#' @title Partial correlation analysis
#' @description A method that integrates differential expression (DE) analysis and differential
#' network (DN) analysis to select biomarker candidates for cancer studies. partial_cor is the
#' second step of the partial correlation calculation after getting the result from select_rho_partial function.
#' @param data_list This is a list of pre-processed data outputted by the select_rho_partial function.
#' @param rho_group1 This is a character string indicating the rule for choosing rho value for group 1,
#' "min": minimum rho, "ste": one standard error from minimum, or user can input rho of their choice. The default
#' is minimum.
#' @param rho_group2 This is a character string indicating the rule for choosing rho value for group 2,
#' "min": minimum rho, "ste": one standard error from minimum, or user can input rho of their choice, the default
#' is minimum.
#' @param p_val This is optional. It is a p*1 dataframe that contains the p-value for each biomolecule from DE analysis.
#' @param permutation This is a positive integer representing the desired number of permutations.
#' The default is 1000.
#' @param permutation_thres This is a integer representing the threshold for the permutation test.
#' The default is 0.05 to achieve 95 percent confidence.
#' @param fdr This is a boolean value indicating whether to apply multiple testing correction (TRUE)
#' or not (FALSE). The default is TRUE. However, if users find the output network is too sparse
#' even after relaxing the permutation_thres, it's probably a good idea to turn off the multiple testing correction.
#' @examples
#' # step 1: select_rho_partial
#' pre_data <- select_rho_partial(data = Met_GU, class_label = Met_Group_GU, id = Met_name_GU, error_curve = TRUE)
#' # step 2: partial_cor
#' result <- partial_cor(data_list = pre_data, rho_group1 = 'min', rho_group2 = "min", p_val = pvalue_M_GU, permutation = 1000,
#' permutation_thres = 0.05, fdr = TRUE)
#' @return A list containing an activity score dataframe with "ID", "P_value", "Node_Degree" and
#' "Activity_Score" as columns and a differential network dataframe with the binary and the
#' weight connection values.
#' @import devtools
#' @importFrom glasso glasso
#' @importFrom stats qnorm cor quantile var sd glm
#' @importFrom graphics abline title plot lines par
#' @export
partial_cor <- function(data_list = NULL, rho_group1 = NULL, rho_group2 = NULL, p_val = NULL,
permutation = 1000, permutation_thres = 0.05, fdr = TRUE){
if(missing(data_list)) {stop("please provide data_list from select_rho_partial function")}
else{
# group 1
if (rho_group1 =='min'){ rho_group_1_opt = data_list$rho_table["minimum",1] }
else if (rho_group1 =='ste'){ rho_group_1_opt = data_list$rho_table["one standard error",1] }
else if (is.numeric(rho_group1) & rho_group1>0) {rho_group_1_opt = rho_group1}
else if (is.numeric(rho_group1) & rho_group1<=0)
{stop("please provide data_list from select_rho_partial function")}
# default is minimum rho if no rule specified and no valid input entered
else {rho_group_1_opt = data_list$rho_table["minimum",1]}
# group 2
if (rho_group2 =='min'){ rho_group_2_opt = data_list$rho_table["minimum",2] }
else if (rho_group2 =='ste'){ rho_group_2_opt = data_list$rho_table["one standard error",2] }
else if (is.numeric(rho_group2) & rho_group2>0) {rho_group_2_opt = rho_group2}
else if (is.numeric(rho_group2) & rho_group2<=0)
{stop("please provide data_list from select_rho_partial function")}
# default is minimum rho if no rule specified and no valid input entered
else {rho_group_2_opt = data_list$rho_table["minimum",2]}
## Compute precision matrix for group 1
pre_group_1 <- glasso(data_list$cov_group_1, rho = rho_group_1_opt)
# thres <- 1e-3
# sum(abs(pre_group_1$wi) > thres)
# pre_group_1$wi[1:10, 1:10]
## Compute partial correlation for group 1
pc_group_1 <- compute_par(pre_group_1$wi)
# # examine the partial correlation matrix
# sum(abs(pc_group_1) > thres)
# pc_group_1[1:10, 1:10]
## Compute precision matrix for group 2
pre_group_2 <- glasso(data_list$cov_group_2, rho = rho_group_2_opt)
# # examine the precision matrix
# sum(abs(pre_group_2$wi) > thres)
# pre_group_2$wi[1:10,1:10]
## Compute partial correlation for group 2
pc_group_2 <- compute_par(pre_group_2$wi)
# # examine the partial correlation matrix
# sum(abs(pc_group_2) > thres)
# pc_group_2[1:10,1:10]
## Differential network
diff <- pc_group_2 - pc_group_1 # from group 1 to group 2
# thres = 1e-3
# sum(abs(diff) > thres)
# diff[1:10, 1:10]
## Permutation test using partial correlation
if(permutation <= 0)
{stop("please provide a valid number of permutation (positive integer)")}
else{
m <- as.numeric(permutation)
diff_p <- permutation_pc(m, data_list$p, data_list$n_group_1, data_list$n_group_2,
data_list$data_group_1, data_list$data_group_2,
rho_group_1_opt, rho_group_2_opt)
p <- data_list$p
## Multiple testing step
# p-value for edges
pvalue_edge <- compute_pvalue_edge(p, diff, diff_p, m)
# fdr to adjust multiple testing
if(fdr == TRUE){
pvalue_edge_fdr <- compute_pvalue_edge_fdr(p, pvalue_edge)
}
else{
pvalue_edge_fdr <- pvalue_edge
}
}
rm(m)
## Get binary and weight matrix
binary_link <- matrix(0, p, p) # binary connection
binary_link[pvalue_edge_fdr < permutation_thres] <- 1
binary_link[(pvalue_edge_fdr < permutation_thres) & (diff < 0)] <- -1
weight_link <- compute_edge_weights(pvalue_edge_fdr, binary_link)
# binary_link[1:10, 1:10]
# weight_link[1:10, 1:10]
# rowSums(abs(binary_link)) # node degree for differential networks
# rm(diff_p)
## Convert adjacent matrix into edge list
i <- rep(seq_len(nrow(binary_link) - 1), times = (nrow(binary_link)-1):1)
k <- unlist(lapply(2:nrow(binary_link), seq, nrow(binary_link)))
binary_link_value <- binary_link[lower.tri(binary_link)]
weight_link_value <- weight_link[lower.tri(weight_link)]
edge <- cbind("Node1" = i, "Node2" = k, "Binary" = binary_link_value,
"Weight" = weight_link_value)
edge_dn <- edge[which(edge[,3] != 0),]
edge_dn <- as.data.frame(edge_dn)
## Compute p-values
if (is.null(p_val) == TRUE) {
# calculate p-values using logistic regression if p-values are not provided by users
pvalue <- pvalue_logit(data_list$data, data_list$class_label, data_list$id)
p.value <- pvalue$p.value
row.names(pvalue)<-NULL
} else { # if the p-value matrix is provided
pvalue <- p_val
p.value <- pvalue$p.value # extract p-values from the table provided
row.names(pvalue)<-NULL
}
## Transfer p-value to z-score
z_score <- abs(qnorm(1 - p.value/2))
## calculate differntial network score
dn_score <- compute_dns(binary_link, z_score)
indeed_df <- cbind(pvalue, rowSums(abs(binary_link)), dn_score )
colnames(indeed_df) <- c("ID", "P_value", "Node_Degree", "Activity_Score")
indeed_df$P_value <- lapply(indeed_df$P_value, round, 3)
indeed_df$Activity_Score <- lapply(indeed_df$Activity_Score, round, 1)
indeed_df <- as.data.frame(lapply(indeed_df, unlist))
## Recopy dataframe with index to help with ighraph formating
indeed_df <- cbind(rownames(indeed_df) , data.frame(indeed_df, row.names=NULL) )
colnames(indeed_df)[1] <- "Node" # rename the previous index column as "Node"
indeed_df<-indeed_df[order(indeed_df$Activity_Score, decreasing=TRUE), ]
row.names(indeed_df) <- NULL # remove index repeat
## Return
result_list <-list(activity_score=indeed_df, diff_network=edge_dn)
return (result_list)
}
}
Datasets
Models
