R: Statistical Inference of Large-Scale Gaussian Graphical Model...

SILGGM {SILGGM}

R Documentation

Statistical Inference of Large-Scale Gaussian Graphical Model in Gene Networks

Description

SILGGM is used to make statistical inference of conditional dependence among gene networks using the Gaussian graphical model (GGM). It includes four methods: (1) the bivariate nodewise scaled Lasso (B_NW_SL) (Ren et al., 2015) (2) the de-sparsified nodewise scaled Lasso (D-S_NW_SL) (Jankova and van de Geer, 2017) (3) the de-sparsified graphical Lasso (D-S_GL) (Jankova and van de Geer, 2015) and (4) the GGM estimation with false discovery rate control (FDR) using scaled Lasso or Lasso (GFC_SL or GFC_L) (Liu, 2013). This is an extensive and efficient package even for a high-dimensional setting.

Usage

SILGGM(x, method = NULL, lambda = NULL, global = FALSE,
alpha = NULL, ndelta = NULL, true_graph = NULL,
cytoscape_format = FALSE, csv_save = FALSE, directory = NULL)

Arguments

`x`	`x` is an `n` by `p` data matrix (`n` is the number of subjects and `p` is the number of genes, where `p` is allowed to be far larger than `n`).
`method`	Methods for statistical inference with 5 options: `"B_NW_SL"`, `"D-S_NW_SL"`, `"D-S_GL"`, `"GFC_SL"` and `"GFC_L"`. The default value is `"D-S_NW_SL"`.
`lambda`	The value of a tuning parameter for a Lasso-type regularization approach. The default value is `sqrt(2*log(p/sqrt(n))/n)` for `method = "B_NW_SL"`, `"D-S_NW_SL"` or `"GFC_SL"` and `sqrt(log(p)/n)` for `method = "D-S_GL"`. NOT applicable when `method = "GFC_L"`.
`global`	If `global = TRUE`, the global inference of all gene pairs is performed. The default value is `FALSE`. ONLY applicable when `method = "B_NW_SL"`, `"D-S_NW_SL"` or `"D-S_GL"`.
`alpha`	A user-supplied sequence of pre-sepecified `alpha` levels for FDR control. The default is `alpha = 0.05, 0.1` if no sequence is provided.
`ndelta`	The number of delta values decreased from `2` to `0` for selection of tuning parameters. The default value is `40`. ONLY applicable when `method = "GFC_L"`.
`true_graph`	The true graph structure in a study if available. The default value is `NULL`. This argument is particularly for global inference. If a true graph is available, both FDR(s) and the corresponding power(s) will be provided in the outputs. Otherwise, only FDR(s) and the associated threshold(s) for all absolute values of test statistics will be provided.
`cytoscape_format`	If `cytoscape_format = TRUE`, the outputs are shown in a table compatible with Cytoscape. The default value is `FALSE`.
`csv_save`	If `csv_save = TRUE`, the table in a Cytoscape format is saved to a directory as a `.csv` file. The file name is `"Cytoscape_method.csv"`, where `"method"` depends on which method is used (e.g. the file name is `"Cytoscape_D-S_NW_SL.csv"` when `method = "D-S_NW_SL"`). The default value is `FALSE`.
`directory`	A user-specified directory to save the `.csv` files and ONLY applicable when `csv_save = TRUE`. If no directory is specified, the default value is `NULL` and a per-session temporary directory is generated in the program using the `tempdir()` function. However, the temporary directory and the saved files will be cleaned up after each R session ends. Therefore, a specified directory is HIGHLY recommended.

Details

In the original papers of the four methods, B_NW_SL, D-S_NW_SL and D-S_GL are developed for individual inference of each entry of a precision matrix, while GFC_SL or GFC_L is proposed particularly for simultaneous inference of all entries. However, GFC_SL or GFC_L essentially relies on p-values of all entries of a precision matrix, so implementations of the other three methods can also be extended to global inference under its FDR framework (Liu, 2013). Each method uses a Lasso-type regularization approach first, and then obtains an asymptotically efficient test statistic (e.g. z-score or a newly-constructed standardized test statistic) for each off-diagonal entry of a precision matrix under a certain sparseness condition. For individual inference of each gene pair, the package not only estimates the conditional dependence (each off-diagonal entry of a precision matrix) between each pair of genes but also provides the associated confidence interval, z-score and p-value. For global inference, it shows the FDR(s), the corresponding power(s) (if possible) and the decision(s) of the conditional dependence of each gene pair corresponding to the pre-specified alpha level(s) for FDR control. All of the outputs can be displayed in a table compatible with Cytoscape (Shannon et al., 2003), a popular and powerful software for network visualization. In addition, the table can be saved as a .csv file for a direct use in Cytoscape. The package performs each approach in a time-efficient manner and is able to accelerate the existing implementations to several orders of magnitudes without loss of accuracy.

Value

If cytoscape_format = FALSE, a list is returned including the following elements:

`precision`	A precision matrix including each gene pair. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`z_score_precision`	A matrix of z-score for each off-diagonal entry of the precision matrix. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`p_precision`	A matrix of p-value for each off-diagonal entry of the precision matrix. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`CI_low_precision`	A matrix of lower value of 95% confidence interval for precision of the GGM. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`CI_high_precision`	A matrix of higher value of 95% confidence interval for precision of the GGM. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`partialCor`	A partial correlation matrix including each gene pair. NOT applicable when `method = "GFC_SL"` or `"GFC_L"`.
`z_score_partialCor`	A matrix of z-score for each off-diagonal entry of the partial correlation matrix. ONLY applicable when `method = "B_NW_SL"`.
`p_partialCor`	A matrix of p-value for each off-diagonal entry of the partial correlation matrix. ONLY applicable when `method = "B_NW_SL"`.
`CI_low_partialCor`	A matrix of lower value of 95% confidence interval for partial correlation of the GGM. ONLY applicable when `method = "B_NW_SL"`.
`CI_high_partialCor`	A matrix of higher value of 95% confidence interval for partial correlation of the GGM. ONLY applicable when `method = "B_NW_SL"`.
`T_stat`	A matrix of newly-constructed standardized test statistic for each off-diagonal entry of the precision matrix. ONLY applicable when `method = "GFC_SL"` or `"GFC_L"`.
`FDR`	The estimated FDR sequence for global inference of all off-diagonal entries of a precision matrix or all gene pairs based on the pre-specified `alpha` level(s).
`threshold`	The threshold sequence for absolute values of test statistics associated with the estimated FDR sequence.
`power`	The estimated power sequence for global inference of all off-diagonal entries of a precision matrix or all gene pairs associated with the estimated FDR sequence. ONLY applicable if `true_graph` is available.
`global_decision`	A list of `p` by `p` adjacency matrices of inferred graphs under the global inference corrsponding to the sequence of pre-sepecified `alpha` levels. A value of `1` in the matrix means that there is conditional dependence (or an edge) between the gene pair, while a value of `0` means condtional independence (or no edge).

If cytoscape_format = TRUE, a list is returned including the following elements:

`threshold`	The threshold sequence for absolute values of test statistics associated with the estimated FDR sequence.
`FDR`	The estimated FDR sequence for global inference of all off-diagonal entries of a precision matrix or all gene pairs based on the pre-specified `alpha` level(s).
`power`	The estimated power sequence for global inference of all off-diagonal entries of a precision matrix or all gene pairs associated with the estimated FDR sequence. ONLY applicable if `true_graph` is available.
`cytoscape_format_table`	A table with Cytoscape format including all of the above possible outputs and can be saved to the directory shown in the `directory` argument as a `.csv` file.

Author(s)

Rong Zhang <roz16@pitt.edu>, Zhao Ren <zren@pitt.edu> and Wei Chen <wei.chen@chp.edu>
Maintainers: Rong Zhang <roz16@pitt.edu>

References

1. Eddelbuettel, D. et al. (2011) Rcpp: Seamless R and C++ integration. Journal of Statistical Software, 40, 1-18.
2. Friedman, J. et al. (2008) Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9, 432-441.
3. Friedman, J. et al. (2010) Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.
4. Jankova, J. and van de Geer, S. (2015) Confidence intervals for high-dimensional inverse covariance estimation. Electronic Journal of Statistics, 9, 1205-1229.
5. Jankova, J. and van de Geer, S. (2017) Honest confidence regions and optimality in high-dimensional precision matrix estimation. Test, 26, 143-162.
6. Liu, W. (2013) Gaussian graphical model estimation with false discovery rate control. The Annals of Statistics, 41, 2948-2978.
7. Ren, Z. et al. (2015) Asymptotic normality and optimalities in estimation of large Gaussian graphical models. The Annals of Statistics, 43, 991-1026.
8. Shannon, P. et al. (2003) Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Research, 13, 2498-2504.
9. Wang, T. et al. (2016) FastGGM: an efficient algorithm for the inference of gaussi-an graphical model in biological networks. PLoS Computational Biology, 12, e1004755.
10. Witten, D. M. et al. (2011) New insights and faster computations for the graphical lasso. Journal of Computational and Graphical Statistics, 20, 892-900.

Examples

# Simulate a sparse precision matrix Omega
n <- 50
p <- 100
Omega.tmp <- matrix(0,p,p)
diag(Omega.tmp) <- rep(1,p)
for(k in 1:(p/10)){
    i <- 10*(k-1)+1
    for(j in (10*(k-1)+2):(10*(k-1)+10)){
      Omega.tmp[i,j] <- 0.5
      Omega.tmp[j,i] <- 0.5
    }
}
eigenvalue <- eigen(Omega.tmp)$values
Omega <- Omega.tmp+(abs(min(eigenvalue))+0.05)*diag(p)
cov <- solve(Omega)

# Sample an n by p data matrix X based on it
library(MASS)
X <- mvrnorm(n, rep(0, p), cov)

# Run SILGGM
library(SILGGM)

# Use default method D-S_NW_SL without global inference
outlist1 <- SILGGM(X)

# Use method D-S_GL with global inference
# True graph is available
outlist2 <- SILGGM(X, method = "D-S_GL", global = TRUE, true_graph = Omega)

# Use method B_NW_SL without global inference
outlist3 <- SILGGM(X, method = "B_NW_SL")

# Use method GFC_SL or GFC_L
# True graph is available
outlist4 <- SILGGM(X, method = "GFC_SL", true_graph = Omega)
outlist5 <- SILGGM(X, method = "GFC_L", true_graph = Omega)

# Use method D-S_NW_SL with global inference
# True graph is available
# Show the outputs in a Cytoscape format
outlist6 <- SILGGM(X, method = "D-S_NW_SL", global = TRUE,
true_graph = Omega, cytoscape_format = TRUE)

# Show the above outputs in a Cytoscape format table
# Save the table as a .csv file to a temporary directory
outlist7 <- SILGGM(X, method = "D-S_NW_SL", global = TRUE,
true_graph = Omega, cytoscape_format = TRUE, csv_save = TRUE)

[Package SILGGM version 1.0.0 Index]