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BMIQ.R
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BMIQ.R
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BMIQ <-function(beta.v,design.v,nL=3,doH=TRUE,nfit=50000,th1.v=c(0.2,0.75),th2.v=NULL,niter=5,tol=0.001,plots=TRUE,sampleID=1){
# Beta MIxture Quantile dilation
require(RPMM);
type1.idx <- which(design.v==1);
type2.idx <- which(design.v==2);
beta1.v <- beta.v[type1.idx];
beta2.v <- beta.v[type2.idx];
### check if there are exact 0's or 1's. If so, regularise using minimum positive and maximum below 1 values.
if(min(beta1.v)==0){
beta1.v[beta1.v==0] <- min(setdiff(beta1.v,0));
}
if(min(beta2.v)==0){
beta2.v[beta2.v==0] <- min(setdiff(beta2.v,0));
}
if(max(beta1.v)==1){
beta1.v[beta1.v==1] <- max(setdiff(beta1.v,1));
}
if(max(beta2.v)==1){
beta2.v[beta2.v==1] <- max(setdiff(beta2.v,1));
}
### estimate initial weight matrix from type1 distribution
w0.m <- matrix(0,nrow=length(beta1.v),ncol=nL);
w0.m[which(beta1.v <= th1.v[1]),1] <- 1;
w0.m[intersect(which(beta1.v > th1.v[1]),which(beta1.v <= th1.v[2])),2] <- 1;
w0.m[which(beta1.v > th1.v[2]),3] <- 1;
### fit type1
print("Fitting EM beta mixture to type1 probes");
rand.idx <- sample(1:length(beta1.v),nfit,replace=FALSE)
em1.o <- blc(matrix(beta1.v[rand.idx],ncol=1),w=w0.m[rand.idx,],maxiter=niter,tol=tol);
subsetclass1.v <- apply(em1.o$w,1,which.max);
subsetth1.v <- c(mean(c(max(beta1.v[rand.idx[subsetclass1.v==1]]),min(beta1.v[rand.idx[subsetclass1.v==2]]))),mean(c(max(beta1.v[rand.idx[subsetclass1.v==2]]),min(beta1.v[rand.idx[subsetclass1.v==3]]))));
class1.v <- rep(2,length(beta1.v));
class1.v[which(beta1.v < subsetth1.v[1])] <- 1;
class1.v[which(beta1.v > subsetth1.v[2])] <- 3;
nth1.v <- subsetth1.v;
print("Done");
### generate plot from estimated mixture
if(plots){
print("Check");
tmpL.v <- as.vector(rmultinom(1:nL,length(beta1.v),prob=em1.o$eta));
tmpB.v <- vector();
for(l in 1:nL){
tmpB.v <- c(tmpB.v,rbeta(tmpL.v[l],em1.o$a[l,1],em1.o$b[l,1]));
}
pdf(paste("Type1fit-",sampleID,".pdf",sep=""),width=6,height=4);
plot(density(beta1.v));
d.o <- density(tmpB.v);
points(d.o$x,d.o$y,col="green",type="l")
legend(x=0.5,y=3,legend=c("obs","fit"),fill=c("black","green"),bty="n");
dev.off();
}
### Estimate Modes
d1U.o <- density(beta1.v[class1.v==1])
d1M.o <- density(beta1.v[class1.v==3])
mod1U <- d1U.o$x[which.max(d1U.o$y)]
mod1M <- d1M.o$x[which.max(d1M.o$y)]
d2U.o <- density(beta2.v[which(beta2.v<0.4)]);
d2M.o <- density(beta2.v[which(beta2.v>0.6)]);
mod2U <- d2U.o$x[which.max(d2U.o$y)]
mod2M <- d2M.o$x[which.max(d2M.o$y)]
### now deal with type2 fit
th2.v <- vector();
th2.v[1] <- nth1.v[1] + (mod2U-mod1U);
th2.v[2] <- nth1.v[2] + (mod2M-mod1M);
### estimate initial weight matrix
w0.m <- matrix(0,nrow=length(beta2.v),ncol=nL);
w0.m[which(beta2.v <= th2.v[1]),1] <- 1;
w0.m[intersect(which(beta2.v > th2.v[1]),which(beta2.v <= th2.v[2])),2] <- 1;
w0.m[which(beta2.v > th2.v[2]),3] <- 1;
print("Fitting EM beta mixture to type2 probes");
rand.idx <- sample(1:length(beta1.v),nfit,replace=FALSE)
em2.o <- blc(matrix(beta2.v[rand.idx],ncol=1),w=w0.m[rand.idx,],maxiter=niter,tol=tol);
print("Done");
### for type II probes assign to state (unmethylated, hemi or full methylation)
subsetclass2.v <- apply(em2.o$w,1,which.max);
subsetth2.v <- c(mean(max(beta2.v[rand.idx[subsetclass2.v==1]]),min(beta2.v[rand.idx[subsetclass2.v==2]])),mean(max(beta2.v[rand.idx[subsetclass2.v==2]]),min(beta2.v[rand.idx[subsetclass2.v==3]])));
class2.v <- rep(2,length(beta2.v));
class2.v[which(beta2.v < subsetth2.v[1])] <- 1;
class2.v[which(beta2.v > subsetth2.v[2])] <- 3;
### generate plot
if(plots){
tmpL.v <- as.vector(rmultinom(1:nL,length(beta2.v),prob=em2.o$eta));
tmpB.v <- vector();
for(lt in 1:nL){
tmpB.v <- c(tmpB.v,rbeta(tmpL.v[lt],em2.o$a[lt,1],em2.o$b[lt,1]));
}
pdf(paste("Type2fit-",sampleID,".pdf",sep=""),width=6,height=4);
plot(density(beta2.v));
d.o <- density(tmpB.v);
points(d.o$x,d.o$y,col="green",type="l")
legend(x=0.5,y=3,legend=c("obs","fit"),fill=c("black","green"),bty="n");
dev.off();
}
classAV1.v <- vector();classAV2.v <- vector();
for(l in 1:nL){
classAV1.v[l] <- em1.o$mu[l,1];
classAV2.v[l] <- em2.o$mu[l,1];
}
### start normalising type2 probes
print("Start normalising type 2 probes");
nbeta2.v <- beta2.v;
### select U probes
lt <- 1;
selU.idx <- which(class2.v==lt);
selUR.idx <- selU.idx[which(beta2.v[selU.idx] > classAV2.v[lt])];
selUL.idx <- selU.idx[which(beta2.v[selU.idx] < classAV2.v[lt])];
### find prob according to typeII distribution
p.v <- pbeta(beta2.v[selUR.idx],em2.o$a[lt,1],em2.o$b[lt,1],lower.tail=FALSE);
### find corresponding quantile in type I distribution
q.v <- qbeta(p.v,em1.o$a[lt,1],em1.o$b[lt,1],lower.tail=FALSE);
nbeta2.v[selUR.idx] <- q.v;
p.v <- pbeta(beta2.v[selUL.idx],em2.o$a[lt,1],em2.o$b[lt,1],lower.tail=TRUE);
### find corresponding quantile in type I distribution
q.v <- qbeta(p.v,em1.o$a[lt,1],em1.o$b[lt,1],lower.tail=TRUE);
nbeta2.v[selUL.idx] <- q.v;
### select M probes
lt <- 3;
selM.idx <- which(class2.v==lt);
selMR.idx <- selM.idx[which(beta2.v[selM.idx] > classAV2.v[lt])];
selML.idx <- selM.idx[which(beta2.v[selM.idx] < classAV2.v[lt])];
### find prob according to typeII distribution
p.v <- pbeta(beta2.v[selMR.idx],em2.o$a[lt,1],em2.o$b[lt,1],lower.tail=FALSE);
### find corresponding quantile in type I distribution
q.v <- qbeta(p.v,em1.o$a[lt,1],em1.o$b[lt,1],lower.tail=FALSE);
nbeta2.v[selMR.idx] <- q.v;
if(doH){ ### if TRUE also correct type2 hemimethylated probes
### select H probes and include ML probes (left ML tail is not well described by a beta-distribution).
lt <- 2;
selH.idx <- c(which(class2.v==lt),selML.idx);
minH <- min(beta2.v[selH.idx])
maxH <- max(beta2.v[selH.idx])
deltaH <- maxH - minH;
#### need to do some patching
deltaUH <- -max(beta2.v[selU.idx]) + min(beta2.v[selH.idx])
deltaHM <- -max(beta2.v[selH.idx]) + min(beta2.v[selMR.idx])
## new maximum of H probes should be
nmaxH <- min(nbeta2.v[selMR.idx]) - deltaHM;
## new minimum of H probes should be
nminH <- max(nbeta2.v[selU.idx]) + deltaUH;
ndeltaH <- nmaxH - nminH;
### perform conformal transformation (shift+dilation)
## new_beta_H(i) = a + hf*(beta_H(i)-minH);
hf <- ndeltaH/deltaH ;
### fix lower point first
nbeta2.v[selH.idx] <- nminH + hf*(beta2.v[selH.idx]-minH);
}
pnbeta.v <- beta.v;
pnbeta.v[type1.idx] <- beta1.v;
pnbeta.v[type2.idx] <- nbeta2.v;
### generate final plot to check normalisation
if(plots){
print("Generating final plot");
d1.o <- density(beta1.v);
d2.o <- density(beta2.v);
d2n.o <- density(nbeta2.v);
ymax <- max(d2.o$y,d1.o$y,d2n.o$y);
pdf(paste("CheckBMIQ-",sampleID,".pdf",sep=""),width=6,height=4)
plot(density(beta2.v),type="l",ylim=c(0,ymax),xlim=c(0,1));
points(d1.o$x,d1.o$y,col="red",type="l");
points(d2n.o$x,d2n.o$y,col="blue",type="l");
legend(x=0.5,y=ymax,legend=c("type1","type2","type2-BMIQ"),bty="n",fill=c("red","black","blue"));
dev.off();
}
print(paste("Finished for sample ",sampleID,sep=""));
return(list(nbeta=pnbeta.v,class1=class1.v,class2=class2.v,av1=classAV1.v,av2=classAV2.v,hf=hf,th1=nth1.v,th2=th2.v));
}