# This document contains two functions, stand.path.score and Bayes.model. The first one computes 
# the standardized pathway score for any given pathway, and the second function performs Bayesian 
# logistic regression for 1 or more than 1 pathways. 

# Two examples are provided in this document. Input data and example output are attached. The gene expression
# data for illustration were a subset of the data with accession number GSE69240 from NCBI GEO database.

# Note: For the Bayesian analysis, "OpenBUGS" and the R packages "R2OpenBIGS" need to be installed 
install.packages("R2OpenBUGS")
library(R2OpenBUGS)

### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 
### For each pathway, this function computes the standardized pathway scores for all samples.  
### Function "stand.path.score" computes the standardized pathway scores in each pathway.  
### This function is called in "Bayes.model" for each pathway to compute pathway score. 
# 
stand.path.score <- function(exp.data, path.data, refgene.ID, exp.ID, path.ID){
# exp.data: matrix of complete gene expression data, number of rows is the number of genes, 
#	number of columns is the number of subjects+2, the 1st column contains gene entry IDs 
#	and 2nd column contains gene symbols 
# path.data: 2-column matrix, containing gene information in the pathway of interest (1st 
#	column  contains gene entry IDs and 2nd gene symbols respectively) 
# refgene.ID: character, the entry ID of the reference gene in this pathway 
# exp.ID: character, the variable name of the first column of exp.data   
# path.ID: character, the variable name of the first column of path.data  

     # ------ combine expression data and pathway data ------
     mydata <- merge(exp.data, path.data, by.x=exp.ID, by.y=path.ID, all=F)[, -(dim(exp.data)[2]+1)]

     # ------ 4 steps to compute standardized pathway scores ------
     # 1. gene-gene correlation
	mymatrix <- as.matrix(mydata[1:dim(mydata)[1], 3:dim(mydata)[2]])
	ref.gene <- c(which(mydata[,1]==refgene.ID)[1])
	gene.corr <- c()
	for(i in 1:dim(mydata)[1]){
		genecorr <- cor(mymatrix[ref.gene,], mymatrix[i,])
		gene.corr[i] <- sign(genecorr)
	}

	# 2. rank gene expression
	rank.matrix <- matrix(,dim(mydata)[1], (dim(mydata)[2]-2))
	for(j in 1:dim(mydata)[1]){
		rank.matrix[j,] <- rank(abs(mydata[j, 3:dim(mydata)[2]]))
	}

	# 3. pathway score  
	path.score <- colSums(gene.corr*rank.matrix)/dim(mydata)[1]

	# 4. standardized pathway score
	standardized.pathway.score <- (path.score - mean(path.score))/sd(path.score)
	standardized.pathway.score
}
### End of computing standardized pathway scores. Repeat this function for multiple pathways. 
#############################################################################################


### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 
### Function for conducting the Bayesian logistic regression with r2openbugs. 
#
Bayes.model <- function(exp.data, status, pathway.name, pathway.data, no.path, ref.gene.ID, 
	exp.ID, path.ID, model.file, no.iter=6000, no.chains=1, no.burnin=1000, no.thin=10){ 
# exp.data: matrix of complete gene expression data, 
#     	number of rows is the number of genes, number of columns is the number of subjects+2, 
#     	the 1st column contains gene entry IDs and 2nd column contains gene symbols 
# status: vector of disease status, length is the number of subjects 
# pathway.name: vector of pathway names 
# pathway.data: list of information of the competing pathways, each sublist corresponds to a 
#     	single pathway and contains 2 columns (1st for gene IDs and 2nd for gene symbols)  
# no.path: number of competing pathways
# ref.gene.ID: a vector of reference gene IDs for each competing pathway  
# exp.ID: character, the variable name of the first column of exp.data   
# path.ID: character, the variable name of the first column of path.data 
# model.file: user-defined filename containing the path to save the Bayesian model, required 
#     	in OpenBUGS 
# no.iter: number of iterations for Bayesian model (Default is 6000)
# no.chains: number of Markov chains in the MCMC procedure (Default is 1)
# no.burnin: length of burn in (Default is 1000)
# no.thin: thinning rate (Default is 10) 
# A total of 5000 posterior samples will be included based on default settings 

	basename(model.file)   # save the full Bayesian model in "model.file"
	# ------ model specification ------
	model <- function(){   # Specify prior distributions for regression coefficients
		beta0 ~ dnorm(0, 1.0E-2);   # prior for intercept 
   		for(j in 1:(nob-1)){   # prior for pathway effects, nob-1= number of pathways 
   		   beta1[j] ~ dnorm(0, 1.0E-2);
		}

		for(i in 1:I){   # likelihood
    		pathdata[i, 1] ~ dbin(p[i], 1);
			logit(p[i])<- beta0 + inprod(beta1[], pathdata[i,2:nob]);
    	}
 	}   
	# ----- End of model specification ----- 
	write.model(model, model.file)

	# ------ data input ----- 
	data0 <- status    
	for(t in 1:no.path){
		data1 <- stand.path.score(exp.data, path.data=pathway.data[[t]], 
		refgene.ID=ref.gene.ID[t], exp.ID, path.ID)
  	 data0 <- cbind(data0, data1)
	}
	colnames(data0) <- c("status", pathway.name)

	pathdata <- as.matrix(data0)
	I <- dim(pathdata)[1]
	nob <- dim(pathdata)[2]   # number of competing pathways+1 
	data <- list("I", "nob", "pathdata")  # complete data input 
	inits <- function() { list(beta0=0, beta1=c(rep(0,(nob-1)))) }
	params <- c("beta0", "beta1")

	# ----- BUGS analysis ----- 
	out <- bugs(data, inits, params, model.file, n.iter=no.iter, n.chains=no.chains, 
		n.burnin=no.burnin, n.thin=no.thin)
	pD <- out$pD
	DIC <- out$DIC

	# ----- compute posterior probability ----- 
	betapositive <- c()
	betanegative <- c()
	mysize <- length(out$sims.matrix[,1])
	for(u in 2:(length(out$sims.matrix[2,])-1)){
		betapositive[u] <- length(which(out$sims.matrix[,u]>0))/mysize
   		betanegative[u] <- length(which(out$sims.matrix[,u]<0))/mysize
	}
	posterior.prob <- c()
	for(v in 2:(length(out$sims.matrix[2,])-1)){
		posterior.prob[v-1] <- max(betapositive[v], betanegative[v])
	}

	# ----- table for ranks -----
	myrank <- rank(-posterior.prob)
	out.put <- as.data.frame(cbind(pathway.name, myrank, posterior.prob))
	colnames(out.put) <- c("Pathway", "Rank", "Posterior probability")

	# ----- prepare output, explained below ----- 
	infor <- as.data.frame(matrix(c(pD, DIC, I), 1, 3))
	colnames(infor) <- c("pD", "DIC", "Sample size")
	list(rank.table=out.put[order(myrank),], summary=out$summary, infor=infor, 
		posterior.sample=out$sims.matrix, history=out$sims.array[, 1, ], 
		stand.pathway.score=data0)

}   # End of function 
# Variables in the above output are: 
# rank.table: includes the ranks of pathways and corresponding posterior probabilities.
# summary: summary statistics of posterior samples of effect size including mean, sd, 
#   	2.5% quantile, 25% quantile, 50% quantile, 75% quantile and 97.5% quantile.
# infor: infor includes pD, DIC, and Sample size.
# posterior.sample: all posterior.samples of effect size.
# history: history of all posterior samples 
# stand.pathway.score: now includes disease status and standardized pathway score.
### End of function for conducting the Bayesian logistic regression with r2openbugs. 
##############################################################################################
# --------- Example  --------- --------- Example  --------- --------- Example  --------- # 
# Details are in the R markdown document.
# The file "exp_data" contains information about genes and gene expression data.
##############################################################################################
# Example 1: Bayesian analysis with two competing pathways A and B

# "path_A" is a pathway including 20 genes.
# "path_B" is a pathway including 16 genes.
path_data_AB <- list(path_A, path_B)
result_AB <- Bayes.model(exp.data=exp_data, status=c(rep(0,5),rep(1,5)),
                      pathway.name=c("path_A","path_B"), pathway.data=path_data_AB,
                      no.path=2, ref.gene.ID=c(396, 62), exp.ID="EntrezGeneID",
                      path.ID="geneid", model.file="C:/mymodel_1.odc", no.iter=6000,
                      no.chains=1, no.burnin=1000, no.thin=10)
##############################################################################################
# Example 2: Bayesian analysis with two competing pathways C and D

# "path_C1" is a pathway including 10 genes and two subpathways called "path_C2" and "path_C3".
# "path_C2" is a subpathway of "path_C1" and it includes 10 genes.
# "path_C3" is a subpathway of "path_C1" and it includes 10 genes.
# "path_D1" is a pathway and it includes 6 genes and a subpathway called "path_D2".
# "path_D2" is a subpathway of "path_D1" and it includes 10 genes.
path_data_CD <- list(rbind(path_C1, path_C2, path_C3), rbind(path_D1, path_D2))
result_CD <- Bayes.model(exp.data=exp_data, status=c(rep(0,5),rep(1,5)),
                         pathway.name=c("path_C", "path_D"), pathway.data=path_data_CD,
                         no.path=2, ref.gene.ID=c(397, 61), exp.ID="EntrezGeneID",
                         path.ID="geneid", model.file="C:/mymodel_2.odc", no.iter=6000,
                         no.chains=1, no.burnin=1000, no.thin=10)
##############################################################################################