Nothing
## Fit hazard model
sscox <- function(formula,type=NULL,data=list(),weights=NULL,subset,
na.action=na.omit,partial=NULL,alpha=1.4,
id.basis=NULL,nbasis=NULL,seed=NULL,random=NULL,
prec=1e-7,maxiter=30,skip.iter=FALSE)
{
## Local functions handling formula
Surv <- function(time,status,start=0) {
if (!is.numeric(time)|!is.vector(time))
stop("gss error in sscox: time should be a numerical vector")
if ((nobs <- length(time))-length(status))
stop("gss error in sscox: time and status mismatch in size")
if ((length(start)-nobs)&(length(start)-1))
stop("gss error in sscox: time and start mismatch in size")
if (any(start>time))
stop("gss error in sscox: start after follow-up time")
if (min(start)<0)
warning("gss warning in sscox: start before time 0")
time <- cbind(start,time)
list(start=time[,1],end=time[,2],status=as.logical(status))
}
## Obtain model frame and model terms
mf <- match.call()
mf$type <- mf$alpha <- mf$random <- mf$partial <- NULL
mf$id.basis <- mf$nbasis <- mf$seed <- NULL
mf$prec <- mf$maxiter <- mf$skip.iter <- NULL
term.wk <- terms.formula(formula)
## response
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 sscox: response should be Surv(...)")
yy <- with(data,eval(resp))
## model frame
term.labels <- attr(term.wk,"term.labels")
mf[[1]] <- as.name("model.frame")
mf[[2]] <- eval(parse(text=paste("~",paste(term.labels,collapse="+"),"-1")))
mf <- eval(mf,parent.frame())
## trim yy if subset is used
nobs <- nrow(mf)
if (nobs<length(yy$end)) {
yy$start <- yy$start[subset]
yy$end <- yy$end[subset]
yy$status <- yy$status[subset]
}
## Generate sub-basis
cnt <- model.weights(mf)
if (!is.null(cnt)) mf["(weights)"] <- NULL
if (is.null(id.basis)) {
if (is.null(nbasis)) nbasis <- max(30,ceiling(10*nobs^(2/9)))
if (nbasis>sum(yy$status)) nbasis <- sum(yy$status)
if (!is.null(seed)) set.seed(seed)
id.basis <- sample((1:nobs)[yy$status],nbasis,prob=cnt[yy$status])
}
else {
if (!all(id.basis%in%(1:nobs)[yy$status]))
stop("gss error in sscox: id.basis not all at failure cases")
nbasis <- length(id.basis)
}
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[i]])
}
## Generate terms
term <- mkterm(mf,type)
term$labels <- term$labels[term$labels!="1"]
## Generate random
if (!is.null(random)) {
if (inherits(random,"formula")) random <- mkran(random,data)
random$qd.z <- random$z
random$z <- random$z[yy$status,]
}
## Generate s and r
s <- qd.s <- r <- qd.r <- NULL
nq <- 0
for (label in term$labels) {
x.basis <- mf[id.basis,term[[label]]$vlist]
qd.x <- mf[,term[[label]]$vlist]
nphi <- term[[label]]$nphi
nrk <- term[[label]]$nrk
if (nphi) {
phi <- term[[label]]$phi
for (i in 1:nphi) {
s.wk <- phi$fun(qd.x,nu=i,env=phi$env)
s <- cbind(s,s.wk[yy$status])
qd.s <- cbind(qd.s,s.wk)
}
}
if (nrk) {
rk <- term[[label]]$rk
for (i in 1:nrk) {
nq <- nq+1
r.wk <- rk$fun(qd.x,x.basis,nu=i,env=rk$env,out=TRUE)
r <- array(c(r,r.wk[yy$status,]),c(nT,nbasis,nq))
qd.r <- array(c(qd.r,r.wk),c(nobs,nbasis,nq))
}
}
}
## Add the partial term
if (!is.null(partial)) {
mf.p <- model.frame(partial,data)
for (lab in colnames(mf.p)) mf[,lab] <- mf.p[,lab]
mt.p <- attr(mf.p,"terms")
lab.p <- labels(mt.p)
matx.p <- model.matrix(mt.p,data)[,-1,drop=FALSE]
if (dim(matx.p)[1]!=dim(mf)[1])
stop("gss error in sscox: partial data are of wrong size")
matx.p <- scale(matx.p)
center.p <- attr(matx.p,"scaled:center")
scale.p <- attr(matx.p,"scaled:scale")
s <- cbind(s,matx.p[yy$status,])
qd.s <- cbind(qd.s,matx.p)
part <- list(mt=mt.p,center=center.p,scale=scale.p)
}
else part <- lab.p <- NULL
## Check s rank
if (!is.null(s)) {
nnull <- dim(s)[2]
if (qr(s)$rank<nnull)
stop("gss error in sscox: unpenalized terms are linearly dependent")
}
## Generate quadrature and biasing weights
if (is.null(cnt)) {
qd.wt <- rep(1,dim(mf)[1])
cntt <- NULL
b.wt <- rep(1/nT,nT)
}
else {
qd.wt <- cnt
cntt <- cnt[yy$status]
b.wt <- cntt/sum(cntt)
}
tt <- yy$end[yy$status]
t.wt <- (outer(yy$end,tt,">=")&outer(yy$start,tt,"<="))/1
bias0 <- list(nt=nT,wt=b.wt,qd.wt=t.wt)
## Fit the model
if (nq==1) {
r <- r[,,1]
qd.r <- qd.r[,,1]
z <- sspcox(s,r,r[id.wk,],cntt,qd.s,qd.r,qd.wt,prec,maxiter,alpha,random,bias0)
}
else z <- mspcox(s,r,id.wk,cntt,qd.s,qd.r,qd.wt,prec,maxiter,alpha,random,bias0,skip.iter)
## Brief description of model terms
desc <- NULL
for (label in term$labels)
desc <- rbind(desc,as.numeric(c(term[[label]][c("nphi","nrk")])))
if (!is.null(partial)) {
desc <- rbind(desc,matrix(c(1,0),length(lab.p),2,byrow=TRUE))
}
desc <- rbind(desc,apply(desc,2,sum))
if (is.null(partial)) rownames(desc) <- c(term$labels,"total")
else rownames(desc) <- c(term$labels,lab.p,"total")
colnames(desc) <- c("Unpenalized","Penalized")
## Return the results
obj <- c(list(call=match.call(),mf=mf,cnt=cnt,terms=term,desc=desc,
alpha=alpha,id.basis=id.basis,partial=part,lab.p=lab.p,
random=random,bias=bias0,skip.iter=skip.iter),z)
Nobs <- ifelse(is.null(cnt),nT,sum(cntt))
obj$se.aux$v <- sqrt(Nobs)*obj$se.aux$v
class(obj) <- c("sscox")
obj
}
## Fit single smoothing parameter density
sspcox <- function(s,r,q,cnt,qd.s,qd.r,qd.wt,prec,maxiter,alpha,random,bias)
{
nobs <- dim(r)[1]
nxi <- dim(r)[2]
nqd <- length(qd.wt)
if (!is.null(s)) nnull <- dim(s)[2]
else nnull <- 0
if (!is.null(random)) nz <- ncol(as.matrix(random$z))
else nz <- 0
nxiz <- nxi + nz
nn <- nxiz + nnull
if (is.null(cnt)) cnt <- 0
## cv function
cv <- function(lambda) {
if (is.null(random)) q.wk0 <- 10^(lambda+theta)*q
else {
q.wk0 <- matrix(0,nxiz,nxiz)
q.wk0[1:nxi,1:nxi] <- 10^(lambda[1]+theta)*q
q.wk0[(nxi+1):nxiz,(nxi+1):nxiz] <-
10^(2*ran.scal)*random$sigma$fun(lambda[-1],random$sigma$env)
}
fit <- .Fortran("dnewton",
cd=as.double(cd), as.integer(nn),
as.double(q.wk0), as.integer(nxiz),
as.double(t(cbind(r.wk,s))), as.integer(nobs),
as.double(sum(cnt)), as.double(cnt),
as.double(cbind(qd.r.wk,qd.s)), as.integer(nqd),
as.integer(bias$nt), as.double(bias$wt),
as.double(t(qd.wt*bias$qd.wt)),
as.double(prec), as.integer(maxiter),
as.double(.Machine$double.eps), integer(nn),
wk=double(2*((nqd+1)*bias$nt+nobs)+nn*(2*nn+4)+max(nn,3)),
info=integer(1),PACKAGE="gss")
if (fit$info==1) stop("gss error in sscox: Newton iteration diverges")
if (fit$info==2) warning("gss warning in sscox: Newton iteration fails to converge")
assign("cd",fit$cd,inherits=TRUE)
cv <- alpha*fit$wk[2]-fit$wk[1]
alpha.wk <- max(0,log.la0-lambda-5)*(3-alpha) + alpha
alpha.wk <- min(alpha.wk,3)
adj <- ifelse (alpha.wk>alpha,(alpha.wk-alpha)*fit$wk[2],0)
cv+adj
}
cv.wk <- function(lambda) cv.scale*cv(lambda)+cv.shift
## initialization
if (!nnull) {
vv.r <- 0
for (i in 1:bias$nt) {
wt.wk <- qd.wt*bias$qd.wt[,i]
mu.r <- apply(wt.wk*qd.r,2,sum)/sum(wt.wk)
v.r <- apply(wt.wk*qd.r^2,2,sum)/sum(wt.wk)
v.r <- v.r - mu.r^2
vv.r <- vv.r + bias$wt[i]*v.r
}
theta <- 0
}
else {
vv.s <- vv.r <- 0
for (i in 1:bias$nt) {
wt.wk <- qd.wt*bias$qd.wt[,i]
mu.s <- apply(wt.wk*qd.s,2,sum)/sum(wt.wk)
v.s <- apply(wt.wk*qd.s^2,2,sum)/sum(wt.wk)
v.s <- v.s - mu.s^2
mu.r <- apply(wt.wk*qd.r,2,sum)/sum(wt.wk)
v.r <- apply(wt.wk*qd.r^2,2,sum)/sum(wt.wk)
v.r <- v.r - mu.r^2
vv.s <- vv.s + bias$wt[i]*v.s
vv.r <- vv.r + bias$wt[i]*v.r
}
theta <- log10(sum(vv.s)/nnull/sum(vv.r)*nxi) / 2
}
log.la0 <- log10(sum(vv.r)/sum(diag(q))) + theta
if (!is.null(random)) {
mu.z <- apply(qd.wt*random$qd.z,2,sum)
v.z <- apply(qd.wt*random$qd.z^2,2,sum)
ran.scal <- theta - log10(sum(v.z-mu.z^2)/nz/sum(v.r-mu.r^2)*nxi) / 2
r.wk <- cbind(10^theta*r,10^ran.scal*random$z)
qd.r.wk <- cbind(10^theta*qd.r,10^ran.scal*random$qd.z)
}
else {
ran.scal <- NULL
r.wk <- 10^theta*r
qd.r.wk <- 10^theta*qd.r
}
## lambda search
cd <- rep(0,nn)
if (is.null(random)) la <- log.la0
else la <- c(log.la0,random$init)
if (length(la)-1) {
counter <- 0
## scale and shift cv
tmp <- abs(cv(la))
cv.scale <- 1
cv.shift <- 0
if (tmp<1&tmp>10^(-4)) {
cv.scale <- 10/tmp
cv.shift <- 0
}
if (tmp<10^(-4)) {
cv.scale <- 10^2
cv.shift <- 10
}
repeat {
zz <- nlm(cv.wk,la,stepmax=1,ndigit=7)
if (zz$code<=3) break
la <- zz$est
counter <- counter + 1
if (counter>=5) {
warning("gss warning in sscox: iteration for model selection fails to converge")
break
}
}
cv <- (zz$min-cv.shift)/cv.scale
}
else {
mn0 <- log.la0-6
mx0 <- log.la0+6
repeat {
mn <- max(la-1,mn0)
mx <- min(la+1,mx0)
zz <- nlm0(cv,c(mn,mx))
if ((min(zz$est-mn,mx-zz$est)>=1e-1)||
(min(zz$est-mn0,mx0-zz$est)<1e-1)) break
else la <- zz$est
}
cv <- zz$min
}
## return
if (is.null(random)) {
lambda <- zz$est
zeta <- NULL
}
else {
lambda <- zz$est[1]
zeta <- zz$est[-1]
}
if (is.null(random)) {
q.wk0 <- 10^(lambda+theta)*q
qd.r.wk <- 10^theta*qd.r
}
else {
q.wk0 <- matrix(0,nxiz,nxiz)
q.wk0[1:nxi,1:nxi] <- 10^(lambda+theta)*q
q.wk0[(nxi+1):nxiz,(nxi+1):nxiz] <-
10^(2*ran.scal)*random$sigma$fun(zeta,random$sigma$env)
qd.r.wk <- cbind(10^theta*qd.r,10^ran.scal*random$qd.z)
}
se.aux <- .Fortran("coxaux",
as.double(cd), as.integer(nn),
as.double(q.wk0), as.integer(nxiz),
as.double(cbind(qd.r.wk,qd.s)), as.integer(nqd),
as.integer(bias$nt), as.double(bias$wt),
as.double(.Machine$double.eps),
as.double(qd.wt*bias$qd.wt),
double(nqd*bias$nt), double(bias$nt),
double(nn), v=double(nn*nn), double(nn*nn),
jpvt=integer(nn), PACKAGE="gss")[c("v","jpvt")]
c <- cd[1:nxi]
if (nz) b <- 10^ran.scal*cd[nxi+(1:nz)]
else b <- NULL
if (nnull) d <- cd[nxiz+(1:nnull)]
else d <- NULL
return(list(lambda=lambda,zeta=zeta,theta=theta,ran.scal=ran.scal,
c=c,b=b,d=d,cv=cv,se.aux=se.aux))
}
## Fit multiple smoothing parameter density
mspcox <- function(s,r,id.basis,cnt,qd.s,qd.r,qd.wt,prec,maxiter,alpha,random,bias,skip.iter)
{
nobs <- dim(r)[1]
nxi <- dim(r)[2]
nq <- dim(r)[3]
nqd <- length(qd.wt)
if (!is.null(s)) nnull <- dim(s)[2]
else nnull <- 0
if (!is.null(random)) nz <- ncol(as.matrix(random$z))
else nz <- 0
nxiz <- nxi + nz
nn <- nxiz + nnull
if (is.null(cnt)) cnt <- 0
## cv function
cv <- function(theta) {
ind.wk <- theta[1:nq]!=theta.old
if (sum(ind.wk)==nq) {
r.wk0 <- qd.r.wk0 <- 0
for (i in 1:nq) {
r.wk0 <- r.wk0 + 10^theta[i]*r[,,i]
qd.r.wk0 <- qd.r.wk0 + 10^theta[i]*qd.r[,,i]
}
assign("r.wk",r.wk0+0,inherits=TRUE)
assign("qd.r.wk",qd.r.wk0+0,inherits=TRUE)
assign("theta.old",theta[1:nq]+0,inherits=TRUE)
}
else {
r.wk0 <- r.wk
qd.r.wk0 <- qd.r.wk
for (i in (1:nq)[ind.wk]) {
theta.wk <- (10^(theta[i]-theta.old[i])-1)*10^theta.old[i]
r.wk0 <- r.wk0 + theta.wk*r[,,i]
qd.r.wk0 <- qd.r.wk0 + theta.wk*qd.r[,,i]
}
}
q.wk <- r.wk0[id.basis,]
if (is.null(random)) q.wk0 <- 10^(lambda)*q.wk
else {
r.wk0 <- cbind(r.wk0,10^ran.scal*random$z)
qd.r.wk0 <- cbind(qd.r.wk0,10^ran.scal*random$qd.z)
q.wk0 <- matrix(0,nxiz,nxiz)
q.wk0[1:nxi,1:nxi] <- 10^(lambda)*q.wk
q.wk0[(nxi+1):nxiz,(nxi+1):nxiz] <-
10^(2*ran.scal)*random$sigma$fun(theta[-(1:nq)],random$sigma$env)
}
fit <- .Fortran("dnewton",
cd=as.double(cd), as.integer(nn),
as.double(q.wk0), as.integer(nxiz),
as.double(t(cbind(r.wk0,s))), as.integer(nobs),
as.double(sum(cnt)), as.double(cnt),
as.double(cbind(qd.r.wk0,qd.s)), as.integer(nqd),
as.integer(bias$nt), as.double(bias$wt),
as.double(t(qd.wt*bias$qd.wt)),
as.double(prec), as.integer(maxiter),
as.double(.Machine$double.eps), integer(nn),
wk=double(2*((nqd+1)*bias$nt+nobs)+nn*(2*nn+4)+max(nn,3)),
info=integer(1),PACKAGE="gss")
if (fit$info==1) stop("gss error in ssden: Newton iteration diverges")
if (fit$info==2) warning("gss warning in ssden: Newton iteration fails to converge")
assign("cd",fit$cd,inherits=TRUE)
cv <- alpha*fit$wk[2]-fit$wk[1]
alpha.wk <- max(0,theta-log.th0-5)*(3-alpha) + alpha
alpha.wk <- min(alpha.wk,3)
adj <- ifelse (alpha.wk>alpha,(alpha.wk-alpha)*fit$wk[2],0)
cv+adj
}
cv.wk <- function(theta) cv.scale*cv(theta)+cv.shift
## initialization
theta <- -log10(apply(r[id.basis,,],3,function(x)sum(diag(x))))
r.wk <- qd.r.wk <- 0
for (i in 1:nq) {
r.wk <- r.wk + 10^theta[i]*r[,,i]
qd.r.wk <- qd.r.wk + 10^theta[i]*qd.r[,,i]
}
## theta adjustment
z <- sspcox(s,r.wk,r.wk[id.basis,],cnt,qd.s,qd.r.wk,qd.wt,prec,maxiter,alpha,random,bias)
theta <- theta + z$theta
r.wk <- qd.r.wk <- 0
for (i in 1:nq) {
theta[i] <- 2*theta[i] + log10(t(z$c)%*%r[id.basis,,i]%*%z$c)
r.wk <- r.wk + 10^theta[i]*r[,,i]
qd.r.wk <- qd.r.wk + 10^theta[i]*qd.r[,,i]
}
mu <- apply(qd.wt*qd.r.wk,2,sum)/sum(qd.wt)
v <- apply(qd.wt*qd.r.wk^2,2,sum)/sum(qd.wt)
log.la0 <- log10(sum(v-mu^2)/sum(diag(r.wk[id.basis,])))
log.th0 <- theta-log.la0
## lambda search
z <- sspcox(s,r.wk,r.wk[id.basis,],cnt,qd.s,qd.r.wk,qd.wt,prec,maxiter,alpha,random,bias)
## early return
if (skip.iter) {
z$theta <- theta
return(z)
}
## theta search
lambda <- z$lambda
log.th0 <- log.th0 + z$lambda
theta <- theta + z$theta
ran.scal <- z$ran.scal
cd <- c(z$c,z$b,z$d)
counter <- 0
r.wk <- qd.r.wk <- 0
for (i in 1:nq) {
r.wk <- r.wk + 10^theta[i]*r[,,i]
qd.r.wk <- qd.r.wk + 10^theta[i]*qd.r[,,i]
}
theta.old <- theta
if (!is.null(random)) theta <- c(theta,zeta)
## scale and shift cv
tmp <- abs(cv(theta))
cv.scale <- 1
cv.shift <- 0
if (tmp<1&tmp>10^(-4)) {
cv.scale <- 10/tmp
cv.shift <- 0
}
if (tmp<10^(-4)) {
cv.scale <- 10^2
cv.shift <- 10
}
repeat {
zz <- nlm(cv.wk,theta,stepmax=1,ndigit=7)
if (zz$code<=3) break
theta <- zz$est
counter <- counter + 1
if (counter>=5) {
warning("gss warning in sscox: CV iteration fails to converge")
break
}
}
cv <- (zz$min-cv.shift)/cv.scale
if (is.null(random)) {
theta <- zz$est
zeta <- NULL
}
else {
theta <- zz$est[1:nq]
zeta <- zz$est[-(1:nq)]
}
## return
q.wk <- qd.r.wk <- 0
for (i in 1:nq) {
q.wk <- q.wk + 10^theta[i]*r[id.basis,,i]
qd.r.wk <- qd.r.wk + 10^theta[i]*qd.r[,,i]
}
if (is.null(random)) q.wk0 <- 10^(lambda)*q.wk
else {
q.wk0 <- matrix(0,nxiz,nxiz)
q.wk0[1:nxi,1:nxi] <- 10^(lambda)*q.wk
q.wk0[(nxi+1):nxiz,(nxi+1):nxiz] <-
10^(2*ran.scal)*random$sigma$fun(zeta,random$sigma$env)
qd.r.wk <- cbind(qd.r.wk,10^ran.scal*random$qd.z)
}
se.aux <- .Fortran("coxaux",
as.double(cd), as.integer(nn),
as.double(q.wk0), as.integer(nxiz),
as.double(cbind(qd.r.wk,qd.s)), as.integer(nqd),
as.integer(bias$nt), as.double(bias$wt),
as.double(.Machine$double.eps),
as.double(qd.wt*bias$qd.wt),
double(nqd*bias$nt), double(bias$nt),
double(nn), v=double(nn*nn), double(nn*nn),
jpvt=integer(nn), PACKAGE="gss")[c("v","jpvt")]
c <- cd[1:nxi]
if (nz) b <- 10^ran.scal*cd[nxi+(1:nz)]
else b <- NULL
if (nnull) d <- cd[nxiz+(1:nnull)]
else d <- NULL
return(list(lambda=lambda,zeta=zeta,theta=theta,ran.scal=ran.scal,
c=c,b=b,d=d,cv=cv,se.aux=se.aux))
}
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