This script reproduces the results in

• Title: EXACT HYPOTHESIS TESTING FOR SHRINKAGE BASED GGM
• Authors : Victor Bernal*, Rainer Bischoff, Victor Guryev, Marco Grzegorczyk, Peter Horvatovich
• Date created : 2018-11-15
• Submitted to Bionformatics Journal
• DOI: [] (https://doi.org/10.1093/bioinformatics/btz357)

Update history : 2020-04-26, 2019- 03-09

Please cite this paper when you have used it in your publications.

Prerequisite requires R libraries (CRAN): "GeneNet" , "stats4", "ggplot2", and "Hmisc".

The aim is to show that the reconstruction of (shrinkage based) GGMs is biased unless the shrinkage parameter is included in the inference. To illustrate thi we will highlight that with the new shrunk density (i) p values are correctly distributed i.e. uniform [0 1] under the null hypothesis: no partial correlation (ii) expected false positives rate are accurate controlled (iii) the positive predicted values is superior As gold standard we will use the computationally expensive Monte Carlo estimation

GitHUB-GGM_ Shrinkage_v2.R is the R script that reproduces all the analysis. shrinkagefunctions.R is the source file with the implementation (i.e. R functions).

p= number of variables (e.g. genes)
n= number of data points

Simulate a GGM with a percentage (etaA) of non-zero edges
sim.pcor<-ggm.simulate.pcor(p, etaA)
Simulate data of length n
sim.data<- ggm.simulate.data( n , sim.pcor)
Reconstruct the GGM from the data with the optimal shrinkage (lambda)
GGM <- pcor.shrink(sim.data, verbose=TRUE)
lambda<-attr(GGM, "lambda")
r<-sm2vec(GGM)
Compare p-values for each edge with
Our method (Shrunk MLE)
p.shrunk( r, p ,n , lambda)
Monte Carlo (MC, the goldstandard)
p.montecarlo( r, number, p , n ,lambda)
Empirical null fitting (currently implemented in GeneNet 1.2.13)
network.test.edges(GGM, fdr=TRUE, plot=FALSE)

The p- values from Empirical null fitting are biased (not uniform).The standard prob density minus the "shrunk" density (larger tails=> more false positives) Comparison Positive Predictive Values (superior Shrunk MLE, agrees with the gold standard)