R code for Multinormal Simulation

# PARAMETERS

# g = number of genes

# m = number of important genes

# n = number of samples

# rho = correlation

# ncom = number of PLS-components

# P = number of data sets to be generated

# g = 100

# m = 10

# n = 20

# rho = 0.9

# ncom = 3

# P = 2

sim.multin.data <- function(g, m, n, rho, ncom, P){

library(MASS)

library(mgcv)

library(SimSeq)

# lists for results

data.list <- list()

score.list <- list()

## PARAMETRIT MULTINORMAALIJAKAUMALLE

# covariance matrix

# only positive covariance elements

m1 <- diag(m)

for(i in 1:m){

for(j in 1:(i-1)){

if(i == j){

m1[i,j] <- 1

} else{

m1[i,j] <- rho

}

m2 <- t(m1) + m1

m3 <- diag(2, g)

m3[1:m, 1:m] <- m2

cov.m <- m3 - diag(g)

## EXPECTED VALUES

mu.v <- rep(0, g)

# CONDITION POSITIVE

cond.pos <- matrix(0, ncol = g, nrow = g)

cov.up <- ifelse(upper.tri(cov.m), cov.m, 0)

cond.pos[which(abs(cov.up) == rho, arr.ind = TRUE)] <- 1

pos.m <- cond.pos

# CONDITION NEGATIVE

cond.neg <- matrix(1, ncol = g, nrow = g)

cond.neg <- ifelse(upper.tri(cond.neg), 1, 0)

cond.neg <- cond.neg - cond.pos

neg.m <- cond.neg

# NUMBER OF CONNECTIONS

con <- m*(m-1)*0.5

## DATA for sampling total counts

data(kidney)

kidney.data <- t(kidney$counts)

## GENERATE TOTAL READ COUNT C FOR SUBJECT j FROM A DISTRIBUTION THAT IS REALISTIC

t.counts <- c()

for(j in 1:nrow(kidney.data)){

t.counts[j] <- sum(sample(kidney.data[j,], g, replace = TRUE))

}

for(p in 1:P){

cat("sim = ", iter <- p, "\n")

s <- matrix(0, g, g)

data.sim <- matrix(NA, nrow = n, ncol = g)

## GENERATE DATA

## MULTIVARIATE NORMAL DATA

mvn.m <- mvrnorm(n, mu.v, cov.m)/5

## EXP(X_i)

exp.mvn.m <- exp(mvn.m)

## GENERATE A VECTOR OF READ COUNTS FOR EACH SAMPLE FROM MULTINOMIAL DISTRIBUTION WITH PARAMETERS

## C (NUMBER OF TRIALS) AND SUCCESS PROPABILITIES lambda_j / lambda_tot

# lambda_tot = sum of lambda_i = sum of exp(x_i)

lambda.tot <- apply(exp.mvn.m, 1, sum)

# loop over subjects i, i = 1, ..., n

count.m <- matrix(0, nrow = n, ncol = g)

for(j in 1:n){

# resample C from t.counts

C <- sample(t.counts, 1, replace = TRUE) # t.counts are computed from random p genes

# succes probabilities for each gene for subject i and counts from multin. dist.

prob <- c()

# one sample (here are the \lambda_1 - \lambda_G)

sample <- exp.mvn.m[j,]

# probabilities: \lambda_1 / \lambda_tot from sample j

prob <- sample / lambda.tot[j]

count.m[j,] <- t(rmultinom(1, C, prob))

}

data.sim <- count.m

data.list[[p]] <- data.sim

# scale data

data.sc <- scale(data.sim)

# PLS-components

standr <- function(x) x/as.numeric(sqrt(t(x)%*%x))

tot.c <- as.vector(apply(data.sim, 1, sum))

for(i in 1:g){

X <- data.sc[,-i]

y <- data.sc[,i]

c <- matrix(0, g-1, ncom)

TT <- matrix(0, nrow(data.sc), ncom)

c.var <- rep(0, ncom)

SS <- rep(0, ncom)

var.expl <- rep(0, ncom)

tX<- X

for(k in 1:ncom){ # construct ncom PLS components

c[,k] <- standr(t(tX)%*%y)

TT[,k] <- tX%*%c[,k]

c.var[k] <- (t(y)%*%TT[,k])/(t(TT[,k])%*%TT[,k])

SS[k] <- (t(TT[,k])%*%TT[,k])%*%(t(c.var[k])%*%c.var[k])

var.expl[k] <- SS[k] / sum(diag(t(y)%*%y))

tX <- tX-TT[,k]%*%solve(t(TT[,k])%*%TT[,k])%*%t(TT[,k])%*%tX

}

w <- var.expl / sum(var.expl) # weights

# glm with negative-binomial link

temp.data <- as.data.frame(cbind(data.sim[,i], TT, tot.c))

comp.names <- paste("C", 1:ncom, sep = '')

colnames(temp.data) <- c('y', comp.names, 't.counts')

names <- colnames(temp.data[2:(ncom+1)])

osa1 <- paste("y~")

osa2 <- paste(names, collapse = "+")

form <- paste(osa1, osa2, sep = "")

form2 <- as.formula(form)

mod <- gam(form2, offset=log(t.counts), family=nb(),data=temp.data)

summary(mod)

b <- as.matrix(coef(mod)[-1])

temp.beta <- c%*%b

if (i == 1){

s[i,] <- c(0,temp.beta)

} else {

if (i == g){

s[i,] <- c(temp.beta,0)

} else {

s[i,] <- c(temp.beta[1:(i-1)],0,temp.beta[i:(g-1)])

}

# lopullinen symmetrisoitu ja skaalattu (max score = 1, min = -1) assosiaatiomatriisi

s <- 0.5*(s+t(s))

s <- s-0.5*(max(s)+min(s))

s <- s/(0.5*(max(s)-min(s)))

diag(s) <- 1

score.list[[p]] <- s

}

return(list(data.list = data.list, score.list = score.list,

pos.m = pos.m, neg.m = neg.m, con.m = con ))

}

# CALL FUNCTION

data1 <- sim.multin.data(100, 3, 20, 0.9, 3, 1000)

data2 <- sim.multin.data(1000, 10, 20, 0.9, 3, 100)

data3 <- sim.multin.data(100, 3, 100, 0.9, 3, 1000)

data4 <- sim.multin.data(1000, 10, 100, 0.9, 3, 100)

###################################################

# FUNCTION COMPUTING FDR WITH DIFFERENT LEVELS OF QVALUE

fdr.fun <- function(qvals, score, pos, neg){

# save the results

tp.data <- list()

sens.data <- list()

# condition positive

cond.pos <- pos

# condition negative

cond.neg <- neg

# loop over all selected qvalues

j <- 1

for(qvalue in qvals){

cat("qval = ", iter <- qvalue , "\n")

i <- 1

tp.q <- matrix(0, ncol = 5, nrow = length(score))

sens.q <- matrix(0, ncol = 5, nrow = length(score))

# loop over all generated data sets

for(d in 1:length(score)){

s <- score[[d]]

s.up <- s[upper.tri(s)]

m <- ncol(s)

b <- matrix(0, m, m)

out.density <- density(s.up, adjust = 2, from = -1, to = 1)

b[upper.tri(b, diag=FALSE)] <- (dnorm(s.up,mean(s.up),sd(s.up))/approx(out.density$x, out.density$y,

s.up, method = "linear")$y)

apu <- matrix(0, m, m)

apu[upper.tri(b, diag=FALSE)] <- 1

apu[which(b > qvalue, arr.ind = TRUE)] <- 0

fdr.m <- which(apu == 1, arr.ind=T)

# test positive

test.pos.fdr <- matrix(0, ncol = m, nrow = m)

test.pos.fdr[fdr.m] <- 1

# test negative

test.neg.fdr <- matrix(1, ncol = m, nrow = m)

test.neg.fdr <- ifelse(upper.tri(test.neg.fdr), 1, 0)

test.neg.fdr[fdr.m] <- 0

# true positives

tp.m.fdr <- cond.pos+test.pos.fdr

tp.fdr <- length(which(tp.m.fdr == 2))

# false positives

fp.m.fdr <- cond.neg + test.pos.fdr

fp.fdr <- length(which(fp.m.fdr == 2))

# true negatives

tn.m.fdr <- cond.neg + test.neg.fdr

tn.fdr <- length(which(tn.m.fdr == 2))

# false negatives

fn.m.fdr <- cond.pos + test.neg.fdr

fn.fdr <- length(which(fn.m.fdr == 2))

# sensitivity

if(tp.fdr+fn.fdr == 0){

sens.fdr <- 0

} else {

sens.fdr <- tp.fdr/(tp.fdr+fn.fdr)

}

# specificity

if(fp.fdr+tn.fdr == 0){

spec.fdr <- 0

} else {

spec.fdr <- tn.fdr/(fp.fdr+tn.fdr)

}

# true discovery rate

if(tp.fdr+fp.fdr == 0){

tdr.fdr <- 0

} else {

tdr.fdr <- tp.fdr/(tp.fdr+fp.fdr)

}

# true non-discovery rate

if(tn.fdr+fn.fdr == 0){

tnr.fdr <- 0

} else {

tnr.fdr <- tn.fdr/(tn.fdr+fn.fdr)

}

# save the results into ith row of a matrix

tp.q[i,1] <- qvalue

tp.q[i,2] <- tp.fdr

tp.q[i,3] <- fp.fdr

tp.q[i,4] <- tn.fdr

tp.q[i,5] <- fn.fdr

sens.q[i,1] <- qvalue

sens.q[i,2] <- sens.fdr

sens.q[i,3] <- spec.fdr

sens.q[i,4] <- tdr.fdr

sens.q[i,5] <- tnr.fdr

i <- i+1

}

tp.data[[j]] <- tp.q

sens.data[[j]] <- sens.q

j <- j+1

}

return(list(tp.list = tp.data, sens.list = sens.data ))

}

## CALL FUNCTION

qvals <- seq(0.0, 1.0, by = 0.05)

# no weights

FDR1 <- fdr.fun(qvals, data1$score.list, data1$pos.m, data1$neg.m)

FDR2 <- fdr.fun(qvals, data2$score.list, data2$pos.m, data2$neg.m)

FDR3 <- fdr.fun(qvals, data3$score.list, data3$pos.m, data3$neg.m)

FDR4 <- fdr.fun(qvals, data4$score.list, data4$pos.m, data4$neg.m)

## correction for SEs, qvalue = 0.2

# list with qval = 0.2

# P <- 100

# temp1 <- FDR4$sens.list[[4]]

# temp.mean <- mean(temp1[,2])

# temp.mean

# var.sens <- var(temp1[,2])

# se.sens <- sqrt(1/P*(var.sens))

# round(se.sens, 3)

# temp.mean <- mean(temp1[,4])

# temp.mean

# var.spec <- var(temp1[,4])

# se.spec <- sqrt(1/P*(var.spec))

# round(se.spec, 3)

# temp.mean <- mean(temp1[,6])

# temp.mean

# var.tdr <- var(temp1[,6])

# se.tdr <- sqrt(1/P*(var.tdr))

# round(se.tdr, 3)

# temp.mean <- mean(temp1[,8])

# temp.mean

# var.tnr <- var(temp1[,8])

# se.tnr <- sqrt(1/P*(var.tnr))

# round(se.tnr, 3)

# # hist(data1$score.list[[1]][upper.tri(data1$score.list[[1]])])

means1fdr <- lapply(FDR1$sens.list, colMeans)

means2 <- lapply(FDR2$sens.list, colMeans)

means3fdr <- lapply(FDR3$sens.list, colMeans)

means4 <- lapply(FDR4$sens.list, colMeans)