glmSparseNet

• Overview
• Citation
• Instalation
• Details
  • Function definition
• Example for survival analysis using RNA-seq data
• Visualization and Analytical tools
  • Survival curves with separate2groupsCox

Elastic-Net models with additional regularization based on network centrality metrics

Overview

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.

Citation

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.

Instalation

Bioconductor is necessary for the installation of this package.

if (!require("BiocManager")) {
  install.packages("BiocManager")
}
BiocManager::install("glmSparseNet")

Details

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:

1. Correlation matrix with cutoff;
2. Covariance matrix with cutoff;

Alternatively, the network can be passed as an adjancency matrix or an already calculate metric for each node.

Function definition

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 Features
• ydata: Response object that can take different forms depending on the model family that is used
• family: 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 penalties
• experiment.name: Optional parameter used with a “MultiAssayExperiment” object as input
• network.options: Optional parameter defining the options to process the network, such as:
  • cutoff: A real number to use to remove edges from the network
  • minDegree: 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 problems
  • transFun: Transformation function to the vector of penalty weights after these are calculated from the network

note: 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
  )
)

Example for survival analysis using RNA-seq data

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'

plot(fit3)

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.

Visualization and Analytical tools

Survival curves with separate2groupsCox

This 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

separate2GroupsCox(
  bestModelCoef, t(assay(xdata[["RNASeq2GeneNorm"]])), ydataKM, ylim = c(0, 1)
)

## 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