to convergence problemstransFun: Transformation function to the vector of
penalty weights after these are calculated from the networknote: These functions can take any additional arguments that
glmnet or cv.glmnet accept (e.g. number of
folds in cross validation)
cv.glmSparseNet(
xdata,
ydata,
family = "cox",
network = "correlation",
options = networkOptions(
cutoff = .6,
minDegree = 0.2
)
)This example uses an adrenal cancer dataset using the correlation to calculate the network and cross-validation to find the optimal model. The network itself if filtered using a cutoff value of 0.6, i.e. all edges that have a correlation between the two features (genes) below the cutoff value are discarded.
The data was retrieved from TCGA database and the Adrenocortical
Carcinoma project with 92 patients and a reduced RNASeq data. See
Bioconductor package MultiAssayExperiment for more
information on the miniACC dataset.
To run the following examples, the next libraries are also needed:
library(futile.logger)
library(dplyr)
library(ggplot2)
library(reshape2)
library(MultiAssayExperiment)
library(survival)
library(glmnet)
library(glmSparseNet)There is some pre-processing needed to remove patients with invalid follow-up date or death date:
# load data
data("miniACC", package = "MultiAssayExperiment")
xdata <- miniACC
# build valid data with days of last follow up or to event
eventIx <- which(!is.na(xdata$days_to_death))
censIx <- which(!is.na(xdata$days_to_last_followup))
survEventTime <- array(NA, nrow(colData(xdata)))
survEventTime[eventIx] <- xdata$days_to_death[eventIx]
survEventTime[censIx] <- xdata$days_to_last_followup[censIx]
# Keep only valid individuals
#
# they are valid if they have:
# - either a follow_up time or event time
# - a valid vital_status (i.e. not missing)
# - folloup_time or event_time > 0
validIx <- as.vector(!is.na(survEventTime) & !is.na(xdata$vital_status) & survEventTime > 0)
ydata <- data.frame(
time = survEventTime[validIx],
status = xdata$vital_status[validIx],
row.names = xdata$patientID[validIx]
)The function cv.glmSparseNet fits the survival data
using 10-fold cross validation and using a cutoff value of 0.6 to reduce
the size of the network.
# build response object for glmnet
fit3 <- cv.glmSparseNet(
xdata,
ydata,
family = "cox",
network = "correlation",
experiment = "RNASeq2GeneNorm",
alpha = .7,
nlambda = 1000,
options = networkOptions(
cutoff = .6,
minDegree = 0.2,
transFun = hubHeuristic
)
)## Warning: 'experiments' dropped; see 'drops()'
## harmonizing input:
## removing 306 sampleMap rows not in names(experiments)
## removing 13 colData rownames not in sampleMap 'primary'
Cross validation plot, showing all 1000 lambdas tested and the error for each, vertical lines show best model and another with fewer variables selected within one standard error of the best.
separate2groupsCoxThis function generates Kaplan-Meier survival model based on the estimated coefficients of the Cox model. It creates two groups based on the relative risk and displays both survival curves (high vs. low-risk patients, as defined by the median) and the corresponding results of log-rank tests.
# Data to use in draw.kaplan function
# * it takes the input data, response and coefficients
# * calculates the relative risk
# * separates individuals based on relative risk into High/Low risk groups
xdataReduced <- as(xdata[, , "RNASeq2GeneNorm"], "MatchedAssayExperiment")## Warning: 'experiments' dropped; see 'drops()'
## harmonizing input:
## removing 306 sampleMap rows not in names(experiments)
## removing 13 colData rownames not in sampleMap 'primary'ydataKM <- ydata[rownames(colData(xdataReduced)), ]
bestModelCoef <- coef(fit3, s = "lambda.min")[, 1]Kaplan-Meier plot
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
## $pvalue
## [1] 2.728306e-07
##
## $plot
##
## $km
## Call: survfit(formula = survival::Surv(time, status) ~ group, data = prognosticIndexDf)
##
## n events median 0.95LCL 0.95UCL
## Low risk - 1 40 5 NA NA NA
## High risk - 1 39 23 1105 579 NA