Nothing
R/DPmultmeta.R
In DPpackage: Bayesian Nonparametric Modeling in R
### DPmultmeta.R
### Fit a semiparametric random effects model for multivariate meta-analysis
### using a Dirichlet Process prior for the distribution of
### the random effects.
###
### Copyright: Alejandro Jara and Peter Mueller, 2008-2012.
###
### Last modification: 02-06-2008.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The author's contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
### Peter Mueller
### Department of Mathematics
### The University of Texas Austin
### 1, University Station, C1200
### Austin TX 78712, USA
### Voice: (512) 471-7168 URL : http://www.math.utexas.edu/users/pmueller
### Fax : (512) 471-9038 Email: pmueller@math.utexas.edu
###
"DPmultmeta"<-
function(y,asymvar,prior,mcmc,state,status,data=sys.frame(sys.parent()))
UseMethod("DPmultmeta")
"DPmultmeta.default"<-
function(y,
asymvar,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()))
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
#########################################################################################
# data structure
#########################################################################################
nameresp <- colnames(y)
nvar <- dim(y)[2]
nrec <- dim(y)[1]
if(nvar < 2)
{
stop("Use the function DPMmeta for univariate meta-analysis")
}
sigma2e <- asymvar
nrecs <- dim(sigma2e)[1]
nvars <- dim(sigma2e)[2]
if(nrec != nrecs)
{
stop("Different number of subjects in the response and the assymptotic variance matrix")
}
nuniq <- nvar*(nvar+1)/2
if(nuniq != nvars)
{
stop("Different dimension in the response vector and the corresponding assymptotic variance")
}
#########################################################################################
# prior information
#########################################################################################
if(is.null(prior$a0))
{
a0 <--1
b0 <--1
alpha <- prior$alpha
alpharand <- 0
}
else
{
a0 <- prior$a0
b0 <- prior$b0
alpha <- 1
alpharand <- 1
}
a0b0 <- c(a0,b0)
if(is.null(prior$m2))
{
s2inv <- matrix(0,nrow=nvar,ncol=nvar)
s2invm2 <- matrix(0,nrow=nvar,ncol=1)
m1 <- prior$m1
m1rand <- 0
}
else
{
s2inv <- solve(prior$s2)
s2invm2 <- s2inv%*%prior$m2
m1 <- rep(0,nvar)
for(i in 1:nvar)
{
m1[i] <- mean(y[,i])+rnorm(1,0,100)
}
m1rand <- 1
}
if(is.null(prior$nu))
{
s1 <- matrix(prior$s1,nvar,nvar)
psiinv <- matrix(0,nvar,nvar)
s1rand <- 0
nu <- -1
}
else
{
s1 <- matrix(var(y),nvar,nvar)
psiinv <- matrix(prior$psiinv,nvar,nvar)
s1rand <- 1
nu <- prior$nu
}
#########################################################################################
# mcmc specification
#########################################################################################
if(missing(mcmc))
{
nburn <- 1000
nsave <- 1000
nskip <- 0
ndisplay <- 100
mcmcvec <- c(nburn,nskip,ndisplay)
}
else
{
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay)
nsave <-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
thetasave <- matrix(0,nrow=nsave,ncol=nvar+nvar*(nvar+1)/2+2)
randsave <- matrix(0,nrow=nsave,ncol=(nrec+1)*nvar)
#########################################################################################
# parameters depending on status
#########################################################################################
nuniq <- nvar*(nvar+1)/2
if(status==TRUE)
{
muclus <- matrix(0,nrow=nrec+1,ncol=nvar)
for(i in 1:1)
{
for(j in 1:nvar)
{
muclus[i,j] <- m1[j]
}
}
ncluster <- 1
ss <- rep(1,nrec)
}
if(status==FALSE)
{
alpha <- state$alpha
m1 <- state$m1
s1 <- state$s1
muclus <- state$muclus
ncluster <- state$ncluster
ss <- state$ss
}
#########################################################################################
# working space
#########################################################################################
ccluster <- rep(0,nrec)
cstrt <- matrix(0,nrow=nrec,ncol=nrec)
iflag <- rep(0,nvar)
prob <- rep(0,(nrec+1))
sigma2ei <- matrix(0,nrow=nrec,ncol=nvar*(nvar+1)/2)
seed1 <- sample(1:29000,1)
seed2 <- sample(1:29000,1)
seed <- c(seed1,seed2)
theta <- rep(0,nvar)
s1inv <- matrix(0,nrow=nvar,ncol=nvar)
s1invm1 <- rep(0,nvar)
workm1 <- matrix(0,nrow=nvar,ncol=nvar)
workm2 <- matrix(0,nrow=nvar,ncol=nvar)
workm3 <- matrix(0,nrow=nvar,ncol=nvar)
workmh1 <- rep(0,nvar*(nvar+1)/2)
workmh2 <- rep(0,nvar*(nvar+1)/2)
workv1 <- rep(0,nvar)
workv2 <- rep(0,nvar)
ywork <- rep(0,nvar)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmultmeta",
nrec =as.integer(nrec),
nvar =as.integer(nvar),
y =as.double(y),
sigma2e =as.double(sigma2e),
a0b0 =as.double(a0b0),
m1rand =as.integer(m1rand),
s2inv =as.double(s2inv),
s2invm2 =as.double(s2invm2),
nu =as.integer(nu),
s1rand =as.integer(s1rand),
psiinv =as.double(psiinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
cpo =as.double(cpo),
randsave =as.double(randsave),
thetasave =as.double(thetasave),
alpha =as.double(alpha),
m1 =as.double(m1),
s1 =as.double(s1),
ncluster =as.integer(ncluster),
muclus =as.double(muclus),
ss =as.integer(ss),
ccluster =as.integer(ccluster),
cstrt =as.integer(cstrt),
iflag =as.integer(iflag),
prob =as.double(prob),
sigma2ei =as.double(sigma2ei),
seed =as.integer(seed),
s1inv =as.double(s1inv),
s1invm1 =as.double(s1invm1),
theta =as.double(theta),
workm1 =as.double(workm1),
workm2 =as.double(workm2),
workm3 =as.double(workm3),
workmh1 =as.double(workmh1),
workmh2 =as.double(workmh2),
workv1 =as.double(workv1),
workv2 =as.double(workv2),
ywork =as.double(ywork),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
model.name<-"Bayesian semiparametric random effects model for multivariate meta-analysis"
thetasave <- matrix(foo$thetasave,nrow=nsave,ncol=nvar+nvar*(nvar+1)/2+2)
randsave <- matrix(foo$randsave,nrow=nsave,ncol=(nrec+1)*nvar)
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
varnames <- colnames(y)
if(is.null(varnames))
{
varnames <- all.vars(cl)[1:nvar]
}
indip <- rep(0,(nvar+nvar*(nvar+1)/2+2))
coeff <- NULL
pnames1 <- NULL
pnames2 <- NULL
renames <- NULL
for(i in 1:nvar)
{
pnames2 <- c(pnames2,paste("m1",varnames[i],sep="-"))
}
for(i in 1:nvar)
{
for(j in i:nvar)
{
tmp <- paste(varnames[i],varnames[j],sep=":")
pnames2 <- c(pnames2,paste("s1",tmp,sep="-"))
}
}
pnames2 <- c(pnames2,"ncluster","alpha")
for(i in 1:nrec)
{
for(j in 1:nvar)
{
tmp1 <- paste("m1",varnames[i],sep="-")
tmp2 <- paste("Subject=",i,sep="")
renames <- c(renames,paste(tmp2,tmp1,sep=";"))
}
}
for(j in 1:nvar)
{
tmp1 <- paste("m1",varnames[i],sep="-")
renames <- c(renames,paste("Prediction",tmp1,sep=";"))
}
colnames(thetasave) <- pnames2
colnames(randsave) <- renames
count <- 0
if(m1rand==1)
{
for(i in 1:nvar)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,i]))
pnames1 <- c(pnames1,paste("m1",varnames[i],sep="-"))
indip[i] <- 1
}
}
count <- nvar
if(s1rand==1)
{
for(i in 1:nvar)
{
for(j in i:nvar)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,count]))
tmp <- paste(varnames[i],varnames[j],sep=":")
pnames1 <- c(pnames1,paste("s1",tmp,sep="-"))
indip[count] <- 1
}
}
}
count <- nvar+nvar*(nvar+1)/2 + 1
coeff <- c(coeff,mean(thetasave[,count]))
pnames1 <- c(pnames1,"ncluster")
indip[count] <- 1
count <- nvar+nvar*(nvar+1)/2 + 1
if(alpharand==1)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,count]))
pnames1 <- c(pnames1,"alpha")
indip[count] <- 1
}
names(coeff) <- pnames1
save.state <- list(thetasave=thetasave,
randsave=randsave)
state <- list(alpha=foo$alpha,
m1=matrix(foo$m1,nrow=nvar,ncol=1),
s1=matrix(foo$s1,nrow=nvar,ncol=nvar),
muclus=matrix(foo$muclus,nrow=nrec+1,ncol=nvar),
ncluster=foo$ncluster,
ss=foo$ss)
z<-list(call=cl,
y=y,
asymvar=asymvar,
varnames=varnames,
modelname=model.name,
cpo=cpo,
fso=fso,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
nvar=foo$nvar,
alpharand=alpharand,
s1rand=s1rand,
m1rand=m1rand,
coefficients=coeff,
indip=indip)
cat("\n\n")
class(z)<-c("DPmultmeta")
return(z)
}
###
### Tools: print, summary, plot
###
### Copyright: Alejandro Jara, 2008
### Last modification: 02-06-2008.
"print.DPmultmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Variables:",x$nvar,"\n")
cat("\n\n")
invisible(x)
}
"summary.DPmultmeta"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave<-object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo<-object$cpo
### Baseline Information
mat<-NULL
coef.p<-NULL
dimen1 <- object$nvar+object$nvar*(object$nvar+1)/2
for(i in 1:dimen1)
{
if(object$indip[i]==1)
{
coef.p <- c(coef.p,object$coefficients[i])
mat <- cbind(mat,thetasave[,i])
}
}
dimen1 <- dim(mat)[2]
if(dimen1>0)
{
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
}
### Precision parameter
dimen1<-object$nvar+object$nvar*(object$nvar+1)/2
if(is.null(object$prior$a0))
{
dimen2<-1
coef.p<-object$coefficients[(dimen1+1)]
mat<-matrix(thetasave[,(dimen1+1)],ncol=1)
}
else
{
dimen2<-2
coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
mat<-thetasave[,(dimen1+1):(dimen1+2)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
ans$nrec<-object$nrec
ans$nvar<-object$nvar
class(ans) <- "summaryDPmultmeta"
return(ans)
}
"print.summaryDPmultmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Variables:",x$nvar,"\n")
cat("\n\n")
invisible(x)
}
"plot.DPmultmeta"<-function(x, ask=TRUE, output="density", param=NULL, hpd=TRUE, nfigr=1, nfigc=1, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2006
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
"bivk"<-function(x, y, h, n = 25, lims = c(range(x), range(y)))
{
nx <- length(x)
if (length(y) != nx)
stop("Data vectors must be the same length")
gx <- seq(lims[1], lims[2], length = n)
gy <- seq(lims[3], lims[4], length = n)
if (missing(h))
h <- c(band(x), band(y))
h <- h/4
ax <- outer(gx, x, "-")/h[1]
ay <- outer(gy, y, "-")/h[2]
z <- matrix(dnorm(ax), n, nx) %*% t(matrix(dnorm(ay), n,
nx))/(nx * h[1] * h[2])
return(list(x = gx, y = gy, z = z))
}
"band"<-function(x)
{
r <- quantile(x, c(0.25, 0.75))
h <- (r[2] - r[1])/1.34
4 * 1.06 * min(sqrt(var(x)), h) * length(x)^(-1/5)
}
if(is(x, "DPmultmeta"))
{
if(output=="density")
{
# Density estimation
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1),nrow=nfigr,ncol=nfigc,byrow=TRUE))
start <- x$nrec*x$nvar
for(i in 1:x$nvar)
{
tmp <- paste("m1",x$varnames[i],sep="-")
title1 <- paste("Density of",tmp,sep=' ')
plot(density(x$save.state$randsave[,(start+i)]),type="l",lwd=2,,xlab="values", ylab="density",main=title1)
}
for(i in 1:(x$nvar-1))
{
for(j in (i+1):x$nvar)
{
varsn1 <- paste("m1",x$varnames[i],sep="-")
varsn2 <- paste("m1",x$varnames[j],sep="-")
tmp <- paste(varsn1,varsn2,sep=":")
title1<-paste("Density of ",tmp,sep='')
xx<-x$save.state$randsave[,(start+i)]
yy<-x$save.state$randsave[,(start+j)]
est<-bivk(xx,yy,n=200)
contour(est,main=title1,xlab=varsn1,ylab=varsn2)
persp(est,theta=-30,phi=15,expand = 0.9, ltheta = 120,main=title1,
xlab=varsn1,ylab=varsn2,zlab="density")
}
}
}
else
{
if(is.null(param))
{
pnames<-colnames(x$save.state$thetasave)
n<-dim(x$save.state$thetasave)[2]
cnames<-names(x$coefficients)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:(n-1))
{
if(x$indip[i]==1)
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(x$save.state$thetasave[,i],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
if(!is.null(x$prior$a0))
{
title1<-paste("Trace of",pnames[n],sep=" ")
title2<-paste("Density of",pnames[n],sep=" ")
plot(x$save.state$thetasave[,n],type='l',main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
pnames<-colnames(x$save.state$thetasave)
n<-dim(x$save.state$thetasave)[2]
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if (poss==0)
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
title1<-paste("Trace of",pnames[poss],sep=" ")
title2<-paste("Density of",pnames[poss],sep=" ")
plot(x$save.state$thetasave[,poss],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[poss]=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
}
}
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### DPmultmeta.R
### Fit a semiparametric random effects model for multivariate meta-analysis
### using a Dirichlet Process prior for the distribution of
### the random effects.
###
### Copyright: Alejandro Jara and Peter Mueller, 2008-2012.
###
### Last modification: 02-06-2008.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The author's contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
### Peter Mueller
### Department of Mathematics
### The University of Texas Austin
### 1, University Station, C1200
### Austin TX 78712, USA
### Voice: (512) 471-7168 URL : http://www.math.utexas.edu/users/pmueller
### Fax : (512) 471-9038 Email: pmueller@math.utexas.edu
###
"DPmultmeta"<-
function(y,asymvar,prior,mcmc,state,status,data=sys.frame(sys.parent()))
UseMethod("DPmultmeta")
"DPmultmeta.default"<-
function(y,
asymvar,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()))
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
#########################################################################################
# data structure
#########################################################################################
nameresp <- colnames(y)
nvar <- dim(y)[2]
nrec <- dim(y)[1]
if(nvar < 2)
{
stop("Use the function DPMmeta for univariate meta-analysis")
}
sigma2e <- asymvar
nrecs <- dim(sigma2e)[1]
nvars <- dim(sigma2e)[2]
if(nrec != nrecs)
{
stop("Different number of subjects in the response and the assymptotic variance matrix")
}
nuniq <- nvar*(nvar+1)/2
if(nuniq != nvars)
{
stop("Different dimension in the response vector and the corresponding assymptotic variance")
}
#########################################################################################
# prior information
#########################################################################################
if(is.null(prior$a0))
{
a0 <--1
b0 <--1
alpha <- prior$alpha
alpharand <- 0
}
else
{
a0 <- prior$a0
b0 <- prior$b0
alpha <- 1
alpharand <- 1
}
a0b0 <- c(a0,b0)
if(is.null(prior$m2))
{
s2inv <- matrix(0,nrow=nvar,ncol=nvar)
s2invm2 <- matrix(0,nrow=nvar,ncol=1)
m1 <- prior$m1
m1rand <- 0
}
else
{
s2inv <- solve(prior$s2)
s2invm2 <- s2inv%*%prior$m2
m1 <- rep(0,nvar)
for(i in 1:nvar)
{
m1[i] <- mean(y[,i])+rnorm(1,0,100)
}
m1rand <- 1
}
if(is.null(prior$nu))
{
s1 <- matrix(prior$s1,nvar,nvar)
psiinv <- matrix(0,nvar,nvar)
s1rand <- 0
nu <- -1
}
else
{
s1 <- matrix(var(y),nvar,nvar)
psiinv <- matrix(prior$psiinv,nvar,nvar)
s1rand <- 1
nu <- prior$nu
}
#########################################################################################
# mcmc specification
#########################################################################################
if(missing(mcmc))
{
nburn <- 1000
nsave <- 1000
nskip <- 0
ndisplay <- 100
mcmcvec <- c(nburn,nskip,ndisplay)
}
else
{
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay)
nsave <-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
thetasave <- matrix(0,nrow=nsave,ncol=nvar+nvar*(nvar+1)/2+2)
randsave <- matrix(0,nrow=nsave,ncol=(nrec+1)*nvar)
#########################################################################################
# parameters depending on status
#########################################################################################
nuniq <- nvar*(nvar+1)/2
if(status==TRUE)
{
muclus <- matrix(0,nrow=nrec+1,ncol=nvar)
for(i in 1:1)
{
for(j in 1:nvar)
{
muclus[i,j] <- m1[j]
}
}
ncluster <- 1
ss <- rep(1,nrec)
}
if(status==FALSE)
{
alpha <- state$alpha
m1 <- state$m1
s1 <- state$s1
muclus <- state$muclus
ncluster <- state$ncluster
ss <- state$ss
}
#########################################################################################
# working space
#########################################################################################
ccluster <- rep(0,nrec)
cstrt <- matrix(0,nrow=nrec,ncol=nrec)
iflag <- rep(0,nvar)
prob <- rep(0,(nrec+1))
sigma2ei <- matrix(0,nrow=nrec,ncol=nvar*(nvar+1)/2)
seed1 <- sample(1:29000,1)
seed2 <- sample(1:29000,1)
seed <- c(seed1,seed2)
theta <- rep(0,nvar)
s1inv <- matrix(0,nrow=nvar,ncol=nvar)
s1invm1 <- rep(0,nvar)
workm1 <- matrix(0,nrow=nvar,ncol=nvar)
workm2 <- matrix(0,nrow=nvar,ncol=nvar)
workm3 <- matrix(0,nrow=nvar,ncol=nvar)
workmh1 <- rep(0,nvar*(nvar+1)/2)
workmh2 <- rep(0,nvar*(nvar+1)/2)
workv1 <- rep(0,nvar)
workv2 <- rep(0,nvar)
ywork <- rep(0,nvar)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmultmeta",
nrec =as.integer(nrec),
nvar =as.integer(nvar),
y =as.double(y),
sigma2e =as.double(sigma2e),
a0b0 =as.double(a0b0),
m1rand =as.integer(m1rand),
s2inv =as.double(s2inv),
s2invm2 =as.double(s2invm2),
nu =as.integer(nu),
s1rand =as.integer(s1rand),
psiinv =as.double(psiinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
cpo =as.double(cpo),
randsave =as.double(randsave),
thetasave =as.double(thetasave),
alpha =as.double(alpha),
m1 =as.double(m1),
s1 =as.double(s1),
ncluster =as.integer(ncluster),
muclus =as.double(muclus),
ss =as.integer(ss),
ccluster =as.integer(ccluster),
cstrt =as.integer(cstrt),
iflag =as.integer(iflag),
prob =as.double(prob),
sigma2ei =as.double(sigma2ei),
seed =as.integer(seed),
s1inv =as.double(s1inv),
s1invm1 =as.double(s1invm1),
theta =as.double(theta),
workm1 =as.double(workm1),
workm2 =as.double(workm2),
workm3 =as.double(workm3),
workmh1 =as.double(workmh1),
workmh2 =as.double(workmh2),
workv1 =as.double(workv1),
workv2 =as.double(workv2),
ywork =as.double(ywork),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
model.name<-"Bayesian semiparametric random effects model for multivariate meta-analysis"
thetasave <- matrix(foo$thetasave,nrow=nsave,ncol=nvar+nvar*(nvar+1)/2+2)
randsave <- matrix(foo$randsave,nrow=nsave,ncol=(nrec+1)*nvar)
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
varnames <- colnames(y)
if(is.null(varnames))
{
varnames <- all.vars(cl)[1:nvar]
}
indip <- rep(0,(nvar+nvar*(nvar+1)/2+2))
coeff <- NULL
pnames1 <- NULL
pnames2 <- NULL
renames <- NULL
for(i in 1:nvar)
{
pnames2 <- c(pnames2,paste("m1",varnames[i],sep="-"))
}
for(i in 1:nvar)
{
for(j in i:nvar)
{
tmp <- paste(varnames[i],varnames[j],sep=":")
pnames2 <- c(pnames2,paste("s1",tmp,sep="-"))
}
}
pnames2 <- c(pnames2,"ncluster","alpha")
for(i in 1:nrec)
{
for(j in 1:nvar)
{
tmp1 <- paste("m1",varnames[i],sep="-")
tmp2 <- paste("Subject=",i,sep="")
renames <- c(renames,paste(tmp2,tmp1,sep=";"))
}
}
for(j in 1:nvar)
{
tmp1 <- paste("m1",varnames[i],sep="-")
renames <- c(renames,paste("Prediction",tmp1,sep=";"))
}
colnames(thetasave) <- pnames2
colnames(randsave) <- renames
count <- 0
if(m1rand==1)
{
for(i in 1:nvar)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,i]))
pnames1 <- c(pnames1,paste("m1",varnames[i],sep="-"))
indip[i] <- 1
}
}
count <- nvar
if(s1rand==1)
{
for(i in 1:nvar)
{
for(j in i:nvar)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,count]))
tmp <- paste(varnames[i],varnames[j],sep=":")
pnames1 <- c(pnames1,paste("s1",tmp,sep="-"))
indip[count] <- 1
}
}
}
count <- nvar+nvar*(nvar+1)/2 + 1
coeff <- c(coeff,mean(thetasave[,count]))
pnames1 <- c(pnames1,"ncluster")
indip[count] <- 1
count <- nvar+nvar*(nvar+1)/2 + 1
if(alpharand==1)
{
count <- count + 1
coeff <- c(coeff,mean(thetasave[,count]))
pnames1 <- c(pnames1,"alpha")
indip[count] <- 1
}
names(coeff) <- pnames1
save.state <- list(thetasave=thetasave,
randsave=randsave)
state <- list(alpha=foo$alpha,
m1=matrix(foo$m1,nrow=nvar,ncol=1),
s1=matrix(foo$s1,nrow=nvar,ncol=nvar),
muclus=matrix(foo$muclus,nrow=nrec+1,ncol=nvar),
ncluster=foo$ncluster,
ss=foo$ss)
z<-list(call=cl,
y=y,
asymvar=asymvar,
varnames=varnames,
modelname=model.name,
cpo=cpo,
fso=fso,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
nvar=foo$nvar,
alpharand=alpharand,
s1rand=s1rand,
m1rand=m1rand,
coefficients=coeff,
indip=indip)
cat("\n\n")
class(z)<-c("DPmultmeta")
return(z)
}
###
### Tools: print, summary, plot
###
### Copyright: Alejandro Jara, 2008
### Last modification: 02-06-2008.
"print.DPmultmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Variables:",x$nvar,"\n")
cat("\n\n")
invisible(x)
}
"summary.DPmultmeta"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave<-object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo<-object$cpo
### Baseline Information
mat<-NULL
coef.p<-NULL
dimen1 <- object$nvar+object$nvar*(object$nvar+1)/2
for(i in 1:dimen1)
{
if(object$indip[i]==1)
{
coef.p <- c(coef.p,object$coefficients[i])
mat <- cbind(mat,thetasave[,i])
}
}
dimen1 <- dim(mat)[2]
if(dimen1>0)
{
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
}
### Precision parameter
dimen1<-object$nvar+object$nvar*(object$nvar+1)/2
if(is.null(object$prior$a0))
{
dimen2<-1
coef.p<-object$coefficients[(dimen1+1)]
mat<-matrix(thetasave[,(dimen1+1)],ncol=1)
}
else
{
dimen2<-2
coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
mat<-thetasave[,(dimen1+1):(dimen1+2)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
ans$nrec<-object$nrec
ans$nvar<-object$nvar
class(ans) <- "summaryDPmultmeta"
return(ans)
}
"print.summaryDPmultmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Variables:",x$nvar,"\n")
cat("\n\n")
invisible(x)
}
"plot.DPmultmeta"<-function(x, ask=TRUE, output="density", param=NULL, hpd=TRUE, nfigr=1, nfigc=1, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2006
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
"bivk"<-function(x, y, h, n = 25, lims = c(range(x), range(y)))
{
nx <- length(x)
if (length(y) != nx)
stop("Data vectors must be the same length")
gx <- seq(lims[1], lims[2], length = n)
gy <- seq(lims[3], lims[4], length = n)
if (missing(h))
h <- c(band(x), band(y))
h <- h/4
ax <- outer(gx, x, "-")/h[1]
ay <- outer(gy, y, "-")/h[2]
z <- matrix(dnorm(ax), n, nx) %*% t(matrix(dnorm(ay), n,
nx))/(nx * h[1] * h[2])
return(list(x = gx, y = gy, z = z))
}
"band"<-function(x)
{
r <- quantile(x, c(0.25, 0.75))
h <- (r[2] - r[1])/1.34
4 * 1.06 * min(sqrt(var(x)), h) * length(x)^(-1/5)
}
if(is(x, "DPmultmeta"))
{
if(output=="density")
{
# Density estimation
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1),nrow=nfigr,ncol=nfigc,byrow=TRUE))
start <- x$nrec*x$nvar
for(i in 1:x$nvar)
{
tmp <- paste("m1",x$varnames[i],sep="-")
title1 <- paste("Density of",tmp,sep=' ')
plot(density(x$save.state$randsave[,(start+i)]),type="l",lwd=2,,xlab="values", ylab="density",main=title1)
}
for(i in 1:(x$nvar-1))
{
for(j in (i+1):x$nvar)
{
varsn1 <- paste("m1",x$varnames[i],sep="-")
varsn2 <- paste("m1",x$varnames[j],sep="-")
tmp <- paste(varsn1,varsn2,sep=":")
title1<-paste("Density of ",tmp,sep='')
xx<-x$save.state$randsave[,(start+i)]
yy<-x$save.state$randsave[,(start+j)]
est<-bivk(xx,yy,n=200)
contour(est,main=title1,xlab=varsn1,ylab=varsn2)
persp(est,theta=-30,phi=15,expand = 0.9, ltheta = 120,main=title1,
xlab=varsn1,ylab=varsn2,zlab="density")
}
}
}
else
{
if(is.null(param))
{
pnames<-colnames(x$save.state$thetasave)
n<-dim(x$save.state$thetasave)[2]
cnames<-names(x$coefficients)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:(n-1))
{
if(x$indip[i]==1)
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(x$save.state$thetasave[,i],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
if(!is.null(x$prior$a0))
{
title1<-paste("Trace of",pnames[n],sep=" ")
title2<-paste("Density of",pnames[n],sep=" ")
plot(x$save.state$thetasave[,n],type='l',main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
pnames<-colnames(x$save.state$thetasave)
n<-dim(x$save.state$thetasave)[2]
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if (poss==0)
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
title1<-paste("Trace of",pnames[poss],sep=" ")
title2<-paste("Density of",pnames[poss],sep=" ")
plot(x$save.state$thetasave[,poss],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[poss]=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
}
}
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