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app_functions.R
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Fstrong <- function(exposure)
{
F.strong <- data.frame()
for(j in 1:length(exposure)){
F.analysis <- data.frame(Fstat[,exposure[j]])
keep <- as.vector(as.numeric(F.analysis> 5))
F.analysis <- F.analysis*keep
F.analysis[F.analysis == 0] <- NA
F.analysis<- na.omit(F.analysis)
F.strong[j,1] <- apply(F.analysis,2, mean)
F.strong[j,2] <- dim(F.analysis)[1]
}
row.names(F.strong) <- exposure
colnames(F.strong) <- c("F.stat", "no.snps")
return(F.strong)
}
conditionalF <- function(exposures)
{
F.analysis <- data.frame(Fstat[,exposures])
ex.analysis <- data.frame(exp[,exposures])
se.analysis <- data.frame(dat_se[,exposures])
cor.analysis <- data.frame(correlations[exposures,exposures])
maxF_row <- apply(F.analysis,1,function(x) max(as.numeric(x)))
keep <- as.vector(as.numeric(maxF_row > 5))
n.snp <- sum(keep)
F.analysis <- F.analysis*keep
F.analysis[F.analysis == 0] <- NA
F.analysis<- na.omit(F.analysis)
ex.analysis <- ex.analysis[,1:length(exposures)]*keep
ex.analysis[ex.analysis == 0] <- NA
ex.analysis<- na.omit(ex.analysis)
se.analysis <- se.analysis[,1:length(exposures)]*keep
se.analysis[se.analysis == 0] <- NA
se.analysis<- na.omit(se.analysis)
Q <- data.frame()
F.conditional <- data.frame()
F.mean <- data.frame()
for(j in 1:length(exposures)){
F.mean <- apply(F.analysis,2,function(b) mean(as.numeric(b)))
X1 <- ex.analysis[,exposures[j]]
X2 <- data.frame(ex.analysis[,-which(names(ex.analysis) == exposures[j])])
X2 <- (matrix(unlist(X2), ncol = length(exposures)-1))
X1se <- se.analysis[,exposures[j]]
X2se <- se.analysis[,-which(names(ex.analysis) == exposures[j])]
X2se <- (matrix(unlist(X2se), ncol = length(exposures)-1))
delta <- as.vector(lm(X1~ -1 + X2)$coefficients)
delta1 <- c(1,delta)
vx <- NULL
for(i in 1:n.snp){
covariances <- data.frame()
for(l in 1:length(exposures)){
for(m in 1:length(exposures)){
covariances[l,m] <- correlations[exposures[l],exposures[m]]*se.analysis[i,exposures[l]]*se.analysis[i,exposures[m]]
}
}
colnames(covariances) <- exposures
rownames(covariances) <- exposures
covX1a <- data.frame(covariances[exposures[j],])
colnames(covX1a) <- exposures
covX1 <- covX1a[,-which(names(covX1a) == exposures[j])]
covX2 <- as.matrix(covariances[-which(names(covariances) == exposures[j]),-which(names(covariances) == exposures[j])])
vx[i] <- X1se[i]^2 - 2*delta%*%t(covX1) + t(delta)%*%covX2%*%delta
}
Q[1,j] <- sum((1/vx)*((lm(X1~ -1 + X2)$residuals)^2))
F.conditional[1,j]<-Q[1,j]/length(X1)
no.snps <- length(X1)
}
F.conditional <- t(F.conditional)
rownames(F.conditional)<-exposures
colnames(F.conditional)<-"Conditional F"
results <- data.frame(F.conditional, F.mean, no.snps)
return(results)
}
MRfunction_jk <- function(exposures)
{
PL_MVMR = function(a){
tau2 = a[1]
PL2_MVMR = function(ab){
b=ab
cov = data.frame()
w=NULL
for(i in 1:n.snp){
for(l in 1:length(exposures)){
for(m in 1:length(exposures)){
cov[l,m] <- correlations[exposures[l],exposures[m]]*X_se[i,subexp_se[l]]*X_se[i,subexp_se[m]]
}
}
cov <- as.matrix(cov)
w[i] <- Y1_se[i]^2+t(b)%*%cov%*%b + tau2
}
q = sum((1/w)*((Y1 - X1%*%b)^2))
}
st_PL2 = cbind(rep(1,kx))
bc = optim(st_PL2, PL2_MVMR)
bcresults <- bc$par
cov = data.frame()
w=NULL
for(i in 1:n.snp){
for(l in 1:length(exposures)){
for(m in 1:length(exposures)){
cov[l,m] <- correlations[exposures[l],exposures[m]]*X_se[i,subexp_se[l]]*X_se[i,subexp_se[m]]
}
}
cov <- as.matrix(cov)
w[i] <- Y1_se[i]^2+t(bcresults)%*%cov%*%bcresults + tau2
}
q = (sum((1/w)*((Y1 - X1%*%bcresults)^2))-(n.snp-kx))^2
}
PL2_MVMR = function(ab){
b=ab
w=NULL
cov = data.frame()
for(i in 1:n.snp){
for(l in 1:length(exposures)){
for(m in 1:length(exposures)){
cov[l,m] <- correlations[exposures[l],exposures[m]]*X_se[i,subexp_se[l]]*X_se[i,subexp_se[m]]
}
}
cov <- as.matrix(cov)
w[i] <- Y1_se[i]^2+t(b)%*%cov%*%b + tau_i
}
q = sum((1/w)*((Y1 - X1%*%b)^2))
}
ex.analysis <- analysis.dat[,c("amd",subexp)]
se.analysis <- analysis.dat[,c("amd_se",subexp_se)]
F.analysis <- analysis.dat[,c(subexp_f)]
cor.analysis <- data.frame(correlations[exposures,exposures])
kx <- length(exposures)
n.snp <- length(analysis.dat[,"amd"])
X <- ex.analysis[,exposures]
X1 <- (matrix(unlist(X), ncol = length(exposures)))
X_se <- se.analysis[,subexp_se]
X1_se <- (matrix(unlist(X_se), ncol = length(exposures)))
Y <- ex.analysis[,"amd"]
Y1 <- (matrix(unlist(Y), ncol = 1))
Y_se <- se.analysis[,"amd_se"]
Y1_se <- (matrix(unlist(Y_se), ncol = 1))
##simple IVW
MR.IVW <- summary(lm(Y1 ~ -1 + X1, weights = (Y1_se)^-2))$coefficients
beta <- as.vector(lm(Y1 ~ -1 + X1, weights = (Y1_se)^-2))$coefficients
for(k in 1:10){
vx <- NULL
for(i in 1:n.snp){
covariances <- data.frame()
for(l in 1:length(exposures)){
for(m in 1:length(exposures)){
covariances[l,m] <- correlations[exposures[l],exposures[m]]*X_se[i,subexp_se[l]]*X_se[i,subexp_se[m]]
}
}
colnames(covariances) <- exposures
rownames(covariances) <- exposures
covar <- as.matrix(covariances)
vx[i] <- Y1_se[i]^2 + t(beta)%*%covar%*%beta
}
beta <- as.vector(lm(Y1 ~ -1 + X1, weights = (vx)^-1))$coefficients
}
MR.IVW_update <- summary(lm(Y1 ~ -1 + X1, weights = (vx)^-2))$coefficients
#liml estimation with the heterogeneity statistic
tau_i = 0
liml <- optim(rep(0,kx), PL2_MVMR)
Q_cov <- liml$value
MR.liml <- liml$par
MR.liml <- cbind(MR.liml)
tau_i = optimize(PL_MVMR,interval=c(-10,10))$minimum
MR.liml_results<- optim(rep(0,kx), PL2_MVMR, hessian=TRUE)
MR.liml_het <- cbind(MR.liml_results$par)
Hess <- MR.liml_results$hessian
var.cov <- solve(Hess)
MR.liml_het.se <- as.matrix(sqrt(diag(var.cov)),ncol=1)
rownames(MR.IVW)<-exposures
rownames(MR.IVW_update)<-exposures
rownames(MR.liml)<-exposures
rownames(MR.liml_het)<-exposures
rownames(MR.liml_het.se)<-exposures
results <- data.frame(n.snp, MR.IVW, MR.IVW_update, MR.liml, Q_cov, MR.liml_het, MR.liml_het.se, tau_i)
return(results)
}