Nothing
## Fit hazard model
sshzd2d1 <- function(formula1,formula2,symmetry=FALSE,data,alpha=1.4,weights=NULL,
subset=NULL,rho="marginal",id.basis=NULL,nbasis=NULL,
seed=NULL,prec=1e-7,maxiter=30,skip.iter=FALSE)
{
## Prepare data
if (!is.null(subset)) {
data <- data[subset,]
if (!is.null(weights)) {
id.wk <- apply(!is.na(data),1,all)
cnt <- weights[id.wk]
}
else cnt <- NULL
data <- na.omit(data[subset,])
}
else {
if (!is.null(weights)) {
id.wk <- apply(!is.na(data),1,all)
cnt <- weights[id.wk]
}
else cnt <- NULL
data <- na.omit(data)
}
## Extract formulas
if (class(formula1)=="formula") {
form1 <- formula1
part1 <- random1 <- type1 <- NULL
}
else {
if (class(formula1)!="list")
stop("gss error in sshzd2d1: models must be specified via formulas or lists")
form1 <- formula1[[1]]
part1 <- formula1$partial
random1 <- formula1$random
type1 <- formula1$type
}
if (class(formula2)=="formula") {
form2 <- formula2
part2 <- random2 <- type2 <- NULL
}
else {
if (class(formula2)!="list")
stop("gss error in sshzd2d1: models must be specified via formulas or lists")
form2 <- formula2[[1]]
part2 <- formula2$partial
random2 <- formula2$random
type2 <- formula2$type
}
## Local function handling formula
Surv <- function(time,status,start=0) {
tname <- as.character(as.list(match.call())$time)
if (!is.numeric(time)|!is.vector(time))
stop("gss error in sshzd2d1: time should be a numerical vector")
if ((nobs <- length(time))-length(status))
stop("gss error in sshzd2d1: time and status mismatch in size")
if ((length(start)-nobs)&(length(start)-1))
stop("gss error in sshzd2d1: time and start mismatch in size")
if (any(start>time))
stop("gss error in sshzd2d1: start after follow-up time")
if (min(start)<0)
stop("gss error in sshzd2d1: start before time 0")
time <- cbind(start,time)
list(tname=tname,start=time[,1],end=time[,2],status=as.logical(status))
}
## Obtain model terms
for (i in 1:2) {
## Formula
form.wk <- switch(i,form1,form2)
term.wk <- terms.formula(form.wk)
resp <- attr(term.wk,"variable")[[2]]
ind.wk <- length(strsplit(deparse(resp),'')[[1]])
if ((substr(deparse(resp),1,5)!='Surv(')
|(substr(deparse(resp),ind.wk,ind.wk)!=')'))
stop("gss error in sshzd2d1: response should be Surv(...)")
yy <- with(data,eval(resp))
tname <- yy$tname
term.labels <- attr(term.wk,"term.labels")
if (!(tname%in%term.labels))
stop("gss error in sshzd2d1: time main effect missing in model")
form.wk <- eval(parse(text=paste("~",paste(term.labels,collapse="+"))))
mf.wk <- model.frame(form.wk,data)
## Partial
part.wk <- switch(i,part1,part2)
if (!is.null(part.wk)) {
mf.p.wk <- model.frame(part.wk,data)
mt.p.wk <- attr(mf.p.wk,"terms")
matx.p.wk <- model.matrix(mt.p.wk,data)[,-1,drop=FALSE]
if (dim(matx.p.wk)[1]!=dim(mf.wk)[1])
stop("gss error in sshzd2d1: partial data are of wrong size")
}
else mf.p.wk <- mt.p.wk <- matx.p.wk <- NULL
## Random
random.wk <- switch(i,random1,random2)
if (!is.null(random.wk)) {
if (class(random.wk)=="formula") random.wk <- mkran(random.wk,data)
}
else random.wk <- NULL
## Set domain and type for time
type.wk <- switch(i,type1,type2)
mn <- min(yy$start)
mx <- max(yy$end)
tdomain <- c(max(mn-.05*(mx-mn),0),mx)
tname <- yy$tname
if (is.null(type.wk[[tname]])) type.wk[[tname]] <- list("cubic",tdomain)
if (length(type.wk[[tname]])==1) type.wk[[tname]] <- c(type.wk[[tname]],tdomain)
if (!(type.wk[[tname]][[1]]%in%c("cubic","linear")))
stop("gss error in sshzd2d1: wrong type")
if ((min(type.wk[[tname]][[2]])>min(tdomain))|
(max(type.wk[[tname]][[2]])<max(tdomain)))
stop("gss error in sshzd2d1: time range not covering domain")
## Save
if (i==1) {
mf1 <- mf.wk
yy1 <- yy
mf.p1 <- mf.p.wk
mt.p1 <- mt.p.wk
matx.p1 <- matx.p.wk
random1 <- random.wk
type1 <- type.wk
tdomain1 <- tdomain
}
else {
mf2 <- mf.wk
yy2 <- yy
mf.p2 <- mf.p.wk
mt.p2 <- mt.p.wk
matx.p2 <- matx.p.wk
random2 <- random.wk
type2 <- type.wk
tdomain2 <- tdomain
}
}
## Generate sub-basis
nobs <- dim(mf1)[1]
if (is.null(id.basis)) {
if (is.null(nbasis)) nbasis <- max(30,ceiling(10*nobs^(2/9)))
if (nbasis>=nobs) nbasis <- nobs
if (!is.null(seed)) set.seed(seed)
id.basis <- sample(nobs,nbasis,prob=cnt)
}
else {
if (max(id.basis)>nobs|min(id.basis)<1)
stop("gss error in sshzd2d1: id.basis out of range")
nbasis <- length(id.basis)
}
## Generate terms
if (symmetry) {
nhzd <- 1
if (dim(mf2)[2]!=dim(mf1)[2])
stop("gss error in sshzd2d1: variables in parallel formulas must match")
mf1.wk <- mf1
mf2.wk <- mf2
names(mf1.wk) <- names(mf2)
names(mf2.wk) <- names(mf1)
tdomain1 <- c(min(tdomain1,tdomain2),max(tdomain1,tdomain2))
type1[[yy1$tname]][[2]] <- tdomain1
type2[[yy2$tname]][[2]] <- tdomain1
term1 <- mkterm(rbind(mf1,mf2.wk),type1)
term2 <- mkterm(rbind(mf2,mf1.wk),type2)
mf1 <- rbind(mf1,mf2.wk)
yy1.sv <- yy1
yy1$start <- c(yy1$start,yy2$start)
yy1$end <- c(yy1$end,yy2$end)
yy1$status <- c(yy1$status,yy2$status)
id.basis.wk <- c(id.basis,id.basis+nobs)
if (!is.null(mf.p1)) {
if (is.null(mf.p2)||(dim(mf.p2)[2]!=dim(mf.p1)[2]))
stop("gss error in sshzd2d1: variables in parallel formulas must match")
matx.p1 <- rbind(matx.p1,matx.p2)
}
if (!is.null(random1)) {
if (is.null(random2)||(dim(random2$z)[2]!=dim(random1$z)[2]))
stop("gss error in sshzd2d1: variables in parallel formulas must match")
random1$z <- rbind(random1$z,random2$z)
}
if (!is.null(cnt)) cnt.wk <- c(cnt,cnt)
else cnt.wk <- NULL
}
else {
nhzd <- 2
term1 <- mkterm(mf1,type1)
term2 <- mkterm(mf2,type2)
id.basis.wk <- id.basis
cnt.wk <- cnt
}
## Fit marginal hazard models
for (ii in 1:nhzd) {
## Extract model components
mf <- switch(ii,mf1,mf2)
yy <- switch(ii,yy1,yy2)
term <- switch(ii,term1,term2)
mf.p <- switch(ii,mf.p1,mf.p2)
mt.p <- switch(ii,mt.p1,mt.p2)
matx.p <- switch(ii,matx.p1,matx.p2)
random <- switch(ii,random1,random2)
tdomain <- switch(ii,tdomain1,tdomain2)
if (rho=="weibull") partt <- switch(ii,part1,part2)
## Finalize id.basis
nobs <- length(yy$status)
id.basis.wk <- id.basis.wk[yy$status[id.basis.wk]]
nbasis <- length(id.basis.wk)
id.wk <- NULL
nT <- sum(yy$status)
for (i in 1:nbasis) {
id.wk <- c(id.wk,(1:nT)[(1:nobs)[yy$status]%in%id.basis.wk[i]])
}
## Generate Gauss-Legendre quadrature
nmesh <- 200
quad <- gauss.quad(nmesh,tdomain)
## set up partial terms
if (!is.null(mf.p)) {
for (lab in colnames(mf.p)) mf[,lab] <- mf.p[,lab]
lab.p <- labels(mt.p)
matx.p <- scale(matx.p)
center.p <- attr(matx.p,"scaled:center")
scale.p <- attr(matx.p,"scaled:scale")
part <- list(mt=mt.p,center=center.p,scale=scale.p)
}
else part <- lab.p <- NULL
## Obtain unique covariate observations
tname <- yy$tname
xnames <- names(mf)
xnames <- xnames[!xnames%in%tname]
if (length(xnames)) {
xx <- mf[,xnames,drop=FALSE]
if (!is.null(part)) xx <- cbind(xx,matx.p)
if (!is.null(random)) xx <- cbind(xx,random$z)
xx <- apply(xx,1,function(x)paste(x,collapse="\r"))
ux <- unique(xx)
nx <- length(ux)
x.dup.ind <- duplicated(xx)
x.dup <- as.vector(xx[x.dup.ind])
x.pt <- mf[!x.dup.ind,xnames,drop=FALSE]
## xx[i,]==x.pt[x.ind[i],]
x.ind <- 1:nobs
x.ind[!x.dup.ind] <- 1:nx
if (nobs-nx) {
x.ind.wk <- range <- 1:(nobs-nx)
for (i in 1:nx) {
range.wk <- NULL
for (j in range) {
if (identical(ux[i],x.dup[j])) {
x.ind.wk[j] <- i
range.wk <- c(range.wk,j)
}
}
if (!is.null(range.wk)) range <- range[!(range%in%range.wk)]
}
x.ind[x.dup.ind] <- x.ind.wk
}
if (!is.null(random)) {
qd.z <- random$z[!x.dup.ind,]
random$z <- random$z[yy$status,]
}
}
else stop("gss error in sshzd2d1: missing covariate")
## calculate rho
if (is.null(cnt.wk)) yy$cnt <- rep(1,nobs)
else yy$cnt <- cnt.wk
if (rho=="marginal") {
rho.wk <- sshzd(Surv(end,status,start)~end,data=yy,
id.basis=id.basis.wk,weights=cnt,alpha=2)
rho.qd <- hzdcurve.sshzd(rho.wk,quad$pt)
rhowk <- hzdcurve.sshzd(rho.wk,yy$end[yy$status])
}
if (rho=="weibull") {
y.wk <- cbind(yy$end,yy$status,yy$start)
form <- as.formula(paste("y.wk~",paste(xnames,collapse="+")))
rho.wk <- gssanova(form,family="weibull",partial=partt,data=mf,
id.basis=id.basis.wk,weights=cnt,alpha=2)
yhat <- predict(rho.wk,rho.wk$mf)
rho.qd <- exp(rho.wk$nu*outer(log(quad$pt),yhat[!x.dup.ind],"-"))/quad$pt
rhowk <- (exp(rho.wk$nu*(log(yy$end)-yhat))/yy$end)[yy$status]
}
## integration weights at x.pt[i,]
qd.wt <- matrix(0,nmesh,nx)
for (i in 1:nobs) {
wk <- (quad$pt<=yy$end[i])&(quad$pt>yy$start[i])
if (is.vector(rho.qd)) wk <- wk*rho.qd
else wk <- wk*rho.qd[,x.ind[i]]
if (is.null(cnt.wk)) qd.wt[,x.ind[i]] <- qd.wt[,x.ind[i]]+wk
else qd.wt[,x.ind[i]] <- qd.wt[,x.ind[i]]+cnt.wk[i]*wk
}
if (is.null(cnt.wk)) qd.wt <- quad$wt*qd.wt/nobs
else qd.wt <- quad$wt*qd.wt/sum(cnt.wk)
## Generate s, r, int.s, and int.r
s <- r <- int.s <- int.r <- NULL
nq <- 0
for (label in term$labels) {
if (label=="1") {
s <- cbind(s,rep(1,len=nT))
int.s <- c(int.s,sum(qd.wt))
next
}
vlist <- term[[label]]$vlist
x.list <- xnames[xnames%in%vlist]
xy <- mf[yy$status,vlist]
xy.basis <- mf[id.basis.wk,vlist]
qd.xy <- data.frame(matrix(0,nmesh,length(vlist)))
names(qd.xy) <- vlist
if (tname%in%vlist) qd.xy[,tname] <- quad$pt
if (length(x.list)) xx <- x.pt[,x.list,drop=FALSE]
else xx <- NULL
nphi <- term[[label]]$nphi
nrk <- term[[label]]$nrk
if (nphi) {
phi <- term[[label]]$phi
for (i in 1:nphi) {
s <- cbind(s,phi$fun(xy,nu=i,env=phi$env))
if (is.null(xx)) {
qd.wk <- phi$fun(qd.xy[,,drop=TRUE],nu=i,env=phi$env)
int.s <- c(int.s,sum(qd.wk*apply(qd.wt,1,sum)))
}
else {
int.s.wk <- 0
for (j in 1:nx) {
qd.xy[,x.list] <- xx[rep(j,nmesh),]
qd.wk <- phi$fun(qd.xy[,,drop=TRUE],i,phi$env)
int.s.wk <- int.s.wk + sum(qd.wk*qd.wt[,j])
}
int.s <- c(int.s,int.s.wk)
}
}
}
if (nrk) {
rk <- term[[label]]$rk
for (i in 1:nrk) {
nq <- nq+1
r <- array(c(r,rk$fun(xy,xy.basis,nu=i,env=rk$env,out=TRUE)),c(nT,nbasis,nq))
if (is.null(xx)) {
qd.wk <- rk$fun(qd.xy[,,drop=TRUE],xy.basis,i,rk$env,out=TRUE)
int.r <- cbind(int.r,apply(apply(qd.wt,1,sum)*qd.wk,2,sum))
}
else {
int.r.wk <- 0
for (j in 1:nx) {
qd.xy[,x.list] <- xx[rep(j,nmesh),]
qd.wk <- rk$fun(qd.xy[,,drop=TRUE],xy.basis,i,rk$env,TRUE)
int.r.wk <- int.r.wk + apply(qd.wt[,j]*qd.wk,2,sum)
}
int.r <- cbind(int.r,int.r.wk)
}
}
}
}
## Add the partial term
if (!is.null(part)) {
s <- cbind(s,matx.p[yy$status,])
int.s <- c(int.s,t(matx.p[!x.dup.ind,])%*%apply(qd.wt,2,sum))
}
## generate int.z
if (!is.null(random)) random$int.z <- t(qd.z)%*%apply(qd.wt,2,sum)
## Check s rank
if (!is.null(s)) {
nnull <- dim(s)[2]
if (qr(s)$rank<nnull)
stop("gss error in sshzd2d1: unpenalized terms are linearly dependent")
}
## Fit the model
Nobs <- ifelse(is.null(cnt.wk),nobs,sum(cnt.wk))
if (!is.null(cnt.wk)) cntt <- cnt.wk[yy$status]
else cntt <- NULL
z <- msphzd1(s,r,id.wk,Nobs,cntt,int.s,int.r,rhowk,random,prec,maxiter,alpha,skip.iter)
## cfit
if (!is.null(random)) rhowk <- rhowk*exp(-random$z%*%z$b)
if (!is.null(cnt.wk)) cfit <- sum(cntt*rhowk)/Nobs/sum(qd.wt)
else cfit <- sum(rhowk)/Nobs/sum(qd.wt)
## Brief description of model terms
desc <- NULL
for (label in term$labels)
desc <- rbind(desc,as.numeric(c(term[[label]][c("nphi","nrk")])))
if (!is.null(part)) {
desc <- rbind(desc,matrix(c(1,0),length(lab.p),2,byrow=TRUE))
}
desc <- rbind(desc,apply(desc,2,sum))
if (is.null(part)) rownames(desc) <- c(term$labels,"total")
else rownames(desc) <- c(term$labels,lab.p,"total")
colnames(desc) <- c("Unpenalized","Penalized")
## Return the results
hzd <- c(list(call=match.call(),mf=mf,cnt=cnt.wk,terms=term,desc=desc,
alpha=alpha,tname=tname,xnames=xnames,tdomain=tdomain,cfit=cfit,
quad=quad,x.pt=x.pt,qd.wt=qd.wt,id.basis=id.basis.wk,partial=part,
lab.p=lab.p,random=random,skip.iter=skip.iter),z)
hzd$se.aux$v <- sqrt(Nobs)*hzd$se.aux$v
class(hzd) <- c("sshzd1","sshzd")
if (ii==1) hzd1 <- hzd
else hzd2 <- hzd
}
## Finalize hzd2
if (symmetry) {
hzd2 <- hzd1
hzd2$terms <- term2
names(hzd2$mf) <- hzd2$xnames <- c(names(mf2),names(mf.p2))
hzd2$tname <- yy2$tname
hzd2$xnames <- names(hzd2$x.pt) <- hzd2$xnames[!hzd2$xnames%in%hzd2$tname]
hzd2$lab.p <- labels(mt.p2)
if (!is.null(hzd2$partial)) hzd2$partial$mt <- mt.p2
desc <- NULL
for (label in term2$labels)
desc <- rbind(desc,as.numeric(c(term2[[label]][c("nphi","nrk")])))
if (!is.null(part)) {
desc <- rbind(desc,matrix(c(1,0),length(hzd2$lab.p),2,byrow=TRUE))
}
desc <- rbind(desc,apply(desc,2,sum))
if (is.null(part)) rownames(desc) <- c(term2$labels,"total")
else rownames(desc) <- c(term2$labels,hzd2$lab.p,"total")
colnames(desc) <- c("Unpenalized","Penalized")
hzd2$desc <- desc
yy1 <- yy1.sv
}
## Estimate copula
nobs <- length(yy1$status)
s1 <- min(hzd1$tdomain)
s2 <- min(hzd2$tdomain)
u1 <- u2 <- NULL
for (i in 1:nobs) {
u1 <- c(u1,survexp.sshzd(hzd1,yy1$end[i],data[i,,drop=FALSE],s1))
u2 <- c(u2,survexp.sshzd(hzd2,yy2$end[i],data[i,,drop=FALSE],s2))
}
v1 <-v2 <- NULL
if (any(yy1$start&yy2$start)) {
for (i in 1:nobs) {
v1 <- c(v1,survexp.sshzd(hzd1,yy1$start[i],data[i,,drop=FALSE],s1))
v2 <- c(v2,survexp.sshzd(hzd2,yy2$start[i],data[i,,drop=FALSE],s2))
}
}
cens <- as.numeric(!yy1$status)+as.numeric(!yy2$status)*2
if (!is.null(v1)) trun <- cbind(v1,v2)
else trun <- NULL
copu <- sscopu2(cbind(u1,u2),cens,trun,symmetry,id.basis=id.basis)
## Return the fits
obj <- list(call=match.call(),symmetry=symmetry,alpha=alpha,
id.basis=id.basis,hzd1=hzd1,hzd2=hzd2,copu=copu)
class(obj) <- "sshzd2d"
obj
}
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