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R/semUtils.R
In SEMgraph: Network Analysis and Causal Inference Through Structural Equation Modeling
Defines functions
quiet
siblings
parents
descendants
ancestors
attrMatch
orientEdges
graph2dag
dagitty2graph
graph2lavaan
gplot
SEMgsa
Documented in
ancestors
dagitty2graph
descendants
gplot
graph2dag
graph2lavaan
orientEdges
parents
SEMgsa
siblings
# SEMgraph library
# Copyright (C) 2019-2021 Mario Grassi; Fernando Palluzzi; Barbara Tarantino
# e-mail: <mario.grassi@unipv.it>
# University of Pavia, Department of Brain and Behavioral Sciences
# Via Bassi 21, 27100 Pavia, Italy
# SEMgraph is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# SEMgraph is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
# -------------------------------------------------------------------- #
#' @title SEM-based gene set analysis
#'
#' @description Gene Set Analysis (GSA) via self-contained test for group
#' effect on signaling (directed) pathways based on SEM. The core of the
#' methodology is implemented in the RICF algorithm of \code{SEMrun()},
#' recovering from RICF output node-specific group effect p-values, and
#' Brown’s combined permutation p-values of node activation and inhibition.
#'
#' @param g A list of pathways to be tested.
#' @param data A matrix or data.frame. Rows correspond to subjects, and
#' columns to graph nodes (variables).
#' @param group A binary vector. This vector must be as long as the number
#' of subjects. Each vector element must be 1 for cases and 0 for control
#' subjects.
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "BH" (i.e., Benjamini-Hochberg correction).
#' @param alpha Gene set test significance level (default = 0.05).
#' @param n_rep Number of randomization replicates (default = 1000).
#' @param ... Currently ignored.
#'
#' @details For gaining more biological insights into the functional roles
#' of pre-defined subsets of genes, node perturbation obtained from RICF
#' fitting has been combined with up- or down-regulation of genes from KEGG
#' to obtain overall pathway perturbation as follows:
#' \itemize{
#' \item The node perturbation is defined as activated when the minimum among
#' the p-values is positive; if negative, the status is inhibited.
#' \item Up- or down- regulation of genes (derived from KEGG database) has
#' been obtained from the weighted adjacency matrix of each pathway as column
#' sum of weights over each source node. If the overall sum of node weights
#' is below 1, the pathway is flagged as down-regulated otherwise as up-regulated.
#' \item The combination between these two quantities allows to define the
#' direction (up or down) of gene perturbation. Up- or down regulated gene status,
#' associated with node inhibition, indicates a decrease in activation (or
#' increase in inhibition) in cases with respect to control group. Conversely,
#' up- or down regulated gene status, associated with node activation, indicates
#' an increase in activation (or decrease in inhibition) in cases with
#' respect to control group.
#' }
#'
#' @return A list of 2 objects:
#' \enumerate{
#' \item "gsa", A data.frame reporting the following information for each
#' pathway in the input list:
#' \itemize{
#' \item "No.nodes", pathway size (number of nodes);
#' \item "No.DEGs", number of differential espression genes (DEGs) within
#' the pathway, after multiple test correction with one of the methods
#' available in \code{\link[stats]{p.adjust}};
#' \item "pert", pathway perturbation status (see details);
#' \item "pNA", Brown's combined P-value of pathway node activation;
#' \item "pNI", Brown's combined P-value of pathway node inhibition;
#' \item "PVAL", Bonferroni combined P-value of pNA, and pNI; i.e.,
#' 2* min(pNA, PNI);
#' \item "ADJP", Adjusted Bonferroni P-value of pathway perturbation; i.e.,
#' min(No.pathways * PVAL; 1).
#' }
#' \item "DEG", a list with DEGs names per pathways.
#' }
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @references
#'
#' Grassi, M., Tarantino, B. SEMgsa: topology-based pathway enrichment analysis with
#' structural equation models. BMC Bioinformatics 23, 344 (2022).
#' https://doi.org/10.1186/s12859-022-04884-8
#'
#' @examples
#'
#' \dontrun{
#'
#' # Nonparanormal(npn) transformation
#' als.npn <- transformData(alsData$exprs)$data
#'
#' # Selection of FTD-ALS pathways from kegg.pathways.Rdata
#'
#' paths.name <- c("MAPK signaling pathway",
#' "Protein processing in endoplasmic reticulum",
#' "Endocytosis",
#' "Wnt signaling pathway",
#' "Neurotrophin signaling pathway",
#' "Amyotrophic lateral sclerosis")
#'
#' j <- which(names(kegg.pathways) %in% paths.name)
#'
#' GSA <- SEMgsa(kegg.pathways[j], als.npn, alsData$group,
#' method = "bonferroni", alpha = 0.05,
#' n_rep = 1000)
#' GSA$gsa
#' GSA$DEG
#'
#' }
#'
SEMgsa<- function(g=list(), data, group, method = "BH", alpha = 0.05, n_rep = 1000, ...)
{
# set loop objects:
gs <- names(g)
K <- length(g)
res.tbl <- NULL
DEG <- list()
for (k in 1:K){
cat( "k =", k, gs[k], "\n" )
ig <- simplify(g[[k]], remove.loops = TRUE)
if (length(E(ig)$weight) == 0) E(ig)$weight <- 1
adj <- as.matrix(get.adjacency(ig, attr = "weight"))
adj <- colSums(adj)
nodes <- ifelse(adj >= 1, 1, ifelse(adj == 0, 0, -1))
status <- ifelse(sum(nodes) >= 1, 1, ifelse(sum(nodes) == 0, 0, -1))
# RICF fitting:
fit <- NULL
err <- paste(" ValueError: Model converged = FALSE for k =",k,"\n")
tryCatch(fit <- quiet(SEMricf(ig, data, group, n_rep)),
error = function(c) cat(err))
if (length(fit[[1]]) == 0) {
res.tbl<- rbind(res.tbl, rep(NA,6))
colnames(res.tbl) <- c("No.nodes","No.DEGs","pert","pNa","pNi","PVAL")
DEG <- c(DEG, list(NULL))
next
}
pval<- fit$gest$pvalue
genes<- gsub("X", "", rownames(fit$gest))
genes<- genes[p.adjust(pval, method=method) < alpha]
DEG<- c(DEG, list(genes))
# data.frame of combined SEM results :
cpval <- fit$fit$pval
names(cpval) <- c("pNa", "pNi")
pvmin <- names(cpval)[which.min(cpval)]
sign <- ifelse(pvmin == "pNa", "+", "-")
if ( status != 0 ) {
if (status == -1 & sign == "-") pert <- "up inh"
else if (status == -1 & sign == "+") pert <- "down inh"
else if (status == 1 & sign == "+") pert <- "up act"
else if (status == 1 & sign == "-") pert <- "down act"
}else{pert <- NA}
df <- data.frame(
No.nodes = vcount(ig),
No.DEGs = sum(p.adjust(pval, method=method) < alpha),
pert = pert,
pNa = cpval[1],
pNi = cpval[2],
PVAL = min(2 * min(cpval[1], cpval[2]), 1)
)
res.tbl <- rbind(res.tbl,df)
}
ADJP <- p.adjust(res.tbl$PVAL, method="bonferroni")
res.tbl<- cbind(res.tbl, ADJP)
rownames(res.tbl) <- names(DEG) <- names(g)
gsa <- res.tbl[order(res.tbl$ADJP),]
DEG <- DEG[rownames(gsa)]
return( list(gsa=gsa, DEG=DEG) )
}
#' @title SEM-based differential network analysis
#'
#' @description Creates a sub-network with perturbed edges obtained from the
#' output of \code{\link[SEMgraph]{SEMace}}, comparable to the procedure in
#' Jablonski et al (2022), or of \code{\link[SEMgraph]{SEMrun}} with two-group
#' and CGGM solver, comparable to the algorithm 2 in Belyaeva et al (2021).
#' To increase the efficiency of computations for large graphs, users can
#' select to break the network structure into clusters, and select the
#' topological clustering method (see \code{\link[SEMgraph]{clusterGraph}}).
#' The function \code{\link[SEMgraph]{SEMrun}} is applied iteratively on
#' each cluster (with size min > 10 and max < 500) to obtain the graph
#' with the full list of perturbed edges.
#'
#' @param graph Input network as an igraph object.
#' @param data A matrix or data.frame. Rows correspond to subjects, and
#' columns to graph nodes (variables).
#' @param group A binary vector. This vector must be as long as the number
#' of subjects. Each vector element must be 1 for cases and 0 for control
#' subjects.
#' @param type Average Causal Effect (ACE) with two-group, "parents"
#' (back-door) adjustement set, and "direct" effects (\code{type = "ace"},
#' default), or CGGM solver with two-group using a clustering method.
#' If \code{type = "tahc"}, network modules are generated using the tree
#' agglomerative hierarchical clustering method, or non-tree clustering
#' methods from igraph package, i.e., \code{type = "wtc"} (walktrap community
#' structure with short random walks), \code{type ="ebc"} (edge betweeness
#' clustering), \code{type = "fgc"} (fast greedy method), \code{type = "lbc"}
#' (label propagation method), \code{type = "lec"} (leading eigenvector method),
#' \code{type = "loc"} (multi-level optimization), \code{type = "opc"} (optimal
#' community structure), \code{type = "sgc"} (spinglass statistical mechanics),
#' \code{type = "none"} (no breaking network structure into clusters).
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "BH" (i.e., FDR multiple test correction).
#' @param alpha Significance level (default = 0.05) for edge set selection.
#' @param ... Currently ignored.
#'
#' @return An igraph object.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @references
#'
#' Belyaeva A, Squires C, Uhler C (2021). DCI: learning causal differences
#' between gene regulatory networks. Bioinformatics, 37(18): 3067–3069.
#' <https://doi: 10.1093/bioinformatics/btab167>
#'
#' Jablonski K, Pirkl M, Ćevid D, Bühlmann P, Beerenwinkel N (2022).
#' Identifying cancer pathway dysregulations using differential
#' causal effects. Bioinformatics, 38(6):1550–1559.
#' <https://doi.org/10.1093/bioinformatics/btab847>
#'
#' @examples
#'
#' \dontrun{
#'
#' #load SEMdata package for ALS data with 17K genes:
#' #devtools::install_github("fernandoPalluzzi/SEMdata")
#' #library(SEMdata)
#'
#' # Nonparanormal(npn) transformation
#' library(huge)
#' data.npn<- huge.npn(alsData$exprs)
#' dim(data.npn) #160 17695
#'
#' # Extract KEGG interactome (max component)
#' KEGG<- properties(kegg)[[1]]
#' summary(KEGG)
#'
#' # KEGG modules with ALS perturbed edges using fast gready clustering
#' gD<- SEMdci(KEGG, data.npn, alsData$group, type="fgc")
#' summary(gD)
#' gcD<- properties(gD)
#'
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(2,2), mar=rep(2,4))
#' gplot(gcD[[1]], l="fdp", main="max component")
#' gplot(gcD[[2]], l="fdp", main="2nd component")
#' gplot(gcD[[3]], l="fdp", main="3rd component")
#' gplot(gcD[[4]], l="fdp", main="4th component")
#' par(old.par)
#'
#' }
#'
SEMdci<- function (graph, data, group, type = "ace", method = "BH", alpha = 0.05, ...)
{
if (type == "ace") {
dest <- SEMace(graph, data, group, type = "parents",
effect = "direct", method = method, alpha = alpha,
boot = NULL)
ftm <- data.frame(from = dest$source, to = dest$sink)
return(gD = graph_from_data_frame(ftm))
}
if (type != "none") {
C <- clusterGraph(graph, type = type, size = 10)
K <- as.numeric(names(table(C)))
gL <- NULL
for (k in 1:length(K)) {
cat("fit cluster =", K[k], "\n")
V <- names(C)[C == K[k]][names(C)[C == K[k]] %in% colnames(data)]
g <- simplify(induced_subgraph(graph, vids = V))
if (vcount(g) > 500 | ecount(g) < 9) next
dest <- tryCatch(quiet(SEMggm2(g, data, group)$dest),
error = function(err) NULL)
if (is.null(dest)) next
dsub <- subset(dest, p.adjust(dest$pvalue, method = method) < alpha)
if (nrow(dsub) == 0) next
ftm <- data.frame(from = dsub$rhs, to = dsub$lhs)
gC <- graph_from_data_frame(ftm)
if (ecount(gC) > 0) gL <- c(gL, list(gC))
}
cat("Done.\n")
if (is.null(gL))
return(gD = make_empty_graph(n = length(K)))
gD <- graph.union(gL)
}
else if (type == "none") {
dest <- quiet(SEMggm2(g, data, group)$dest)
dsub <- subset(dest, p.adjust(dest$pvalue, method = method) < alpha)
ftm <- data.frame(from = dsub$rhs, to = dsub$lhs)
gD <- graph_from_data_frame(ftm)
}
return(gD)
}
#' @title Graph properties summary and graph decomposition
#'
#' @description Produces a summary of network properties and returns
#' graph components (ordered by decreasing size), without self-loops.
#' @param graph Input network as an igraph object.
#' @param data An optional data matrix (default data = NULL) whith rows
#' corresponding to subjects, and columns to graph nodes (variables).
#' Nodes will be mapped onto variable names.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return List of graph components, ordered by decreasing size (the first
#' component is the giant one), without self-loops.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Extract the "Type II diabetes mellitus" pathway:
#' g <- kegg.pathways[["Type II diabetes mellitus"]]
#' summary(g)
#' properties(g)
#'
properties<- function (graph, data = NULL, ...)
{
if (!is_igraph(graph)){
ig <- graph_from_graphnel(graph)
}else{ ig <- graph }
if (!is.null(data)){
nodes <- colnames(data)[colnames(data) %in% V(graph)$name]
ig <- induced_subgraph(graph, vids = which(V(graph)$name %in% nodes))
}
ig <- simplify(ig, remove.loops = TRUE)
gcs <- igraph::decompose.graph(ig, min.vertices = 2)
vsize <- sapply(1:length(gcs), function(x) vcount(gcs[[x]]))
names(vsize) <- 1:length(vsize)
gcs <- gcs[as.numeric(names(sort(vsize, decreasing = TRUE)))]
cat("Frequency distribution of graph components\n\n")
tab <- table(sapply(gcs, vcount))
tab <- data.frame(n.nodes = as.numeric(names(tab)), n.graphs = as.numeric(tab))
print(tab)
cat("\nPercent of vertices in the giant component:",
round(100 * vcount(gcs[[1]])/vcount(ig), 1), "%\n\n")
print(c(is.simple = is_simple(gcs[[1]]), is.dag = is_dag(gcs[[1]]),
is.directed = is_directed(gcs[[1]]), is.weighted = is_weighted(gcs[[1]])))
cat("\n")
print(c(which.mutual = table(which_mutual(gcs[[1]]))))
return(gcs)
}
#' @title Graph plotting with renderGraph
#'
#' @description Wrapper for function renderGraph of the R package
#' Rgraphwiz.
#'
#' @param graph An igraph or graphNEL object.
#' @param l Any layout supported by \code{Rgraphviz}. It can be one among:
#' "dot" (default), "neato", "circo", "fdp", "osage", "twopi".
#' @param main Plot main title (by default, no title is added).
#' @param cex.main Main title size (default = 1).
#' @param font.main Main title font (default = 1). Available options
#' are: 1 for plain text, 2 for bold, 3 for italics, 4 for bold italics,
#' and 5 for symbol.
#' @param color.txt Node text color (default = "black").
#' @param fontsize Node text size (default = 16).
#' @param cex Another argument to control node text size (default = 0.6).
#' @param shape Node shape (default = "circle").
#' @param color Node border color (default = "gray70").
#' @param lty Node border outline (default = 1).
#' Available options include: 0 for blank, 1 for solid line, 2 for dashed,
#' 3 for dotted, 4 for dotdash, 5 for longdash, and 6 for twodash.
#' @param lwd Node border thickness (default = 1).
#' @param h Manual node height (default = "auto").
#' @param w Manual node width (default = "auto").
#' @param psize Automatic node size (default = 80).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return gplot returns invisibly the graph object produced by Rgraphviz
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' gplot(sachs$graph, main = "input graph")
#'
#' sem <- SEMrun(sachs$graph, sachs$pkc)
#' gplot(sem$graph, main = "output graph")
#'
gplot <- function(graph, l = "dot", main = "", cex.main = 1, font.main = 1,
color.txt = "black", fontsize = 16, cex = 0.6,
shape = "circle", color = "gray70", lty = 1, lwd = 1,
w = "auto", h = "auto", psize = 80, ...)
{
# Set graphNEL object
if(is_igraph(graph)){
g <- as_graphnel(graph)
} else {
g <- graph
graph <- graph_from_graphnel(graph)
}
vcol <- V(graph)$color
vshape <- V(graph)$shape
vsize <- V(graph)$size
vlab <- V(graph)$label
ecol <- E(graph)$color
elwd <- E(graph)$width
elab <- E(graph)$label
if (length(vcol) > 0) {
names(vcol) <- V(graph)$name
vcol <- vcol[graph::nodes(g)]
}
if (length(vshape) > 0) {
names(vshape) <- V(graph)$name
vshape <- vshape[graph::nodes(g)]
}
if (length(vsize) > 0) {
names(vsize) <- V(graph)$name
vsize <- 10*vsize[graph::nodes(g)]
} else {
vsize <- rep(psize, length = vcount(graph))
names(vsize) <- V(graph)$name
}
if (length(vlab) > 0) {
names(vlab) <- V(graph)$name
vlab <- vlab[graph::nodes(g)]
}
if (length(color) > 1) {
names(color) <- V(graph)$name
color <- color[graph::nodes(g)]
}
if (length(ecol) > 0) {
names(ecol) <- gsub("\\|", "~", attr(E(graph), "vnames"))
ecol <- ecol[graph::edgeNames(g, recipEdges = "distinct")]
}
if (length(elwd) > 0) {
names(elwd) <- gsub("\\|", "~", attr(E(graph), "vnames"))
elwd <- elwd[graph::edgeNames(g, recipEdges = "distinct")]
}
if (length(elab) > 0) {
names(elab) <- gsub("\\|", "~", attr(E(graph), "vnames"))
elab <- elab[graph::edgeNames(g,recipEdges = "distinct")]
} else {
elab <- rep("", ecount(graph))
names(elab) <- gsub("\\|", "~", attr(E(graph), "vnames"))
}
if (graph::isDirected(g)) {
g <- Rgraphviz::layoutGraph(g, layoutType = l,
edgeAttrs = list(label = elab))
} else {
g <- Rgraphviz::layoutGraph(g, layoutType = "fdp",
edgeAttrs = list(label = elab))
}
if (w == "auto") w <- vsize
if (h == "auto") h <- vsize
g<- Rgraphviz::layoutGraph(g, layoutType=l, edgeAttrs=list(label=elab))
graph::nodeRenderInfo(g)<- list(col = color, fill = vcol, label = vlab,
lwd = lwd, lty = lty,
textCol = color.txt,
fontsize = fontsize, cex = cex,
shape = vshape, width = w, height = h)
graph::edgeRenderInfo(g) <- list(col = ecol, lty = lty, lwd = elwd)
graph::graphRenderInfo(g) <- list(main = main, cex.main = cex.main,
font.main = font.main)
Rgraphviz::renderGraph(g)
return(invisible(g))
}
#' @title lavaan model to graph
#'
#' @description Convert a model, specified using lavaan syntax,
#' to an igraph object.
#' @param model Model specified using lavaan syntax.
#' @param directed Logical value. If TRUE (default), edge directions from
#' the model will be preserved. If FALSE, the resulting graph will
#' be undirected.
#' @param psi Logical value. If TRUE (default) covariances will be converted
#' into bidirected graph edges. If FALSE, covariances will be excluded from
#' the output graph.
#' @param verbose Logical value. If TRUE, a plot of the output graph will
#' be generated. For large graphs, this could significantly increase
#' computation time. If FALSE (default), graph plotting will be disabled.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return An igraph object.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Writing path diagram in lavaan syntax
#'
#' model<-"
#' #path model
#' Jnk ~ PKA + PKC
#' P38 ~ PKA + PKC
#' Akt ~ PKA + PIP3
#' Erk ~ PKA + Mek
#' Mek ~ PKA + PKC + Raf
#' Raf ~ PKA + PKC
#' PKC ~ PIP2 + Plcg
#' PIP2 ~ PIP3 + Plcg
#' Plcg ~ PIP3
#'
#' #(co)variances
#' PKA ~~ PIP3
#' "
#'
#' # Graph with covariances
#' G0 <- lavaan2graph(model, psi = TRUE)
#' plot(G0, layout = layout.circle)
#'
#' # Graph without covariances
#' G1 <- lavaan2graph(model, psi = FALSE)
#' plot(G1, layout = layout.circle)
#'
lavaan2graph<- function (model, directed = TRUE, psi = TRUE, verbose = FALSE, ...)
{
lav <- lavParTable(model, fixed.x = FALSE)
lavb <- subset(lav, lav$op == "~")
lavc <- subset(lav, lav$op == "~~" & (lav$rhs != lav$lhs))
lavc<- lavc[lavc$user == 1,]
ftm <- data.frame(cbind(from = lavb$rhs, to = lavb$lhs, label = lavb$label),
color = "black")
if (nrow(lavc) != 0 & psi == TRUE) {
ftmc1 <- data.frame(cbind(from = lavc$rhs, to = lavc$lhs,
label = "", color = "red"))
ftmc2 <- data.frame(cbind(from = lavc$lhs, to = lavc$rhs,
label = "", color = "red"))
ftm <- rbind(ftm, ftmc1, ftmc2)
}
graph <- graph_from_data_frame(ftm, directed = directed)
if (verbose) gplot(graph)
return(graph)
}
#' @title Graph to lavaan model
#'
#' @description Convert an igraph object to a model (lavaan syntax).
#' @param graph A graph as an igraph object.
#' @param nodes Subset of nodes to be included in the model. By default,
#' all the input graph nodes will be included in the output model.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Graph (igraph object) to structural model in lavaan syntax
#' model <- graph2lavaan(sachs$graph)
#' cat(model, "\n")
#'
#' @return A model in lavaan syntax.
#'
graph2lavaan <- function(graph, nodes = V(graph)$name, ...)
{
# Set from-to-matrix representation of edge links
ig <- induced_subgraph(graph, vids = which(V(graph)$name %in% nodes))
ftm <- igraph::as_data_frame(ig)
if (is.directed(ig) & sum(which_mutual(ig)) > 0) {
sel <- as.numeric(c(E(ig)[which_mutual(ig)]))
ftm <- igraph::as_data_frame(ig)[-sel,]
uft <- igraph::as_data_frame(ig)[sel,]
ubg <- as.undirected(graph_from_data_frame(uft))
ftb <- igraph::as_data_frame(ubg)
} else {
ftb <- NULL
}
modelY <- modelV <- vector()
if (is.directed(ig)) {
for(j in 1:nrow(ftm)) {
modelY[j] <- paste0(ftm[j, 2], "~", ftm[j, 1])
}
if (length(ftb) > 0) {
for(k in 1:nrow(ftb)) {
modelV[k] <- paste0(ftb[k, 2], "~~", ftb[k, 1])
}
}
} else {
for(j in 1:nrow(ftm)) modelY[j] <- paste0(ftm[j, 2], "~~", ftm[j, 1])
}
model <- paste(c(sort(modelY), modelV), collapse = "\n")
return(model)
}
#' @title Graph conversion from igraph to dagitty
#'
#' @description Convert an igraph object to a dagitty object.
#' @param graph A graph as an igraph or as an adjacency matrix.
#' @param graphType character, is one of "dag" (default)' or "pdag".
#' DAG can contain the directed (->) and bi-directed (<->) edges,
#' while PDAG can contain the edges: ->, <->, and the undirected edges
#' (--) that represent edges whose direction is not known.
#' @param verbose A logical value. If TRUE, the output graph is shown.
#' This argument is FALSE by default.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Graph as an igraph object to dagitty object
#' G <- graph2dagitty(sachs$graph)
#' plot(dagitty::graphLayout(G))
#'
#' @return A dagitty object.
#'
graph2dagitty<- function (graph, graphType = "dag", verbose = FALSE, ...)
{
if (!is.igraph(graph)) graph <- graph_from_adjacency_matrix(graph)
dg <- graph - E(graph)[which_mutual(graph)]
ug <- as.undirected(graph - E(graph)[!which_mutual(graph)])
ed <- attr(E(dg), "vnames")
eb <- attr(E(ug), "vnames")
de <- paste(gsub("\\|", "->", ed), collapse = "\n")
if (length(eb) == 0) {
dagi <- paste0("dag {\n", de, "\n}")
}
else {
be <- paste(gsub("\\|", "<->", eb), collapse = "\n")
dagi <- paste0("dag {\n", de, "\n", be, "\n}")
}
if (graphType == "pdag"){
dagi <- gsub("<->", "--", dagi)
dagi <- gsub("dag", "pdag", dagi) #cat(dagy)
}
if (verbose) plot(dagitty::graphLayout(dagi))
return(dagi)
}
#' @title Graph conversion from dagitty to igraph
#'
#' @description Convert a dagitty object to a igraph object.
#' @param dagi A graph as a dagitty object ("dag" or "pdag").
#' @param verbose A logical value. If TRUE, the output graph is shown.
#' This argument is FALSE by default.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Conversion from igraph to dagitty (and viceversa)
#' dagi <- graph2dagitty(sachs$graph, verbose = TRUE)
#' graph <- dagitty2graph(dagi, verbose = TRUE)
#'
#' @return An igraph object.
#'
dagitty2graph<- function(dagi, verbose = FALSE, ...)
{
# edges to ftm
edges<- dagitty::edges(dagi)
dsel<- which(edges$e == "->")
d1<- data.frame(from=edges$v[dsel], to=edges$w[dsel])
bsel<- which(edges$e == "<->" | edges$e == "--")
b1<- data.frame(from=edges$v[bsel], to=edges$w[bsel])
b2<- data.frame(from=edges$w[bsel], to=edges$v[bsel])
# ftm to graph
ftm<- rbind(d1,b1,b2)
graph<- graph_from_data_frame(ftm)
if (verbose) gplot(graph)
return(graph)
}
#' @title Convert directed graphs to directed acyclic graphs (DAGs)
#'
#' @description Remove cycles and bidirected edges from a directed graph.
#'
#' @param graph A directed graph as an igraph object.
#' @param data A data matrix with subjects as rows and variables as
#' columns.
#' @param bap If TRUE, a bow-free acyclic path (BAP) is returned
#' (default = FALSE).
#' @param time.limit CPU time for the computation, in seconds
#' (default = Inf).
#' @param ... Currently ignored.
#'
#' @details The conversion is performed firstly by removing bidirected
#' edges and then the data matrix is used to compute edge P-values, through
#' marginal correlation testing (see \code{\link[SEMgraph]{weightGraph}},
#' r-to-z method). When a cycle is detected, the edge with highest
#' P-value is removed, breaking the cycle. If the bap argument is TRUE,
#' a BAP is generated merging the output DAG and the bidirected edges
#' from the input graph.
#'
#' @export
#'
#' @return A DAG as an igraph object.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' dag <- graph2dag(graph = sachs$graph, data = log(sachs$pkc))
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(1,2), mar=rep(1, 4))
#' gplot(sachs$graph, main = "Input graph")
#' gplot(dag, main = "Output DAG")
#' par(old.par)
#'
graph2dag<- function(graph, data, bap = FALSE, time.limit = Inf, ...)
{
if (is_dag(graph)) return(dag=graph)
# graph weighting by edge pvalues (r2z)
graph <- weightGraph(graph, data)
E(graph)$weight <- 1/(-log(E(graph )$pv))
ftm <- igraph::as_data_frame(graph)
wE <- ftm$weight
names(wE) <- paste0(ftm[,1],":",ftm[,2])
# delete all mutual edges <-> , i.e. <- & ->
ig <- graph - E(graph)[which_mutual(graph )]
if (is_dag(ig) & bap == FALSE) {
cat("DAG conversion : TRUE\n")
return(dag = ig)
}
if (is_dag(ig) & bap == TRUE) {
cat("BAP conversion : TRUE\n")
return(bap = graph)
}
# subgraph isomorphism algorithm to detect all cycles of a given length
# time limit: CPU time for the computation, in seconds (defaults=Inf)
find.cycles <- function(graph, k, time.limit) {
ring <- graph.ring(k, TRUE)
subgraph_isomorphisms(ring, graph, "lad", time.limit=time.limit)
}
# function that identifies the right subisomorphisms to keep
subisomorphism_rm_permutation <- function(si) {
is_first_min <- function(x) { return(x[1] == min(x)) }
sel <- lapply(si, is_first_min)
return(si[unlist(sel)])
}
# function that search max(weight) edge on each cycle
max_edges <- function(x){
Ec <- vector()
for (i in 1:(length(x)-1)) Ec<- c(Ec, paste0(x[i],":",x[i+1]))
Ew <- wE[which(names(wE) %in% Ec)]
return(unlist(strsplit(names(Ew)[which(Ew == max(Ew))],":")))
}
for (k in 3:vcount(ig)){ #k=6
# find all cycles with k vertices(edges)
l <- find.cycles(ig, k, time.limit)
# remove permutations
l <- subisomorphism_rm_permutation(si=l)
# extract the vertices in each cycle
if (length(l) == 0) next
cycles <- lapply(1:length(l), function(x) names(l[[x]]))
# edges with max(weight)
l <- unique(lapply(cycles, max_edges))
E1 <- unlist(lapply(l, function(x) paste0(x[1],"|",x[2])))
E0 <- attr(E(ig), "vnames")
ig <- delete_edges(ig, which(E0 %in% E1))
}
if (bap == FALSE) {
cat("DAG conversion :", is_dag(ig),"\n")
return(dag = ig)
}
if (bap == TRUE) {
cat("BAP conversion :", is_dag(ig),"\n")
# add all mutual edges <-> , i.e. <- & ->
e <- as_edgelist(graph-E(graph)[!which_mutual(graph)])
return(bap = add_edges(ig, as.vector(t(e))))
}
}
#' @title Assign edge orientation of an undirected graph
#'
#' @description Assign edge orientation of an undirected graph
#' through a given reference directed graph. The vertex (color)
#' and edge (color, width and weight) attributes of the input
#' undirected graph are preserved in the output directed graph.
#'
#' @param ug An undirected graph as an igraph object.
#' @param dg A directed reference graph.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return A directed graph as an igraph object.
#'
#' @examples
#'
#' # Graphs definition
#' G0 <- as.undirected(sachs$graph)
#'
#' # Reference graph-based orientation
#' G1 <- orientEdges(ug = G0, dg = sachs$graph)
#'
#' # Graphs plotting
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(1,2), mar=rep(2,4))
#' plot(G0, layout=layout.circle, main = "Input undirected graph")
#' plot(G1, layout=layout.circle, main = "Output directed graph")
#' par(old.par)
#'
orientEdges<- function(ug, dg, ...)
{
if (is_directed(ug)){
return(message(" ERROR: the input graph is a Directed graph !"))
}
if (!is_directed(dg)){
return(message(" ERROR: the reference graph is an UNdirected graph !"))
}
# graph edge comparison:
mg <- as.directed(ug, mode = "mutual")
exy0 <- attr(E(mg), "vnames")
exy1 <- attr(E(dg)[which_mutual(dg) == FALSE], "vnames")
exy2 <- exy0[which(exy0 %in% exy1)]
if (length(exy2) == 0) return(graph = mg)
str2 <- strsplit(exy2,"\\|")
ftm1 <- matrix(unlist(str2),nrow=length(str2),byrow=TRUE)
g1 <- graph_from_edgelist(ftm1, directed=TRUE)
# plot(g1, layout=layout.circle)
ug0 <- difference(ug, as.undirected(g1))
mg0 <- as.directed(ug0, mode = "mutual")
#output graph with attr matching:
g <- graph.union(mg0, g1)
gattr<- attrMatch(mg, g)
V(g)$color <- gattr[[1]]
E(g)$color <- gattr[[2]]
E(g)$width <- gattr[[3]]
E(g)$weight <- gattr[[4]]
# plot(g, layout=layout.circle)
return(graph = g)
}
attrMatch<- function(g1, g2, ...)
{
if (!is.null(V(g1)$color)) {
idx<- match(V(g2)$name, V(g1)$name)
Vcol<- V(g1)$color[idx]
}else{
Vcol<- rep(NA, vcount(g2))
}
if (!is.null(E(g1)$color)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ecol<- E(g1)$color[idx]
}else{
Ecol<- rep("gray", ecount(g2))
}
if (!is.null(E(g1)$width)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ewid<- E(g1)$width[idx]
}else{
Ewid<- rep(1, ecount(g2))
}
if (!is.null(E(g1)$weight)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ewei<- E(g1)$weight[idx]
}else{
Ewei<- rep(1, ecount(g2))
}
return(list(Vcol, Ecol, Ewid, Ewei))
}
#' @title Vertex and edge graph coloring on the base of fitting
#'
#' @description Add vertex and edge color attributes to an igraph object,
#' based on a fitting results data.frame generated by
#' \code{\link[SEMgraph]{SEMrun}}.
#' @param est A data.frame of estimated parameters and p-values, derived
#' from the \code{fit} object returned by \code{\link[SEMgraph]{SEMrun}}.
#' As an alternative, the user may provide a "gest" or "dest" data.frame
#' generated by \code{\link[SEMgraph]{SEMrun}}.
#' @param graph An igraph object.
#' @param group group A binary vector. This vector must be as long as the
#' number of subjects. Each vector element must be 1 for cases and 0
#' for control subjects.
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "none" (i.e., no multiple test correction).
#' @param alpha Significance level for node and edge coloring
#' (by default, \code{alpha = 0.05}).
#' @param vcolor A vector of three color names. The first color is given
#' to nodes with P-value < alpha and beta < 0, the third color is given
#' to nodes with P-value < alpha and beta > 0, and the second is given
#' to nodes with P-value > alpha. By default,
#' \code{vcolor = c("lightblue", "white", "pink")}.
#' @param ecolor A vector of three color names. The first color is given
#' to edges with P-value < alpha and regression coefficient < 0, the
#' third color is given to edges with P-value < alpha and regression
#' coefficient > 0, and the second is given to edges with P-value > alpha.
#' By default, \code{vcolor = c("blue", "gray50", "red2")}.
#' @param ewidth A vector of two values. The first value refers to the
#' basic edge width (i.e., edges with P-value > alpha), while the second
#' is given to edges with P-value < alpha. By default ewidth = c(1, 2).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return An igraph object with vertex and edge color and width attributes.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' \donttest{
#' # Model fitting: node perturbation
#' sem1 <- SEMrun(graph = alsData$graph, data = alsData$exprs,
#' group = alsData$group,
#' fit = 1)
#' est1 <- parameterEstimates(sem1$fit)
#'
#' # Model fitting: edge perturbation
#' sem2 <- SEMrun(graph = alsData$graph, data = alsData$exprs,
#' group = alsData$group,
#' fit = 2)
#' est20 <- subset(parameterEstimates(sem2$fit), group == 1)[, -c(4, 5)]
#' est21 <- subset(parameterEstimates(sem2$fit), group == 2)[, -c(4, 5)]
#'
#' # Graphs
#' g <- alsData$graph
#' x <- alsData$group
#'
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(2,2), mar=rep(1,4))
#' gplot(colorGraph(est = est1, g, group = x, method = "BH"),
#' main = "vertex differences")
#' gplot(colorGraph(est = sem2$dest, g, group = NULL),
#' main = "edge differences")
#' gplot(colorGraph(est = est20, g, group = NULL),
#' main = "edges for group = 0")
#' gplot(colorGraph(est = est21, g, group = NULL),
#' main = "edges for group = 1")
#' par(old.par)
#' }
#'
colorGraph <- function (est, graph, group, method = "none", alpha = 0.05,
vcolor = c("lightblue","white", "pink"),
ecolor = c("royalblue3", "gray50", "red2"),
ewidth = c(1, 2), ...)
{
E(graph)$color <- "gray50"
if (!is.null(group)) {
if (colnames(est)[4] == "est") {
B <- est[est$op == "~",]
G <- B[B$rhs == "group",]
B <- B[-c(1:nrow(G)),]
vnames <- gsub("z", "", G$lhs)
G$pvalue <- p.adjust(G$pvalue, method = method)
Vr <- vnames[G$pvalue < alpha & G$est < 0]
Va <- vnames[G$pvalue < alpha & G$est > 0]
V(graph)$color <- ifelse(V(graph)$name %in% Vr, vcolor[1],
ifelse(V(graph)$name %in% Va,
vcolor[3], vcolor[2]))
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue <- p.adjust(B$pvalue, method = method)
Er <- enames[B$pvalue < alpha & B$est < 0]
Ea <- enames[B$pvalue < alpha & B$est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
} else if (colnames(est)[2] == "Stat") {
G <- est
vnames <- gsub("X", "", rownames(G))
G$pvalue <- p.adjust(G$pvalue, method = method)
Vr <- vnames[G$pvalue < alpha & G$Stat < 0]
Va <- vnames[G$pvalue < alpha & G$Stat > 0]
V(graph)$color <- ifelse(V(graph)$name %in% Vr, vcolor[1],
ifelse(V(graph)$name %in% Va,
vcolor[3], vcolor[2]))
}
}
if (is.null(group)) {
if (colnames(est)[4] == "est") {
B <- est[est$op == "~", ]
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue <- p.adjust(B$pvalue, method = method)
Er <- enames[B$pvalue < alpha & B$est < 0]
Ea <- enames[B$pvalue < alpha & B$est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
} else if (colnames(est)[4] == "d_est") {
B <- est[est$op == "~", ]
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue<- p.adjust(B$pvalue, method=method)
Er <- enames[B$pvalue < alpha & B$d_est < 0]
Ea <- enames[B$pvalue < alpha & B$d_est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
}
}
return(graph)
}
#' @title Pairwise plotting of multivariate data
#'
#' @description Display a pairwise scatter plot of two datasets for a
#' random selection of variables. If the second dataset is not given,
#' the function displays a histogram with normal curve superposition.
#'
#' @param x A matrix or data.frame (n x p) of continuous data.
#' @param y A matrix or data.frame (n x q) of continuous data.
#' @param size number of rows to be sampled (default \code{size = nrow(x)}).
#' @param r number of rows of the plot layout (default \code{r = 4}).
#' @param c number of columns of the plot layout (default \code{c = 4}).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return No return value
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#' adjdata <- SEMbap(sachs$graph, log(sachs$pkc))$data
#' rawdata <- log(sachs$pkc)
#' pairwiseMatrix(adjdata, rawdata, size = 1000)
#'
pairwiseMatrix<- function (x, y = NULL, size = nrow(x), r = 4, c = 4, ...)
{
if (r * c > ncol(x)) {
p <- 1:ncol(x)
}else{
p <- sample(1:ncol(x), size = r * c)
}
n <- sample(1:nrow(x), size = size)
if (is.null(y)) {
vnames <- colnames(x)
xx <- x[, vnames]
old.par <- par(no.readonly = TRUE)
par(mfrow = c(r, c), mar = rep(3, 4))
for (j in p) {
h <- hist(xx[n, j], breaks = 30, freq = FALSE, col = "lightblue", main = vnames[j])
x <- seq(-4, +4, by = 0.02)
curve(dnorm(x), add = TRUE, col = "blue", lwd = 2)
}
on.exit(par(old.par))
}
else {
vnames <- intersect(colnames(x), colnames(y))
xx <- x[, vnames]
yy <- y[, vnames]
old.par <- par(no.readonly = TRUE)
par(mfrow = c(r, c), mar = rep(2, 4))
for (j in p) {
r <- round(cor(xx[n, j], yy[n, j]), 2)
plot(xx[n, j], yy[n, j], main = vnames[j])
legend("topleft", paste0("r = ", r), bty = "n", cex = 1, text.col = "blue")
}
on.exit(par(old.par))
}
}
#' @title Node ancestry utilities
#'
#' @description Get ancestry for a collection of nodes in a graph.
#' These functions are wrappers for the original \code{SEMID} R package.
#'
#' @param g An igraph object.
#' @param nodes the nodes in the graph of which to get the ancestry.
#'
#' @references
#'
#' Rina Foygel Barber, Mathias Drton and Luca Weihs (2019). SEMID:
#' Identifiability of Linear Structural Equation Models. R package
#' version 0.3.2. <https://CRAN.R-project.org/package=SEMID/>
#'
#' @examples
#'
#' # Get all ancestors
#' an <- V(sachs$graph)[ancestors(sachs$graph, "Erk")]; an
#'
#' # Get parents
#' pa <- V(sachs$graph)[parents(sachs$graph, "PKC")]; pa
#'
#' # Get descendants
#' de <- V(sachs$graph)[descendants(sachs$graph, "PKA")]; de
#'
#' # Get siblings
#' sib <- V(sachs$graph)[siblings(sachs$graph, "PIP3")]; sib
#'
#' @return a sorted vector of nodes.
#' @name ancestry
#' @rdname ancestry
#' @export
ancestors <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
as.numeric(sort(graph.bfs(g, nodes, mode = "in", unreachable = F)$order,
na.last = NA))
}
#' @rdname ancestry
#' @export
descendants <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
as.numeric(sort(graph.bfs(g, nodes, mode = "out", unreachable = F)$order,
na.last = NA))
}
#' @rdname ancestry
#' @export
parents <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
sort(unique(unlist(neighborhood(g, 1, nodes = nodes, mode = "in"))))
}
#' @rdname ancestry
#' @export
siblings <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
sort(unique(unlist(neighborhood(g, 1, nodes = nodes, mode = "out"))))
}
quiet <- function(..., messages=FALSE, cat=FALSE) {
#quiet <- function(x) {
# sink(tempfile())
# on.exit(sink())
# invisible(force(x))
#}
if(!cat){
tmpf <- tempfile()
sink(tmpf)
on.exit({sink(); file.remove(tmpf)})
}
out <- if(messages) eval(...) else suppressMessages(eval(...))
out
}
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Defines functions quiet siblings parents descendants ancestors attrMatch orientEdges graph2dag dagitty2graph graph2lavaan gplot SEMgsa
Documented in ancestors dagitty2graph descendants gplot graph2dag graph2lavaan orientEdges parents SEMgsa siblings
# SEMgraph library
# Copyright (C) 2019-2021 Mario Grassi; Fernando Palluzzi; Barbara Tarantino
# e-mail: <mario.grassi@unipv.it>
# University of Pavia, Department of Brain and Behavioral Sciences
# Via Bassi 21, 27100 Pavia, Italy
# SEMgraph is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# SEMgraph is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
# -------------------------------------------------------------------- #
#' @title SEM-based gene set analysis
#'
#' @description Gene Set Analysis (GSA) via self-contained test for group
#' effect on signaling (directed) pathways based on SEM. The core of the
#' methodology is implemented in the RICF algorithm of \code{SEMrun()},
#' recovering from RICF output node-specific group effect p-values, and
#' Brown’s combined permutation p-values of node activation and inhibition.
#'
#' @param g A list of pathways to be tested.
#' @param data A matrix or data.frame. Rows correspond to subjects, and
#' columns to graph nodes (variables).
#' @param group A binary vector. This vector must be as long as the number
#' of subjects. Each vector element must be 1 for cases and 0 for control
#' subjects.
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "BH" (i.e., Benjamini-Hochberg correction).
#' @param alpha Gene set test significance level (default = 0.05).
#' @param n_rep Number of randomization replicates (default = 1000).
#' @param ... Currently ignored.
#'
#' @details For gaining more biological insights into the functional roles
#' of pre-defined subsets of genes, node perturbation obtained from RICF
#' fitting has been combined with up- or down-regulation of genes from KEGG
#' to obtain overall pathway perturbation as follows:
#' \itemize{
#' \item The node perturbation is defined as activated when the minimum among
#' the p-values is positive; if negative, the status is inhibited.
#' \item Up- or down- regulation of genes (derived from KEGG database) has
#' been obtained from the weighted adjacency matrix of each pathway as column
#' sum of weights over each source node. If the overall sum of node weights
#' is below 1, the pathway is flagged as down-regulated otherwise as up-regulated.
#' \item The combination between these two quantities allows to define the
#' direction (up or down) of gene perturbation. Up- or down regulated gene status,
#' associated with node inhibition, indicates a decrease in activation (or
#' increase in inhibition) in cases with respect to control group. Conversely,
#' up- or down regulated gene status, associated with node activation, indicates
#' an increase in activation (or decrease in inhibition) in cases with
#' respect to control group.
#' }
#'
#' @return A list of 2 objects:
#' \enumerate{
#' \item "gsa", A data.frame reporting the following information for each
#' pathway in the input list:
#' \itemize{
#' \item "No.nodes", pathway size (number of nodes);
#' \item "No.DEGs", number of differential espression genes (DEGs) within
#' the pathway, after multiple test correction with one of the methods
#' available in \code{\link[stats]{p.adjust}};
#' \item "pert", pathway perturbation status (see details);
#' \item "pNA", Brown's combined P-value of pathway node activation;
#' \item "pNI", Brown's combined P-value of pathway node inhibition;
#' \item "PVAL", Bonferroni combined P-value of pNA, and pNI; i.e.,
#' 2* min(pNA, PNI);
#' \item "ADJP", Adjusted Bonferroni P-value of pathway perturbation; i.e.,
#' min(No.pathways * PVAL; 1).
#' }
#' \item "DEG", a list with DEGs names per pathways.
#' }
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @references
#'
#' Grassi, M., Tarantino, B. SEMgsa: topology-based pathway enrichment analysis with
#' structural equation models. BMC Bioinformatics 23, 344 (2022).
#' https://doi.org/10.1186/s12859-022-04884-8
#'
#' @examples
#'
#' \dontrun{
#'
#' # Nonparanormal(npn) transformation
#' als.npn <- transformData(alsData$exprs)$data
#'
#' # Selection of FTD-ALS pathways from kegg.pathways.Rdata
#'
#' paths.name <- c("MAPK signaling pathway",
#' "Protein processing in endoplasmic reticulum",
#' "Endocytosis",
#' "Wnt signaling pathway",
#' "Neurotrophin signaling pathway",
#' "Amyotrophic lateral sclerosis")
#'
#' j <- which(names(kegg.pathways) %in% paths.name)
#'
#' GSA <- SEMgsa(kegg.pathways[j], als.npn, alsData$group,
#' method = "bonferroni", alpha = 0.05,
#' n_rep = 1000)
#' GSA$gsa
#' GSA$DEG
#'
#' }
#'
SEMgsa<- function(g=list(), data, group, method = "BH", alpha = 0.05, n_rep = 1000, ...)
{
# set loop objects:
gs <- names(g)
K <- length(g)
res.tbl <- NULL
DEG <- list()
for (k in 1:K){
cat( "k =", k, gs[k], "\n" )
ig <- simplify(g[[k]], remove.loops = TRUE)
if (length(E(ig)$weight) == 0) E(ig)$weight <- 1
adj <- as.matrix(get.adjacency(ig, attr = "weight"))
adj <- colSums(adj)
nodes <- ifelse(adj >= 1, 1, ifelse(adj == 0, 0, -1))
status <- ifelse(sum(nodes) >= 1, 1, ifelse(sum(nodes) == 0, 0, -1))
# RICF fitting:
fit <- NULL
err <- paste(" ValueError: Model converged = FALSE for k =",k,"\n")
tryCatch(fit <- quiet(SEMricf(ig, data, group, n_rep)),
error = function(c) cat(err))
if (length(fit[[1]]) == 0) {
res.tbl<- rbind(res.tbl, rep(NA,6))
colnames(res.tbl) <- c("No.nodes","No.DEGs","pert","pNa","pNi","PVAL")
DEG <- c(DEG, list(NULL))
next
}
pval<- fit$gest$pvalue
genes<- gsub("X", "", rownames(fit$gest))
genes<- genes[p.adjust(pval, method=method) < alpha]
DEG<- c(DEG, list(genes))
# data.frame of combined SEM results :
cpval <- fit$fit$pval
names(cpval) <- c("pNa", "pNi")
pvmin <- names(cpval)[which.min(cpval)]
sign <- ifelse(pvmin == "pNa", "+", "-")
if ( status != 0 ) {
if (status == -1 & sign == "-") pert <- "up inh"
else if (status == -1 & sign == "+") pert <- "down inh"
else if (status == 1 & sign == "+") pert <- "up act"
else if (status == 1 & sign == "-") pert <- "down act"
}else{pert <- NA}
df <- data.frame(
No.nodes = vcount(ig),
No.DEGs = sum(p.adjust(pval, method=method) < alpha),
pert = pert,
pNa = cpval[1],
pNi = cpval[2],
PVAL = min(2 * min(cpval[1], cpval[2]), 1)
)
res.tbl <- rbind(res.tbl,df)
}
ADJP <- p.adjust(res.tbl$PVAL, method="bonferroni")
res.tbl<- cbind(res.tbl, ADJP)
rownames(res.tbl) <- names(DEG) <- names(g)
gsa <- res.tbl[order(res.tbl$ADJP),]
DEG <- DEG[rownames(gsa)]
return( list(gsa=gsa, DEG=DEG) )
}
#' @title SEM-based differential network analysis
#'
#' @description Creates a sub-network with perturbed edges obtained from the
#' output of \code{\link[SEMgraph]{SEMace}}, comparable to the procedure in
#' Jablonski et al (2022), or of \code{\link[SEMgraph]{SEMrun}} with two-group
#' and CGGM solver, comparable to the algorithm 2 in Belyaeva et al (2021).
#' To increase the efficiency of computations for large graphs, users can
#' select to break the network structure into clusters, and select the
#' topological clustering method (see \code{\link[SEMgraph]{clusterGraph}}).
#' The function \code{\link[SEMgraph]{SEMrun}} is applied iteratively on
#' each cluster (with size min > 10 and max < 500) to obtain the graph
#' with the full list of perturbed edges.
#'
#' @param graph Input network as an igraph object.
#' @param data A matrix or data.frame. Rows correspond to subjects, and
#' columns to graph nodes (variables).
#' @param group A binary vector. This vector must be as long as the number
#' of subjects. Each vector element must be 1 for cases and 0 for control
#' subjects.
#' @param type Average Causal Effect (ACE) with two-group, "parents"
#' (back-door) adjustement set, and "direct" effects (\code{type = "ace"},
#' default), or CGGM solver with two-group using a clustering method.
#' If \code{type = "tahc"}, network modules are generated using the tree
#' agglomerative hierarchical clustering method, or non-tree clustering
#' methods from igraph package, i.e., \code{type = "wtc"} (walktrap community
#' structure with short random walks), \code{type ="ebc"} (edge betweeness
#' clustering), \code{type = "fgc"} (fast greedy method), \code{type = "lbc"}
#' (label propagation method), \code{type = "lec"} (leading eigenvector method),
#' \code{type = "loc"} (multi-level optimization), \code{type = "opc"} (optimal
#' community structure), \code{type = "sgc"} (spinglass statistical mechanics),
#' \code{type = "none"} (no breaking network structure into clusters).
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "BH" (i.e., FDR multiple test correction).
#' @param alpha Significance level (default = 0.05) for edge set selection.
#' @param ... Currently ignored.
#'
#' @return An igraph object.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @references
#'
#' Belyaeva A, Squires C, Uhler C (2021). DCI: learning causal differences
#' between gene regulatory networks. Bioinformatics, 37(18): 3067–3069.
#' <https://doi: 10.1093/bioinformatics/btab167>
#'
#' Jablonski K, Pirkl M, Ćevid D, Bühlmann P, Beerenwinkel N (2022).
#' Identifying cancer pathway dysregulations using differential
#' causal effects. Bioinformatics, 38(6):1550–1559.
#' <https://doi.org/10.1093/bioinformatics/btab847>
#'
#' @examples
#'
#' \dontrun{
#'
#' #load SEMdata package for ALS data with 17K genes:
#' #devtools::install_github("fernandoPalluzzi/SEMdata")
#' #library(SEMdata)
#'
#' # Nonparanormal(npn) transformation
#' library(huge)
#' data.npn<- huge.npn(alsData$exprs)
#' dim(data.npn) #160 17695
#'
#' # Extract KEGG interactome (max component)
#' KEGG<- properties(kegg)[[1]]
#' summary(KEGG)
#'
#' # KEGG modules with ALS perturbed edges using fast gready clustering
#' gD<- SEMdci(KEGG, data.npn, alsData$group, type="fgc")
#' summary(gD)
#' gcD<- properties(gD)
#'
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(2,2), mar=rep(2,4))
#' gplot(gcD[[1]], l="fdp", main="max component")
#' gplot(gcD[[2]], l="fdp", main="2nd component")
#' gplot(gcD[[3]], l="fdp", main="3rd component")
#' gplot(gcD[[4]], l="fdp", main="4th component")
#' par(old.par)
#'
#' }
#'
SEMdci<- function (graph, data, group, type = "ace", method = "BH", alpha = 0.05, ...)
{
if (type == "ace") {
dest <- SEMace(graph, data, group, type = "parents",
effect = "direct", method = method, alpha = alpha,
boot = NULL)
ftm <- data.frame(from = dest$source, to = dest$sink)
return(gD = graph_from_data_frame(ftm))
}
if (type != "none") {
C <- clusterGraph(graph, type = type, size = 10)
K <- as.numeric(names(table(C)))
gL <- NULL
for (k in 1:length(K)) {
cat("fit cluster =", K[k], "\n")
V <- names(C)[C == K[k]][names(C)[C == K[k]] %in% colnames(data)]
g <- simplify(induced_subgraph(graph, vids = V))
if (vcount(g) > 500 | ecount(g) < 9) next
dest <- tryCatch(quiet(SEMggm2(g, data, group)$dest),
error = function(err) NULL)
if (is.null(dest)) next
dsub <- subset(dest, p.adjust(dest$pvalue, method = method) < alpha)
if (nrow(dsub) == 0) next
ftm <- data.frame(from = dsub$rhs, to = dsub$lhs)
gC <- graph_from_data_frame(ftm)
if (ecount(gC) > 0) gL <- c(gL, list(gC))
}
cat("Done.\n")
if (is.null(gL))
return(gD = make_empty_graph(n = length(K)))
gD <- graph.union(gL)
}
else if (type == "none") {
dest <- quiet(SEMggm2(g, data, group)$dest)
dsub <- subset(dest, p.adjust(dest$pvalue, method = method) < alpha)
ftm <- data.frame(from = dsub$rhs, to = dsub$lhs)
gD <- graph_from_data_frame(ftm)
}
return(gD)
}
#' @title Graph properties summary and graph decomposition
#'
#' @description Produces a summary of network properties and returns
#' graph components (ordered by decreasing size), without self-loops.
#' @param graph Input network as an igraph object.
#' @param data An optional data matrix (default data = NULL) whith rows
#' corresponding to subjects, and columns to graph nodes (variables).
#' Nodes will be mapped onto variable names.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return List of graph components, ordered by decreasing size (the first
#' component is the giant one), without self-loops.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Extract the "Type II diabetes mellitus" pathway:
#' g <- kegg.pathways[["Type II diabetes mellitus"]]
#' summary(g)
#' properties(g)
#'
properties<- function (graph, data = NULL, ...)
{
if (!is_igraph(graph)){
ig <- graph_from_graphnel(graph)
}else{ ig <- graph }
if (!is.null(data)){
nodes <- colnames(data)[colnames(data) %in% V(graph)$name]
ig <- induced_subgraph(graph, vids = which(V(graph)$name %in% nodes))
}
ig <- simplify(ig, remove.loops = TRUE)
gcs <- igraph::decompose.graph(ig, min.vertices = 2)
vsize <- sapply(1:length(gcs), function(x) vcount(gcs[[x]]))
names(vsize) <- 1:length(vsize)
gcs <- gcs[as.numeric(names(sort(vsize, decreasing = TRUE)))]
cat("Frequency distribution of graph components\n\n")
tab <- table(sapply(gcs, vcount))
tab <- data.frame(n.nodes = as.numeric(names(tab)), n.graphs = as.numeric(tab))
print(tab)
cat("\nPercent of vertices in the giant component:",
round(100 * vcount(gcs[[1]])/vcount(ig), 1), "%\n\n")
print(c(is.simple = is_simple(gcs[[1]]), is.dag = is_dag(gcs[[1]]),
is.directed = is_directed(gcs[[1]]), is.weighted = is_weighted(gcs[[1]])))
cat("\n")
print(c(which.mutual = table(which_mutual(gcs[[1]]))))
return(gcs)
}
#' @title Graph plotting with renderGraph
#'
#' @description Wrapper for function renderGraph of the R package
#' Rgraphwiz.
#'
#' @param graph An igraph or graphNEL object.
#' @param l Any layout supported by \code{Rgraphviz}. It can be one among:
#' "dot" (default), "neato", "circo", "fdp", "osage", "twopi".
#' @param main Plot main title (by default, no title is added).
#' @param cex.main Main title size (default = 1).
#' @param font.main Main title font (default = 1). Available options
#' are: 1 for plain text, 2 for bold, 3 for italics, 4 for bold italics,
#' and 5 for symbol.
#' @param color.txt Node text color (default = "black").
#' @param fontsize Node text size (default = 16).
#' @param cex Another argument to control node text size (default = 0.6).
#' @param shape Node shape (default = "circle").
#' @param color Node border color (default = "gray70").
#' @param lty Node border outline (default = 1).
#' Available options include: 0 for blank, 1 for solid line, 2 for dashed,
#' 3 for dotted, 4 for dotdash, 5 for longdash, and 6 for twodash.
#' @param lwd Node border thickness (default = 1).
#' @param h Manual node height (default = "auto").
#' @param w Manual node width (default = "auto").
#' @param psize Automatic node size (default = 80).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return gplot returns invisibly the graph object produced by Rgraphviz
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' gplot(sachs$graph, main = "input graph")
#'
#' sem <- SEMrun(sachs$graph, sachs$pkc)
#' gplot(sem$graph, main = "output graph")
#'
gplot <- function(graph, l = "dot", main = "", cex.main = 1, font.main = 1,
color.txt = "black", fontsize = 16, cex = 0.6,
shape = "circle", color = "gray70", lty = 1, lwd = 1,
w = "auto", h = "auto", psize = 80, ...)
{
# Set graphNEL object
if(is_igraph(graph)){
g <- as_graphnel(graph)
} else {
g <- graph
graph <- graph_from_graphnel(graph)
}
vcol <- V(graph)$color
vshape <- V(graph)$shape
vsize <- V(graph)$size
vlab <- V(graph)$label
ecol <- E(graph)$color
elwd <- E(graph)$width
elab <- E(graph)$label
if (length(vcol) > 0) {
names(vcol) <- V(graph)$name
vcol <- vcol[graph::nodes(g)]
}
if (length(vshape) > 0) {
names(vshape) <- V(graph)$name
vshape <- vshape[graph::nodes(g)]
}
if (length(vsize) > 0) {
names(vsize) <- V(graph)$name
vsize <- 10*vsize[graph::nodes(g)]
} else {
vsize <- rep(psize, length = vcount(graph))
names(vsize) <- V(graph)$name
}
if (length(vlab) > 0) {
names(vlab) <- V(graph)$name
vlab <- vlab[graph::nodes(g)]
}
if (length(color) > 1) {
names(color) <- V(graph)$name
color <- color[graph::nodes(g)]
}
if (length(ecol) > 0) {
names(ecol) <- gsub("\\|", "~", attr(E(graph), "vnames"))
ecol <- ecol[graph::edgeNames(g, recipEdges = "distinct")]
}
if (length(elwd) > 0) {
names(elwd) <- gsub("\\|", "~", attr(E(graph), "vnames"))
elwd <- elwd[graph::edgeNames(g, recipEdges = "distinct")]
}
if (length(elab) > 0) {
names(elab) <- gsub("\\|", "~", attr(E(graph), "vnames"))
elab <- elab[graph::edgeNames(g,recipEdges = "distinct")]
} else {
elab <- rep("", ecount(graph))
names(elab) <- gsub("\\|", "~", attr(E(graph), "vnames"))
}
if (graph::isDirected(g)) {
g <- Rgraphviz::layoutGraph(g, layoutType = l,
edgeAttrs = list(label = elab))
} else {
g <- Rgraphviz::layoutGraph(g, layoutType = "fdp",
edgeAttrs = list(label = elab))
}
if (w == "auto") w <- vsize
if (h == "auto") h <- vsize
g<- Rgraphviz::layoutGraph(g, layoutType=l, edgeAttrs=list(label=elab))
graph::nodeRenderInfo(g)<- list(col = color, fill = vcol, label = vlab,
lwd = lwd, lty = lty,
textCol = color.txt,
fontsize = fontsize, cex = cex,
shape = vshape, width = w, height = h)
graph::edgeRenderInfo(g) <- list(col = ecol, lty = lty, lwd = elwd)
graph::graphRenderInfo(g) <- list(main = main, cex.main = cex.main,
font.main = font.main)
Rgraphviz::renderGraph(g)
return(invisible(g))
}
#' @title lavaan model to graph
#'
#' @description Convert a model, specified using lavaan syntax,
#' to an igraph object.
#' @param model Model specified using lavaan syntax.
#' @param directed Logical value. If TRUE (default), edge directions from
#' the model will be preserved. If FALSE, the resulting graph will
#' be undirected.
#' @param psi Logical value. If TRUE (default) covariances will be converted
#' into bidirected graph edges. If FALSE, covariances will be excluded from
#' the output graph.
#' @param verbose Logical value. If TRUE, a plot of the output graph will
#' be generated. For large graphs, this could significantly increase
#' computation time. If FALSE (default), graph plotting will be disabled.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return An igraph object.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Writing path diagram in lavaan syntax
#'
#' model<-"
#' #path model
#' Jnk ~ PKA + PKC
#' P38 ~ PKA + PKC
#' Akt ~ PKA + PIP3
#' Erk ~ PKA + Mek
#' Mek ~ PKA + PKC + Raf
#' Raf ~ PKA + PKC
#' PKC ~ PIP2 + Plcg
#' PIP2 ~ PIP3 + Plcg
#' Plcg ~ PIP3
#'
#' #(co)variances
#' PKA ~~ PIP3
#' "
#'
#' # Graph with covariances
#' G0 <- lavaan2graph(model, psi = TRUE)
#' plot(G0, layout = layout.circle)
#'
#' # Graph without covariances
#' G1 <- lavaan2graph(model, psi = FALSE)
#' plot(G1, layout = layout.circle)
#'
lavaan2graph<- function (model, directed = TRUE, psi = TRUE, verbose = FALSE, ...)
{
lav <- lavParTable(model, fixed.x = FALSE)
lavb <- subset(lav, lav$op == "~")
lavc <- subset(lav, lav$op == "~~" & (lav$rhs != lav$lhs))
lavc<- lavc[lavc$user == 1,]
ftm <- data.frame(cbind(from = lavb$rhs, to = lavb$lhs, label = lavb$label),
color = "black")
if (nrow(lavc) != 0 & psi == TRUE) {
ftmc1 <- data.frame(cbind(from = lavc$rhs, to = lavc$lhs,
label = "", color = "red"))
ftmc2 <- data.frame(cbind(from = lavc$lhs, to = lavc$rhs,
label = "", color = "red"))
ftm <- rbind(ftm, ftmc1, ftmc2)
}
graph <- graph_from_data_frame(ftm, directed = directed)
if (verbose) gplot(graph)
return(graph)
}
#' @title Graph to lavaan model
#'
#' @description Convert an igraph object to a model (lavaan syntax).
#' @param graph A graph as an igraph object.
#' @param nodes Subset of nodes to be included in the model. By default,
#' all the input graph nodes will be included in the output model.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Graph (igraph object) to structural model in lavaan syntax
#' model <- graph2lavaan(sachs$graph)
#' cat(model, "\n")
#'
#' @return A model in lavaan syntax.
#'
graph2lavaan <- function(graph, nodes = V(graph)$name, ...)
{
# Set from-to-matrix representation of edge links
ig <- induced_subgraph(graph, vids = which(V(graph)$name %in% nodes))
ftm <- igraph::as_data_frame(ig)
if (is.directed(ig) & sum(which_mutual(ig)) > 0) {
sel <- as.numeric(c(E(ig)[which_mutual(ig)]))
ftm <- igraph::as_data_frame(ig)[-sel,]
uft <- igraph::as_data_frame(ig)[sel,]
ubg <- as.undirected(graph_from_data_frame(uft))
ftb <- igraph::as_data_frame(ubg)
} else {
ftb <- NULL
}
modelY <- modelV <- vector()
if (is.directed(ig)) {
for(j in 1:nrow(ftm)) {
modelY[j] <- paste0(ftm[j, 2], "~", ftm[j, 1])
}
if (length(ftb) > 0) {
for(k in 1:nrow(ftb)) {
modelV[k] <- paste0(ftb[k, 2], "~~", ftb[k, 1])
}
}
} else {
for(j in 1:nrow(ftm)) modelY[j] <- paste0(ftm[j, 2], "~~", ftm[j, 1])
}
model <- paste(c(sort(modelY), modelV), collapse = "\n")
return(model)
}
#' @title Graph conversion from igraph to dagitty
#'
#' @description Convert an igraph object to a dagitty object.
#' @param graph A graph as an igraph or as an adjacency matrix.
#' @param graphType character, is one of "dag" (default)' or "pdag".
#' DAG can contain the directed (->) and bi-directed (<->) edges,
#' while PDAG can contain the edges: ->, <->, and the undirected edges
#' (--) that represent edges whose direction is not known.
#' @param verbose A logical value. If TRUE, the output graph is shown.
#' This argument is FALSE by default.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Graph as an igraph object to dagitty object
#' G <- graph2dagitty(sachs$graph)
#' plot(dagitty::graphLayout(G))
#'
#' @return A dagitty object.
#'
graph2dagitty<- function (graph, graphType = "dag", verbose = FALSE, ...)
{
if (!is.igraph(graph)) graph <- graph_from_adjacency_matrix(graph)
dg <- graph - E(graph)[which_mutual(graph)]
ug <- as.undirected(graph - E(graph)[!which_mutual(graph)])
ed <- attr(E(dg), "vnames")
eb <- attr(E(ug), "vnames")
de <- paste(gsub("\\|", "->", ed), collapse = "\n")
if (length(eb) == 0) {
dagi <- paste0("dag {\n", de, "\n}")
}
else {
be <- paste(gsub("\\|", "<->", eb), collapse = "\n")
dagi <- paste0("dag {\n", de, "\n", be, "\n}")
}
if (graphType == "pdag"){
dagi <- gsub("<->", "--", dagi)
dagi <- gsub("dag", "pdag", dagi) #cat(dagy)
}
if (verbose) plot(dagitty::graphLayout(dagi))
return(dagi)
}
#' @title Graph conversion from dagitty to igraph
#'
#' @description Convert a dagitty object to a igraph object.
#' @param dagi A graph as a dagitty object ("dag" or "pdag").
#' @param verbose A logical value. If TRUE, the output graph is shown.
#' This argument is FALSE by default.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' # Conversion from igraph to dagitty (and viceversa)
#' dagi <- graph2dagitty(sachs$graph, verbose = TRUE)
#' graph <- dagitty2graph(dagi, verbose = TRUE)
#'
#' @return An igraph object.
#'
dagitty2graph<- function(dagi, verbose = FALSE, ...)
{
# edges to ftm
edges<- dagitty::edges(dagi)
dsel<- which(edges$e == "->")
d1<- data.frame(from=edges$v[dsel], to=edges$w[dsel])
bsel<- which(edges$e == "<->" | edges$e == "--")
b1<- data.frame(from=edges$v[bsel], to=edges$w[bsel])
b2<- data.frame(from=edges$w[bsel], to=edges$v[bsel])
# ftm to graph
ftm<- rbind(d1,b1,b2)
graph<- graph_from_data_frame(ftm)
if (verbose) gplot(graph)
return(graph)
}
#' @title Convert directed graphs to directed acyclic graphs (DAGs)
#'
#' @description Remove cycles and bidirected edges from a directed graph.
#'
#' @param graph A directed graph as an igraph object.
#' @param data A data matrix with subjects as rows and variables as
#' columns.
#' @param bap If TRUE, a bow-free acyclic path (BAP) is returned
#' (default = FALSE).
#' @param time.limit CPU time for the computation, in seconds
#' (default = Inf).
#' @param ... Currently ignored.
#'
#' @details The conversion is performed firstly by removing bidirected
#' edges and then the data matrix is used to compute edge P-values, through
#' marginal correlation testing (see \code{\link[SEMgraph]{weightGraph}},
#' r-to-z method). When a cycle is detected, the edge with highest
#' P-value is removed, breaking the cycle. If the bap argument is TRUE,
#' a BAP is generated merging the output DAG and the bidirected edges
#' from the input graph.
#'
#' @export
#'
#' @return A DAG as an igraph object.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' dag <- graph2dag(graph = sachs$graph, data = log(sachs$pkc))
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(1,2), mar=rep(1, 4))
#' gplot(sachs$graph, main = "Input graph")
#' gplot(dag, main = "Output DAG")
#' par(old.par)
#'
graph2dag<- function(graph, data, bap = FALSE, time.limit = Inf, ...)
{
if (is_dag(graph)) return(dag=graph)
# graph weighting by edge pvalues (r2z)
graph <- weightGraph(graph, data)
E(graph)$weight <- 1/(-log(E(graph )$pv))
ftm <- igraph::as_data_frame(graph)
wE <- ftm$weight
names(wE) <- paste0(ftm[,1],":",ftm[,2])
# delete all mutual edges <-> , i.e. <- & ->
ig <- graph - E(graph)[which_mutual(graph )]
if (is_dag(ig) & bap == FALSE) {
cat("DAG conversion : TRUE\n")
return(dag = ig)
}
if (is_dag(ig) & bap == TRUE) {
cat("BAP conversion : TRUE\n")
return(bap = graph)
}
# subgraph isomorphism algorithm to detect all cycles of a given length
# time limit: CPU time for the computation, in seconds (defaults=Inf)
find.cycles <- function(graph, k, time.limit) {
ring <- graph.ring(k, TRUE)
subgraph_isomorphisms(ring, graph, "lad", time.limit=time.limit)
}
# function that identifies the right subisomorphisms to keep
subisomorphism_rm_permutation <- function(si) {
is_first_min <- function(x) { return(x[1] == min(x)) }
sel <- lapply(si, is_first_min)
return(si[unlist(sel)])
}
# function that search max(weight) edge on each cycle
max_edges <- function(x){
Ec <- vector()
for (i in 1:(length(x)-1)) Ec<- c(Ec, paste0(x[i],":",x[i+1]))
Ew <- wE[which(names(wE) %in% Ec)]
return(unlist(strsplit(names(Ew)[which(Ew == max(Ew))],":")))
}
for (k in 3:vcount(ig)){ #k=6
# find all cycles with k vertices(edges)
l <- find.cycles(ig, k, time.limit)
# remove permutations
l <- subisomorphism_rm_permutation(si=l)
# extract the vertices in each cycle
if (length(l) == 0) next
cycles <- lapply(1:length(l), function(x) names(l[[x]]))
# edges with max(weight)
l <- unique(lapply(cycles, max_edges))
E1 <- unlist(lapply(l, function(x) paste0(x[1],"|",x[2])))
E0 <- attr(E(ig), "vnames")
ig <- delete_edges(ig, which(E0 %in% E1))
}
if (bap == FALSE) {
cat("DAG conversion :", is_dag(ig),"\n")
return(dag = ig)
}
if (bap == TRUE) {
cat("BAP conversion :", is_dag(ig),"\n")
# add all mutual edges <-> , i.e. <- & ->
e <- as_edgelist(graph-E(graph)[!which_mutual(graph)])
return(bap = add_edges(ig, as.vector(t(e))))
}
}
#' @title Assign edge orientation of an undirected graph
#'
#' @description Assign edge orientation of an undirected graph
#' through a given reference directed graph. The vertex (color)
#' and edge (color, width and weight) attributes of the input
#' undirected graph are preserved in the output directed graph.
#'
#' @param ug An undirected graph as an igraph object.
#' @param dg A directed reference graph.
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return A directed graph as an igraph object.
#'
#' @examples
#'
#' # Graphs definition
#' G0 <- as.undirected(sachs$graph)
#'
#' # Reference graph-based orientation
#' G1 <- orientEdges(ug = G0, dg = sachs$graph)
#'
#' # Graphs plotting
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(1,2), mar=rep(2,4))
#' plot(G0, layout=layout.circle, main = "Input undirected graph")
#' plot(G1, layout=layout.circle, main = "Output directed graph")
#' par(old.par)
#'
orientEdges<- function(ug, dg, ...)
{
if (is_directed(ug)){
return(message(" ERROR: the input graph is a Directed graph !"))
}
if (!is_directed(dg)){
return(message(" ERROR: the reference graph is an UNdirected graph !"))
}
# graph edge comparison:
mg <- as.directed(ug, mode = "mutual")
exy0 <- attr(E(mg), "vnames")
exy1 <- attr(E(dg)[which_mutual(dg) == FALSE], "vnames")
exy2 <- exy0[which(exy0 %in% exy1)]
if (length(exy2) == 0) return(graph = mg)
str2 <- strsplit(exy2,"\\|")
ftm1 <- matrix(unlist(str2),nrow=length(str2),byrow=TRUE)
g1 <- graph_from_edgelist(ftm1, directed=TRUE)
# plot(g1, layout=layout.circle)
ug0 <- difference(ug, as.undirected(g1))
mg0 <- as.directed(ug0, mode = "mutual")
#output graph with attr matching:
g <- graph.union(mg0, g1)
gattr<- attrMatch(mg, g)
V(g)$color <- gattr[[1]]
E(g)$color <- gattr[[2]]
E(g)$width <- gattr[[3]]
E(g)$weight <- gattr[[4]]
# plot(g, layout=layout.circle)
return(graph = g)
}
attrMatch<- function(g1, g2, ...)
{
if (!is.null(V(g1)$color)) {
idx<- match(V(g2)$name, V(g1)$name)
Vcol<- V(g1)$color[idx]
}else{
Vcol<- rep(NA, vcount(g2))
}
if (!is.null(E(g1)$color)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ecol<- E(g1)$color[idx]
}else{
Ecol<- rep("gray", ecount(g2))
}
if (!is.null(E(g1)$width)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ewid<- E(g1)$width[idx]
}else{
Ewid<- rep(1, ecount(g2))
}
if (!is.null(E(g1)$weight)) {
idx<- match(attr(E(g2), "vnames"), attr(E(g1), "vnames"))
Ewei<- E(g1)$weight[idx]
}else{
Ewei<- rep(1, ecount(g2))
}
return(list(Vcol, Ecol, Ewid, Ewei))
}
#' @title Vertex and edge graph coloring on the base of fitting
#'
#' @description Add vertex and edge color attributes to an igraph object,
#' based on a fitting results data.frame generated by
#' \code{\link[SEMgraph]{SEMrun}}.
#' @param est A data.frame of estimated parameters and p-values, derived
#' from the \code{fit} object returned by \code{\link[SEMgraph]{SEMrun}}.
#' As an alternative, the user may provide a "gest" or "dest" data.frame
#' generated by \code{\link[SEMgraph]{SEMrun}}.
#' @param graph An igraph object.
#' @param group group A binary vector. This vector must be as long as the
#' number of subjects. Each vector element must be 1 for cases and 0
#' for control subjects.
#' @param method Multiple testing correction method. One of the values
#' available in \code{\link[stats]{p.adjust}}. By default, method is set
#' to "none" (i.e., no multiple test correction).
#' @param alpha Significance level for node and edge coloring
#' (by default, \code{alpha = 0.05}).
#' @param vcolor A vector of three color names. The first color is given
#' to nodes with P-value < alpha and beta < 0, the third color is given
#' to nodes with P-value < alpha and beta > 0, and the second is given
#' to nodes with P-value > alpha. By default,
#' \code{vcolor = c("lightblue", "white", "pink")}.
#' @param ecolor A vector of three color names. The first color is given
#' to edges with P-value < alpha and regression coefficient < 0, the
#' third color is given to edges with P-value < alpha and regression
#' coefficient > 0, and the second is given to edges with P-value > alpha.
#' By default, \code{vcolor = c("blue", "gray50", "red2")}.
#' @param ewidth A vector of two values. The first value refers to the
#' basic edge width (i.e., edges with P-value > alpha), while the second
#' is given to edges with P-value < alpha. By default ewidth = c(1, 2).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return An igraph object with vertex and edge color and width attributes.
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#'
#' \donttest{
#' # Model fitting: node perturbation
#' sem1 <- SEMrun(graph = alsData$graph, data = alsData$exprs,
#' group = alsData$group,
#' fit = 1)
#' est1 <- parameterEstimates(sem1$fit)
#'
#' # Model fitting: edge perturbation
#' sem2 <- SEMrun(graph = alsData$graph, data = alsData$exprs,
#' group = alsData$group,
#' fit = 2)
#' est20 <- subset(parameterEstimates(sem2$fit), group == 1)[, -c(4, 5)]
#' est21 <- subset(parameterEstimates(sem2$fit), group == 2)[, -c(4, 5)]
#'
#' # Graphs
#' g <- alsData$graph
#' x <- alsData$group
#'
#' old.par <- par(no.readonly = TRUE)
#' par(mfrow=c(2,2), mar=rep(1,4))
#' gplot(colorGraph(est = est1, g, group = x, method = "BH"),
#' main = "vertex differences")
#' gplot(colorGraph(est = sem2$dest, g, group = NULL),
#' main = "edge differences")
#' gplot(colorGraph(est = est20, g, group = NULL),
#' main = "edges for group = 0")
#' gplot(colorGraph(est = est21, g, group = NULL),
#' main = "edges for group = 1")
#' par(old.par)
#' }
#'
colorGraph <- function (est, graph, group, method = "none", alpha = 0.05,
vcolor = c("lightblue","white", "pink"),
ecolor = c("royalblue3", "gray50", "red2"),
ewidth = c(1, 2), ...)
{
E(graph)$color <- "gray50"
if (!is.null(group)) {
if (colnames(est)[4] == "est") {
B <- est[est$op == "~",]
G <- B[B$rhs == "group",]
B <- B[-c(1:nrow(G)),]
vnames <- gsub("z", "", G$lhs)
G$pvalue <- p.adjust(G$pvalue, method = method)
Vr <- vnames[G$pvalue < alpha & G$est < 0]
Va <- vnames[G$pvalue < alpha & G$est > 0]
V(graph)$color <- ifelse(V(graph)$name %in% Vr, vcolor[1],
ifelse(V(graph)$name %in% Va,
vcolor[3], vcolor[2]))
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue <- p.adjust(B$pvalue, method = method)
Er <- enames[B$pvalue < alpha & B$est < 0]
Ea <- enames[B$pvalue < alpha & B$est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
} else if (colnames(est)[2] == "Stat") {
G <- est
vnames <- gsub("X", "", rownames(G))
G$pvalue <- p.adjust(G$pvalue, method = method)
Vr <- vnames[G$pvalue < alpha & G$Stat < 0]
Va <- vnames[G$pvalue < alpha & G$Stat > 0]
V(graph)$color <- ifelse(V(graph)$name %in% Vr, vcolor[1],
ifelse(V(graph)$name %in% Va,
vcolor[3], vcolor[2]))
}
}
if (is.null(group)) {
if (colnames(est)[4] == "est") {
B <- est[est$op == "~", ]
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue <- p.adjust(B$pvalue, method = method)
Er <- enames[B$pvalue < alpha & B$est < 0]
Ea <- enames[B$pvalue < alpha & B$est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
} else if (colnames(est)[4] == "d_est") {
B <- est[est$op == "~", ]
enames <- gsub("z", "", paste0(B$rhs, "|", B$lhs))
B$pvalue<- p.adjust(B$pvalue, method=method)
Er <- enames[B$pvalue < alpha & B$d_est < 0]
Ea <- enames[B$pvalue < alpha & B$d_est > 0]
E(graph)$color <- ifelse(attr(E(graph), "vnames") %in%
Er, ecolor[1], ifelse(attr(E(graph), "vnames") %in%
Ea, ecolor[3], ecolor[2]))
E(graph)$width <- ifelse(E(graph)$color == ecolor[2],
ewidth[1], ewidth[2])
}
}
return(graph)
}
#' @title Pairwise plotting of multivariate data
#'
#' @description Display a pairwise scatter plot of two datasets for a
#' random selection of variables. If the second dataset is not given,
#' the function displays a histogram with normal curve superposition.
#'
#' @param x A matrix or data.frame (n x p) of continuous data.
#' @param y A matrix or data.frame (n x q) of continuous data.
#' @param size number of rows to be sampled (default \code{size = nrow(x)}).
#' @param r number of rows of the plot layout (default \code{r = 4}).
#' @param c number of columns of the plot layout (default \code{c = 4}).
#' @param ... Currently ignored.
#'
#' @export
#'
#' @return No return value
#'
#' @author Mario Grassi \email{mario.grassi@unipv.it}
#'
#' @examples
#' adjdata <- SEMbap(sachs$graph, log(sachs$pkc))$data
#' rawdata <- log(sachs$pkc)
#' pairwiseMatrix(adjdata, rawdata, size = 1000)
#'
pairwiseMatrix<- function (x, y = NULL, size = nrow(x), r = 4, c = 4, ...)
{
if (r * c > ncol(x)) {
p <- 1:ncol(x)
}else{
p <- sample(1:ncol(x), size = r * c)
}
n <- sample(1:nrow(x), size = size)
if (is.null(y)) {
vnames <- colnames(x)
xx <- x[, vnames]
old.par <- par(no.readonly = TRUE)
par(mfrow = c(r, c), mar = rep(3, 4))
for (j in p) {
h <- hist(xx[n, j], breaks = 30, freq = FALSE, col = "lightblue", main = vnames[j])
x <- seq(-4, +4, by = 0.02)
curve(dnorm(x), add = TRUE, col = "blue", lwd = 2)
}
on.exit(par(old.par))
}
else {
vnames <- intersect(colnames(x), colnames(y))
xx <- x[, vnames]
yy <- y[, vnames]
old.par <- par(no.readonly = TRUE)
par(mfrow = c(r, c), mar = rep(2, 4))
for (j in p) {
r <- round(cor(xx[n, j], yy[n, j]), 2)
plot(xx[n, j], yy[n, j], main = vnames[j])
legend("topleft", paste0("r = ", r), bty = "n", cex = 1, text.col = "blue")
}
on.exit(par(old.par))
}
}
#' @title Node ancestry utilities
#'
#' @description Get ancestry for a collection of nodes in a graph.
#' These functions are wrappers for the original \code{SEMID} R package.
#'
#' @param g An igraph object.
#' @param nodes the nodes in the graph of which to get the ancestry.
#'
#' @references
#'
#' Rina Foygel Barber, Mathias Drton and Luca Weihs (2019). SEMID:
#' Identifiability of Linear Structural Equation Models. R package
#' version 0.3.2. <https://CRAN.R-project.org/package=SEMID/>
#'
#' @examples
#'
#' # Get all ancestors
#' an <- V(sachs$graph)[ancestors(sachs$graph, "Erk")]; an
#'
#' # Get parents
#' pa <- V(sachs$graph)[parents(sachs$graph, "PKC")]; pa
#'
#' # Get descendants
#' de <- V(sachs$graph)[descendants(sachs$graph, "PKA")]; de
#'
#' # Get siblings
#' sib <- V(sachs$graph)[siblings(sachs$graph, "PIP3")]; sib
#'
#' @return a sorted vector of nodes.
#' @name ancestry
#' @rdname ancestry
#' @export
ancestors <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
as.numeric(sort(graph.bfs(g, nodes, mode = "in", unreachable = F)$order,
na.last = NA))
}
#' @rdname ancestry
#' @export
descendants <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
as.numeric(sort(graph.bfs(g, nodes, mode = "out", unreachable = F)$order,
na.last = NA))
}
#' @rdname ancestry
#' @export
parents <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
sort(unique(unlist(neighborhood(g, 1, nodes = nodes, mode = "in"))))
}
#' @rdname ancestry
#' @export
siblings <- function(g, nodes)
{
if (vcount(g) == 0 || length(nodes) == 0) {
return(numeric(0))
}
sort(unique(unlist(neighborhood(g, 1, nodes = nodes, mode = "out"))))
}
quiet <- function(..., messages=FALSE, cat=FALSE) {
#quiet <- function(x) {
# sink(tempfile())
# on.exit(sink())
# invisible(force(x))
#}
if(!cat){
tmpf <- tempfile()
sink(tmpf)
on.exit({sink(); file.remove(tmpf)})
}
out <- if(messages) eval(...) else suppressMessages(eval(...))
out
}
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