Nothing
R/two-stage-reg.r
In timereg: Flexible Regression Models for Survival Data
Defines functions
predict.two.stage
plot.two.stage
coef.two.stage
vcov.two.stage
two.stage
Documented in
coef.two.stage
plot.two.stage
predict.two.stage
two.stage
vcov.two.stage
#' Fit Clayton-Oakes-Glidden Two-Stage model
#'
#' Fit Clayton-Oakes-Glidden Two-Stage model with Cox-Aalen marginals and
#' regression on the variance parameters.
#'
#' The model specifikatin allows a regression structure on the variance of the
#' random effects, such it is allowed to depend on covariates fixed within
#' clusters \deqn{ \theta_{k} = Q_{k}^T \nu }{}. This is particularly useful to
#' model jointly different groups and to compare their variances.
#'
#' Fits an Cox-Aalen survival model. Time dependent variables and counting
#' process data (multiple events per subject) are not possible !
#'
#' The marginal baselines are on the Cox-Aalen form \deqn{ \lambda_{ki}(t) =
#' Y_{ki}(t) ( X_{ki}^T(t) \alpha(t) ) \exp(Z_{ki}^T \beta ) }{}
#'
#' The model thus contains the Cox's regression model and the additive hazards
#' model as special cases. (see cox.aalen function for more on this).
#'
#' The modelling formula uses the standard survival modelling given in the
#' \bold{survival} package. Only for right censored survival data.
#'
#' The data for a subject is presented as multiple rows or 'observations', each
#' of which applies to an interval of observation (start, stop]. For counting
#' process data with the )start,stop] notation is used the 'id' variable is
#' needed to identify the records for each subject. Only one record per subject
#' is allowed in the current implementation for the estimation of theta. The
#' program assumes that there are no ties, and if such are present random noise
#' is added to break the ties.
#'
#' Left truncation is dealt with. Here the key assumption is that the maginals
#' are correctly estimated and that we have a common truncation time within
#' each cluster.
#'
#' @param margsurv fit of marginal survival cox.aalen model with residuals=2,
#' and resample.iid=1 to get fully correct standard errors. See notaylor below.
#' @param data a data.frame with the variables.
#' @param start.time start of observation period where estimates are computed.
#' @param max.time end of observation period where estimates are computed.
#' Estimates thus computed from [start.time, max.time]. Default is max of data.
#' @param id For timevarying covariates the variable must associate each record
#' with the id of a subject.
#' @param clusters cluster variable for computation of robust variances.
#' @param robust if 0 then totally omits computation of standard errors.
#' @param Nit number of iterations for Newton-Raphson algorithm.
#' @param detail if 0 no details is printed during iterations, if 1 details are
#' given.
#' @param theta starting values for the frailty variance (default=0.1).
#' @param theta.des design for regression for variances. The defauls is NULL
#' that is equivalent to just one theta and the design with only a baseline.
#' @param var.link default "0" is that the regression design on the variances
#' is without a link, and "1" uses the link function exp.
#' @param step step size for Newton-Raphson.
#' @param notaylor if 1 then ignores variation due to survival model, this is
#' quicker and then resample.iid=0 and residuals=0 is ok for marginal survival
#' model that then is much quicker.
#' @param se.clusters cluster variable for sandwich estimator of variance.
#' @return returns an object of type "two.stage". With the following arguments:
#' \item{cum}{cumulative timevarying regression coefficient estimates are
#' computed within the estimation interval.} \item{var.cum}{the martingale
#' based pointwise variance estimates.} \item{robvar.cum}{robust pointwise
#' variances estimates.} \item{gamma}{estimate of parametric components of
#' model.} \item{var.gamma}{variance for gamma.} \item{robvar.gamma}{robust
#' variance for gamma.} \item{D2linv}{inverse of the derivative of the score
#' function from marginal model.} \item{score}{value of score for final
#' estimates.} \item{theta}{estimate of Gamma variance for frailty.}
#' \item{var.theta}{estimate of variance of theta.} \item{SthetaInv}{inverse of
#' derivative of score of theta.} \item{theta.score}{score for theta
#' parameters.}
#' @author Thomas Scheike
#' @references Glidden (2000), A Two-Stage estimator of the dependence
#' parameter for the Clayton Oakes model.
#'
#' Martinussen and Scheike, Dynamic Regression Models for Survival Data,
#' Springer (2006).
#' @keywords survival
#' @examples
#'
#' library(timereg)
#' data(diabetes)
#' # Marginal Cox model with treat as covariate
#' marg <- cox.aalen(Surv(time,status)~prop(treat)+prop(adult)+
#' cluster(id),data=diabetes,resample.iid=1)
#' fit<-two.stage(marg,data=diabetes,theta=1.0,Nit=40)
#' summary(fit)
#'
#' # using coxph and giving clusters, but SE wittout cox uncetainty
#' margph <- coxph(Surv(time,status)~treat,data=diabetes)
#' fit<-two.stage(margph,data=diabetes,theta=1.0,Nit=40,clusters=diabetes$id)
#'
#'
#' # Stratification after adult
#' theta.des<-model.matrix(~-1+factor(adult),diabetes);
#' des.t<-model.matrix(~-1+factor(treat),diabetes);
#' design.treat<-cbind(des.t[,-1]*(diabetes$adult==1),
#' des.t[,-1]*(diabetes$adult==2))
#'
#' # test for common baselines included here
#' marg1<-cox.aalen(Surv(time,status)~-1+factor(adult)+prop(design.treat)+cluster(id),
#' data=diabetes,resample.iid=1,Nit=50)
#'
#' fit.s<-two.stage(marg1,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s)
#'
#' # with common baselines and common treatment effect (although test reject this)
#' fit.s2<-two.stage(marg,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s2)
#'
#' # test for same variance among the two strata
#' theta.des<-model.matrix(~factor(adult),diabetes);
#' fit.s3<-two.stage(marg,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s3)
#'
#' # to fit model without covariates, use beta.fixed=1 and prop or aalen function
#' marg <- aalen(Surv(time,status)~+1+cluster(id),
#' data=diabetes,resample.iid=1,n.sim=0)
#' fita<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fita)
#'
#' # same model but se's without variation from marginal model to speed up computations
#' marg <- aalen(Surv(time,status) ~+1+cluster(id),data=diabetes,
#' resample.iid=0,n.sim=0)
#' fit<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fit)
#'
#' # same model but se's now with fewer time-points for approx of iid decomp of marginal
#' # model to speed up computations
#' marg <- cox.aalen(Surv(time,status) ~+prop(treat)+cluster(id),data=diabetes,
#' resample.iid=1,n.sim=0,max.timepoint.sim=5,beta.fixed=1,beta=0)
#' fit<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fit)
#'
##' @export
two.stage<-function(margsurv,data=parent.frame(),
Nit=60,detail=0,start.time=0,max.time=NULL,id=NULL,clusters=NULL,
robust=1,theta=NULL,theta.des=NULL,var.link=0,step=0.5,notaylor=0,se.clusters=NULL)
{ ## {{{
## {{{ seting up design and variables
rate.sim <- 1; secluster <- NULL
if (!inherits(margsurv,"coxph")) { ## {{{
formula<-attr(margsurv,"Formula");
beta.fixed <- attr(margsurv,"beta.fixed")
if (is.null(beta.fixed)) beta.fixed <- 1;
ldata<-aalen.des(formula,data=data,model="cox.aalen");
id <- attr(margsurv,"id");
mclusters <- attr(margsurv,"cluster")
mclustind <- attr(margsurv,"cluster")
cluster.call <- attr(margsurv,"cluster.call")
X<-ldata$X; time<-ldata$time2; Z<-ldata$Z; status<-ldata$status;
time2 <- attr(margsurv,"stop");
start <- attr(margsurv,"start")
antpers<-nrow(X);
if (beta.fixed==1) Z <- NULL;
if (is.null(Z)==TRUE) {npar<-TRUE; semi<-0;} else { Z<-as.matrix(Z); npar<-FALSE; semi<-1;}
if (npar==TRUE) {Z<-matrix(0,antpers,1); pz<-1; fixed<-0;} else {fixed<-1;pz<-ncol(Z);}
px<-ncol(X);
if (is.null(clusters) && is.null(mclusters))
stop("No cluster variabel specified in marginal or twostage call \n");
if (is.null(clusters)) { clusters <- mclusters; cluster.call <- cluster.call} else {cluster.call <- clusters;}
if (is.null(se.clusters)) secluster <- clusters;
antsecluster <- length(unique(secluster))
if (is.numeric(secluster)) secluster <- sindex.prodlim(unique(secluster),secluster)-1 else {
seclusters <- as.integer(factor(clusters, labels = 1:antsecluster))-1
}
### print("two-stage"); print(head(cluster.call))
if (is.null(cluster.call)) notaylor <- 1
if (is.null(margsurv$gamma.iid)) notaylor <- 1
## }}}
} else { ## coxph ## {{{
notaylor <- 1
antpers <- margsurv$n
id <- 0:(antpers-1)
mt <- model.frame(margsurv)
Y <- model.extract(mt, "response")
if (!inherits(Y, "Surv")) stop("Response must be a survival object")
if (attr(Y, "type") == "right") {
time2 <- Y[, "time"];
status <- Y[, "status"]
start <- rep(0,antpers);
} else {
start <- Y[, 1]; time2 <- Y[, 2];status <- Y[, 3];
}
Z <- matrix(1,antpers,length(coef(margsurv)));
if (is.null(clusters)) stop("must give clusters for coxph\n");
cluster.call <- clusters
X <- matrix(1,antpers,1); ### Z <- matrix(0,antpers,1); ### no use for these
px <- 1; pz <- ncol(Z);
beta.fixed <- 0
semi <- 1
start.time <- 0
} ## }}}
if (any(is.na(clusters))) stop("Missing values in cluster varaibles\n");
out.clust <- cluster.index.timereg(clusters);
clusters <- out.clust$clusters
maxclust <- out.clust$maxclust
antclust <- out.clust$antclust
idiclust <- out.clust$idclust
cluster.size <- out.clust$cluster.size
### if (anyNA(idiclust)) idiclust[is.na(idiclust)] <- 0
### setting secluster after cluster.index call to deal with characters
if (inherits(margsurv,"coxph")) {
if (is.null(se.clusters) & is.null(secluster) ) secluster <- clusters;
antsecluster <- length(unique(secluster))
if (is.numeric(secluster)) secluster <- sindex.prodlim(unique(secluster),secluster)-1 else {
clusters <- as.integer(factor(clusters, labels = 1:antsecluster))-1
}
}
if (length(clusters)!=length(secluster)) stop("length of se.clusters not consistent with cluster length\n");
if (sum(abs(start))>0) lefttrunk <- 1 else lefttrunk <- 0;
cumhazleft <- 0;
RR <- rep(1,antpers);
update <- 1;
if (update==0) { ## {{{
if ((attr(margsurv,"residuals")!=2) || (lefttrunk==1)) { ### compute cum hazards in time point infty;
nn <- nrow(margsurv$cum)
cum <- Cpred(margsurv$cum,time2)[,-1]
if (npar==TRUE) cumhaz <- apply(cum*X,1,sum)
if (npar==FALSE) cumhaz <- apply(cum*X,1,sum)*exp( Z %*% margsurv$gamma)
if (lefttrunk==1) {
cum <- Cpred(margsurv$cum,start)[,-1]
cumhazleft <- apply(cum*X,1,sum)
if (npar==TRUE) cumhazleft <- cumhazleft
if (npar==FALSE) cumhazleft <- cumhazleft * exp( Z %*% margsurv$gamma)
}
} else { residuals<-margsurv$residuals$dM; cumhaz<-status-residuals; }
} ## }}}
if (update==1)
if (inherits(margsurv,c("aalen","cox.aalen"))) { ## {{{
if ((attr(margsurv,"residuals")!=2) || (lefttrunk==1)) {
resi <- residualsTimereg(margsurv,data=data)
residuals <- resi$residuals;
cumhaz <- resi$cumhaz;
cumhazleft <- resi$cumhazleft;
RR <- resi$RR
} else { residuals <- margsurv$residuals$dM;
cumhaz <- status-residuals;
if (inherits(margsurv,"cox.aalen")) RR <- exp( Z %*% margsurv$gamma)
}
}
else if (inherits(margsurv,"coxph")) {
notaylor <- 1
residuals <- residuals(margsurv)
cumhaz <- status-residuals
cumhazleft <- rep(0,antpers)
RR<- exp(margsurv$linear.predictors-sum(margsurv$means*coef(margsurv)))
if ((lefttrunk==1)) {
### baseout <- basehaz(margsurv,centered=FALSE);
sfit <- survfit(margsurv, se.fit=FALSE)
zcoef <- ifelse(is.na(coef(margsurv)), 0, coef(margsurv))
offset <- sum(margsurv$means * zcoef)
chaz <- sfit$cumhaz * exp(-offset)
cum <- cbind(sfit$time,chaz)
cum <- Cpred(cum,start)[,2]
cumhazleft <- cum * RR
}
} ## }}}
### print(head(cbind(residuals,cumhaz,RR,time2,status)))
ratesim<-rate.sim;
inverse<-var.link
pxz <- px + pz;
times<-c(start.time,time2[status==1]);
times<-sort(times);
if (is.null(max.time)==TRUE) maxtimes<-max(times)+0.1 else maxtimes<-max.time;
times<-times[times<maxtimes]
Ntimes <- sum(status[time2<maxtimes])+1;
Biid<-c(); gamma.iid <- 0;
if (is.null(margsurv$B.iid)) notaylor <- 1;
if (notaylor==0) {
nBiid <- length(margsurv$B.iid)
if (nBiid!=antsecluster) stop("Number of clusters for marginal models must be consistent with se.cluster for standard error sandwich\n");
for (i in 1:nBiid) Biid<-cbind(Biid,margsurv$B.iid[[i]]);
if (!is.null(margsurv$gamma.iid)) gamma.iid<-margsurv$gamma.iid;
if (is.null(margsurv$time.sim.resolution)) {
time.group <- (1:nrow(Biid))-1;
maxtimesim <- nrow(Biid);
timereso <- margsurv$cum[,1]
}
else {
timereso <- margsurv$time.sim.resolution
qqc <- cut(times, breaks = margsurv$time.sim.resolution, include.lowest = TRUE)
time.group <- as.integer(factor(qqc, labels = 1:(nrow(Biid)-1)))
maxtimesim <- nrow(Biid);
}
if (inherits(margsurv,"cox.aalen")) {
times <- margsurv$time.sim.resolution
Ntimes <-length(times)
}
} else {time.group <- 1; maxtimesim <- 1; timereso <- 1}
if (is.null(theta.des)==TRUE) ptheta<-1;
if (is.null(theta.des)==TRUE) theta.des<-matrix(1,antpers,ptheta) else
theta.des<-as.matrix(theta.des);
ptheta<-ncol(theta.des);
if (nrow(theta.des)!=antpers) stop("Theta design does not have correct dim");
if (is.null(theta)==TRUE) {
if (var.link==1) theta<- rep(-1,ptheta);
if (var.link==0) theta<- rep(exp(-5),ptheta);
}
if (length(theta)!=ptheta) theta<-rep(theta[1],ptheta);
theta.score<-rep(0,ptheta);Stheta<-var.theta<-matrix(0,ptheta,ptheta);
if (maxclust==1) stop("No clusters !, maxclust size=1\n");
theta.iid <- matrix(0,antsecluster,ptheta)
## }}}
### print(ant.clust)
### print(dim(idiclust))
### print(sum(is.na(idiclust)))
### print(table(clusters))
### print(table(secluster))
DUbeta <- matrix(0,pz,ptheta);
nparout <- .C("twostagereg",
as.double(times), as.integer(Ntimes), as.double(X),
as.integer(antpers), as.integer(px), as.double(Z),
as.integer(antpers), as.integer(pz), as.integer(antpers), ## 9
as.double(start),as.double(time2), as.integer(Nit),
as.integer(detail), as.integer(id), as.integer(status), ## 15
as.integer(ratesim), as.integer(robust), as.integer(clusters),
as.integer(antclust), as.integer(beta.fixed), as.double(theta),
as.double(var.theta), as.double(theta.score), as.integer(inverse),
as.integer(cluster.size), ## 25
as.double(theta.des), as.integer(ptheta), as.double(Stheta),
as.double(step), as.integer(idiclust), as.integer(notaylor),
as.double(gamma.iid),as.double(Biid),as.integer(semi), as.double(cumhaz) ,
as.double(cumhazleft),as.integer(lefttrunk),as.double(RR),
as.integer(maxtimesim),as.integer(time.group),as.integer(secluster),
as.integer(antsecluster),as.double(theta.iid), as.double(timereso),as.double(DUbeta),PACKAGE = "timereg")
## {{{ handling output
gamma <- margsurv$gamma
Varbeta <- margsurv$var.gamma; RVarbeta <- margsurv$robvar.gamma;
score <- margsurv$score; Iinv <- margsurv$D2linv;
cumint <- margsurv$cum; vcum <- margsurv$var.cum; Rvcu <- margsurv$robvar.cum;
theta<-matrix(nparout[[21]],ptheta,1);
var.theta<-matrix(nparout[[22]],ptheta,ptheta);
theta.score<-nparout[[23]];
SthetaI<-matrix(nparout[[28]],ptheta,ptheta);
theta.iid <- matrix(nparout[[43]],antsecluster,ptheta);
theta.iid <- theta.iid %*% SthetaI
### DUbeta <- matrix(nparout[[45]],pz,ptheta);
### if (is.null(call.secluster) & is.null(max.clust)) rownames(theta.iid) <- unique(cluster.call) else rownames(theta.iid) <- unique(se.clusters)
ud <- list(cum = cumint, var.cum = vcum, robvar.cum = Rvcu,
gamma = gamma, var.gamma = Varbeta, robvar.gamma = RVarbeta,
D2linv = Iinv, score = score, theta=theta,var.theta=var.theta,
SthetaInv=SthetaI,theta.score=theta.score,theta.iid=theta.iid)
ptheta<-length(ud$theta);
if (ptheta>1) {
rownames(ud$theta)<-colnames(theta.des);
names(ud$theta.score)<-colnames(theta.des); } else {
names(ud$theta.score)<- rownames(ud$theta)<-"intercept" }
attr(ud,"Call")<- match.call();
class(ud)<-"two.stage"
attr(ud,"Formula")<-formula;
attr(ud,"id")<-id;
attr(ud,"cluster")<-clusters;
attr(ud,"cluster.call")<-cluster.call;
attr(ud,"secluster")<-secluster;
attr(ud,"start")<-start;
attr(ud,"time2")<-time2;
attr(ud,"var.link")<-var.link
attr(ud,"beta.fixed")<-beta.fixed
attr(ud,"marg.model")<-class(margsurv)
### attr(ud,"DUbeta")<-DUbeta
return(ud)
## }}}
} ## }}}
##' @export
summary.two.stage<-function (object,digits=3,...) { ## {{{
if (!(inherits(object, 'two.stage') )) stop("Must be a Two-Stage object")
prop<-TRUE;
if (is.null(object$prop.odds)==TRUE) p.o<-FALSE else p.o<-TRUE
var.link<-attr(object,"var.link");
cat("Dependence parameter for Clayton-Oakes-Glidden model\n");
if (sum(abs(object$theta.score)>0.000001) )
cat("Variance parameters did not converge, allow more iterations\n\n");
resdep <- coef.two.stage(object,...)
prmatrix(resdep[,1:6,drop=FALSE]); cat(" \n");
prmatrix(resdep[,7:9,drop=FALSE]); cat(" \n");
if (attr(object,"marg.model")!="coxph")
if (attr(object,"beta.fixed")==0) { ## {{{
### cat("Marginal Cox-Aalen model fit\n\n");
if (sum(abs(object$score)>0.000001) && sum(object$gamma)!=0)
cat("Marginal model did not converge, allow more iterations\n\n");
### if (prop) {
### if (p.o==FALSE) cat("Proportional Cox terms : \n") else cat("Covariate effects \n")
###
### out=coef.two.stage(object,digits=digits);
### out=signif(out,digits=digits)
### print(out)
###
### }
} ## }}}
### cat(" \n"); cat(" Call: \n"); dput(attr(object, "Call"));
cat("\n");
} ## }}}
##' @export
print.two.stage <- function (x,digits = 3,...) { ## {{{
summary.two.stage(x,digits=digits,...)
### if (!(inherits(x, 'two.stage') )) stop("Must be a Two-Stage object")
### cat(" Two-stage estimation for Clayton-Oakes-Glidden model\n");
### cat(" Marginals of Cox-Aalen form, dependence by variance of Gamma distribution\n\n");
### object <- x; rm(x);
###
### cat(" Nonparametric components : ");
### cat(colnames(object$cum)[-1]); cat(" \n");
### if (!is.null(object$gamma)) {
### cat(" Parametric components : "); cat(rownames(object$gamma));
### cat(" \n");
### }
### cat(" \n");
###
### cat(" Call: \n");
### print(attr(object,'Call'))
} ## }}}
##' @export
vcov.two.stage <- function(object, ...) {
rv <- object$robvar.gamma
if (!identical(rv, matrix(0, nrow = 1L, ncol = 1L))) rv # else return NULL
}
##' @export
coef.two.stage<-function(object,digits=3,d2logl=1,alpha=0.05,...) { ## {{{
if (!(inherits(object, 'two.stage') )) stop("Must be a Two-Stage object")
var.link <- attr(object,"var.link")
ptheta<-nrow(object$theta)
sdtheta<-diag(object$var.theta)^.5
if (var.link==0) {
vari<-object$theta
sdvar<-diag(object$var.theta)^.5
upper <- object$theta-qnorm(alpha/2)*sdvar
lower <- object$theta+qnorm(alpha/2)*sdvar
}
else {
vari<-exp(object$theta)
sdvar<-vari*diag(object$var.theta)^.5
upper <- exp(object$theta-qnorm(alpha/2)*sdtheta)
lower <- exp(object$theta+qnorm(alpha/2)*sdtheta)
}
dep<-cbind(object$theta[,1],sdtheta)
walddep<-object$theta[,1]/sdtheta;
waldpdep<-(1-pnorm(abs(walddep)))*2
kendall<-1/(1+2/vari)
kendall.ll<-1/(1+2/(object$theta+qnorm(alpha/2)*sdvar))
kendall.ul<-1/(1+2/(object$theta-qnorm(alpha/2)*sdvar))
if (var.link==0) resdep<-signif(as.matrix(cbind(dep,lower,upper,walddep,waldpdep,kendall,kendall.ll,kendall.ul)),digits)
else resdep<-signif(as.matrix(cbind(dep,lower,upper,walddep,waldpdep,vari,sdvar,kendall,kendall.ll,kendall.ul)),digits);
slower <- paste("lower",signif(100*alpha/2,2),"%",sep="")
supper <- paste("upper",signif(100*(1-alpha/2),3),"%",sep="")
if (var.link==0) colnames(resdep) <- c("Variance","SE",slower,supper,"z","P-val","Kendall's tau",slower,supper)
else colnames(resdep)<-c("log(Variance)","SE",slower,supper,"z","P-val","Variance","SE Var.","Kendall's tau",slower,supper)
### prmatrix(resdep); cat(" \n");
return(resdep)
} ## }}}
##' @export
plot.two.stage<-function(x,pointwise.ci=1,robust=0,specific.comps=FALSE,
level=0.05,
start.time=0,stop.time=0,add.to.plot=FALSE,mains=TRUE,
xlab="Time",ylab ="Cumulative regression function",...)
{ ## {{{
if (!(inherits(x, 'two.stage'))) stop("Must be a Two-Stage object")
object <- x; rm(x);
B<-object$cum; V<-object$var.cum; p<-dim(B)[[2]];
if (robust>=1) V<-object$robvar.cum;
if (sum(specific.comps)==FALSE) comp<-2:p else comp<-specific.comps+1
if (stop.time==0) stop.time<-max(B[,1]);
med<-B[,1]<=stop.time & B[,1]>=start.time
B<-B[med,]; Bs<-B[1,]; B<-t(t(B)-Bs); B[,1]<-B[,1]+Bs[1];
V<-V[med,]; Vs<-V[1,]; V<-t( t(V)-Vs);
Vrob<-object$robvar.cum;
Vrob<-Vrob[med,]; Vrobs<-Vrob[1,]; Vrob<-t( t(Vrob)-Vrobs);
c.alpha<- qnorm(1-level/2)
for (v in comp) {
c.alpha<- qnorm(1-level/2)
est<-B[,v];ul<-B[,v]+c.alpha*V[,v]^.5;nl<-B[,v]-c.alpha*V[,v]^.5;
if (add.to.plot==FALSE)
{
plot(B[,1],est,ylim=1.05*range(ul,nl),type="s",xlab=xlab,ylab=ylab)
if (mains==TRUE) title(main=colnames(B)[v]); }
else lines(B[,1],est,type="s");
if (pointwise.ci>=1) {
lines(B[,1],ul,lty=pointwise.ci,type="s");
lines(B[,1],nl,lty=pointwise.ci,type="s"); }
if (robust>=1) {
lines(B[,1],ul,lty=robust,type="s");
lines(B[,1],nl,lty=robust,type="s"); }
abline(h=0);
}
} ## }}}
##' @export
predict.two.stage <- function(object,X=NULL,Z=NULL,times=NULL,times2=NULL,X2=NULL,Z2=NULL,
theta=NULL,theta.des=NULL,diag=TRUE,...)
{ ## {{{
time.coef <- data.frame(object$cum)
if (!is.null(times)) cum <- Cpred(object$cum,times) else cum <- object$cum;
if (!is.null(times2)) cum2 <- Cpred(object$cum,times2) else cum2 <- object$cum;
if (is.null(Z) & (!is.null(object$gamma))) Z <- matrix(0,1,nrow(object$gamma));
if (is.null(X) & (!is.null(Z))) { Z <- as.matrix(Z); X <- matrix(1,nrow(Z),1)}
if (is.null(Z) & (!is.null(X))) {X <- as.matrix(X); Z <- matrix(0,nrow(X),1); gamma <- 0}
if (is.null(X)) X <- 1;
X2 <- X;
Z2 <- Z2;
if (diag==FALSE) {
time.part <- X %*% t(cum[,-1])
time.part2 <- X2 %*% t(cum2[,-1])
if (!is.null(object$gamma)) {
gamma <- object$gamma
RR <- exp( Z %*% gamma );
RR2 <- exp( Z2 %*% gamma );
cumhaz <- t( t(time.part) * RR ); cumhaz2 <- t( t(time.part2) * RR2 )}
else { cumhaz <- time.part; cumhaz2 <- time.part2; }
} else {
time.part <- apply(as.matrix(X*cum[,-1]),1,sum)
time.part2 <- apply(as.matrix(X2*cum2[,-1]),1,sum)
}
if (!is.null(object$gamma)) {
RR<- exp(Z%*%object$gamma);
RR2 <- exp(Z2 %*%object$gamma);
cumhaz <- c((time.part) * RR) ;
cumhaz2 <- c((time.part2) * RR2);
} else {
cumhaz <- c(time.part); cumhaz2 <- c(time.part2);
}
S1 <- pmin(1,exp(-cumhaz)); S2 <- pmin(1,exp(-cumhaz2))
###print(length(S1))
###print(length(S2))
if (is.null(theta)) theta <- object$theta
if (!is.null(theta.des)) theta <- c(theta.des %*% theta)
if (attr(object,"var.link")==1) theta <- exp(theta)
### theta is variance
if (diag==FALSE) St1t2<- (outer(c(S1)^{-(theta)},c(S2)^{-(theta)},FUN="+") - 1)^(-(1/theta)) else
St1t2<- ((S1^{-(theta)}+S2^{-(theta)})-1)^(-(1/theta))
###St1t2<- ((S1^{-(1/theta)}+S2^{-(1/theta)})-1)^(-(theta))
out=list(St1t2=St1t2,S1=S1,S2=S2,times=times,times2=times2,theta=theta)
return(out)
} ## }}}
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Defines functions predict.two.stage plot.two.stage coef.two.stage vcov.two.stage two.stage
Documented in coef.two.stage plot.two.stage predict.two.stage two.stage vcov.two.stage
#' Fit Clayton-Oakes-Glidden Two-Stage model
#'
#' Fit Clayton-Oakes-Glidden Two-Stage model with Cox-Aalen marginals and
#' regression on the variance parameters.
#'
#' The model specifikatin allows a regression structure on the variance of the
#' random effects, such it is allowed to depend on covariates fixed within
#' clusters \deqn{ \theta_{k} = Q_{k}^T \nu }{}. This is particularly useful to
#' model jointly different groups and to compare their variances.
#'
#' Fits an Cox-Aalen survival model. Time dependent variables and counting
#' process data (multiple events per subject) are not possible !
#'
#' The marginal baselines are on the Cox-Aalen form \deqn{ \lambda_{ki}(t) =
#' Y_{ki}(t) ( X_{ki}^T(t) \alpha(t) ) \exp(Z_{ki}^T \beta ) }{}
#'
#' The model thus contains the Cox's regression model and the additive hazards
#' model as special cases. (see cox.aalen function for more on this).
#'
#' The modelling formula uses the standard survival modelling given in the
#' \bold{survival} package. Only for right censored survival data.
#'
#' The data for a subject is presented as multiple rows or 'observations', each
#' of which applies to an interval of observation (start, stop]. For counting
#' process data with the )start,stop] notation is used the 'id' variable is
#' needed to identify the records for each subject. Only one record per subject
#' is allowed in the current implementation for the estimation of theta. The
#' program assumes that there are no ties, and if such are present random noise
#' is added to break the ties.
#'
#' Left truncation is dealt with. Here the key assumption is that the maginals
#' are correctly estimated and that we have a common truncation time within
#' each cluster.
#'
#' @param margsurv fit of marginal survival cox.aalen model with residuals=2,
#' and resample.iid=1 to get fully correct standard errors. See notaylor below.
#' @param data a data.frame with the variables.
#' @param start.time start of observation period where estimates are computed.
#' @param max.time end of observation period where estimates are computed.
#' Estimates thus computed from [start.time, max.time]. Default is max of data.
#' @param id For timevarying covariates the variable must associate each record
#' with the id of a subject.
#' @param clusters cluster variable for computation of robust variances.
#' @param robust if 0 then totally omits computation of standard errors.
#' @param Nit number of iterations for Newton-Raphson algorithm.
#' @param detail if 0 no details is printed during iterations, if 1 details are
#' given.
#' @param theta starting values for the frailty variance (default=0.1).
#' @param theta.des design for regression for variances. The defauls is NULL
#' that is equivalent to just one theta and the design with only a baseline.
#' @param var.link default "0" is that the regression design on the variances
#' is without a link, and "1" uses the link function exp.
#' @param step step size for Newton-Raphson.
#' @param notaylor if 1 then ignores variation due to survival model, this is
#' quicker and then resample.iid=0 and residuals=0 is ok for marginal survival
#' model that then is much quicker.
#' @param se.clusters cluster variable for sandwich estimator of variance.
#' @return returns an object of type "two.stage". With the following arguments:
#' \item{cum}{cumulative timevarying regression coefficient estimates are
#' computed within the estimation interval.} \item{var.cum}{the martingale
#' based pointwise variance estimates.} \item{robvar.cum}{robust pointwise
#' variances estimates.} \item{gamma}{estimate of parametric components of
#' model.} \item{var.gamma}{variance for gamma.} \item{robvar.gamma}{robust
#' variance for gamma.} \item{D2linv}{inverse of the derivative of the score
#' function from marginal model.} \item{score}{value of score for final
#' estimates.} \item{theta}{estimate of Gamma variance for frailty.}
#' \item{var.theta}{estimate of variance of theta.} \item{SthetaInv}{inverse of
#' derivative of score of theta.} \item{theta.score}{score for theta
#' parameters.}
#' @author Thomas Scheike
#' @references Glidden (2000), A Two-Stage estimator of the dependence
#' parameter for the Clayton Oakes model.
#'
#' Martinussen and Scheike, Dynamic Regression Models for Survival Data,
#' Springer (2006).
#' @keywords survival
#' @examples
#'
#' library(timereg)
#' data(diabetes)
#' # Marginal Cox model with treat as covariate
#' marg <- cox.aalen(Surv(time,status)~prop(treat)+prop(adult)+
#' cluster(id),data=diabetes,resample.iid=1)
#' fit<-two.stage(marg,data=diabetes,theta=1.0,Nit=40)
#' summary(fit)
#'
#' # using coxph and giving clusters, but SE wittout cox uncetainty
#' margph <- coxph(Surv(time,status)~treat,data=diabetes)
#' fit<-two.stage(margph,data=diabetes,theta=1.0,Nit=40,clusters=diabetes$id)
#'
#'
#' # Stratification after adult
#' theta.des<-model.matrix(~-1+factor(adult),diabetes);
#' des.t<-model.matrix(~-1+factor(treat),diabetes);
#' design.treat<-cbind(des.t[,-1]*(diabetes$adult==1),
#' des.t[,-1]*(diabetes$adult==2))
#'
#' # test for common baselines included here
#' marg1<-cox.aalen(Surv(time,status)~-1+factor(adult)+prop(design.treat)+cluster(id),
#' data=diabetes,resample.iid=1,Nit=50)
#'
#' fit.s<-two.stage(marg1,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s)
#'
#' # with common baselines and common treatment effect (although test reject this)
#' fit.s2<-two.stage(marg,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s2)
#'
#' # test for same variance among the two strata
#' theta.des<-model.matrix(~factor(adult),diabetes);
#' fit.s3<-two.stage(marg,data=diabetes,Nit=40,theta=1,theta.des=theta.des)
#' summary(fit.s3)
#'
#' # to fit model without covariates, use beta.fixed=1 and prop or aalen function
#' marg <- aalen(Surv(time,status)~+1+cluster(id),
#' data=diabetes,resample.iid=1,n.sim=0)
#' fita<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fita)
#'
#' # same model but se's without variation from marginal model to speed up computations
#' marg <- aalen(Surv(time,status) ~+1+cluster(id),data=diabetes,
#' resample.iid=0,n.sim=0)
#' fit<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fit)
#'
#' # same model but se's now with fewer time-points for approx of iid decomp of marginal
#' # model to speed up computations
#' marg <- cox.aalen(Surv(time,status) ~+prop(treat)+cluster(id),data=diabetes,
#' resample.iid=1,n.sim=0,max.timepoint.sim=5,beta.fixed=1,beta=0)
#' fit<-two.stage(marg,data=diabetes,theta=0.95,detail=0)
#' summary(fit)
#'
##' @export
two.stage<-function(margsurv,data=parent.frame(),
Nit=60,detail=0,start.time=0,max.time=NULL,id=NULL,clusters=NULL,
robust=1,theta=NULL,theta.des=NULL,var.link=0,step=0.5,notaylor=0,se.clusters=NULL)
{ ## {{{
## {{{ seting up design and variables
rate.sim <- 1; secluster <- NULL
if (!inherits(margsurv,"coxph")) { ## {{{
formula<-attr(margsurv,"Formula");
beta.fixed <- attr(margsurv,"beta.fixed")
if (is.null(beta.fixed)) beta.fixed <- 1;
ldata<-aalen.des(formula,data=data,model="cox.aalen");
id <- attr(margsurv,"id");
mclusters <- attr(margsurv,"cluster")
mclustind <- attr(margsurv,"cluster")
cluster.call <- attr(margsurv,"cluster.call")
X<-ldata$X; time<-ldata$time2; Z<-ldata$Z; status<-ldata$status;
time2 <- attr(margsurv,"stop");
start <- attr(margsurv,"start")
antpers<-nrow(X);
if (beta.fixed==1) Z <- NULL;
if (is.null(Z)==TRUE) {npar<-TRUE; semi<-0;} else { Z<-as.matrix(Z); npar<-FALSE; semi<-1;}
if (npar==TRUE) {Z<-matrix(0,antpers,1); pz<-1; fixed<-0;} else {fixed<-1;pz<-ncol(Z);}
px<-ncol(X);
if (is.null(clusters) && is.null(mclusters))
stop("No cluster variabel specified in marginal or twostage call \n");
if (is.null(clusters)) { clusters <- mclusters; cluster.call <- cluster.call} else {cluster.call <- clusters;}
if (is.null(se.clusters)) secluster <- clusters;
antsecluster <- length(unique(secluster))
if (is.numeric(secluster)) secluster <- sindex.prodlim(unique(secluster),secluster)-1 else {
seclusters <- as.integer(factor(clusters, labels = 1:antsecluster))-1
}
### print("two-stage"); print(head(cluster.call))
if (is.null(cluster.call)) notaylor <- 1
if (is.null(margsurv$gamma.iid)) notaylor <- 1
## }}}
} else { ## coxph ## {{{
notaylor <- 1
antpers <- margsurv$n
id <- 0:(antpers-1)
mt <- model.frame(margsurv)
Y <- model.extract(mt, "response")
if (!inherits(Y, "Surv")) stop("Response must be a survival object")
if (attr(Y, "type") == "right") {
time2 <- Y[, "time"];
status <- Y[, "status"]
start <- rep(0,antpers);
} else {
start <- Y[, 1]; time2 <- Y[, 2];status <- Y[, 3];
}
Z <- matrix(1,antpers,length(coef(margsurv)));
if (is.null(clusters)) stop("must give clusters for coxph\n");
cluster.call <- clusters
X <- matrix(1,antpers,1); ### Z <- matrix(0,antpers,1); ### no use for these
px <- 1; pz <- ncol(Z);
beta.fixed <- 0
semi <- 1
start.time <- 0
} ## }}}
if (any(is.na(clusters))) stop("Missing values in cluster varaibles\n");
out.clust <- cluster.index.timereg(clusters);
clusters <- out.clust$clusters
maxclust <- out.clust$maxclust
antclust <- out.clust$antclust
idiclust <- out.clust$idclust
cluster.size <- out.clust$cluster.size
### if (anyNA(idiclust)) idiclust[is.na(idiclust)] <- 0
### setting secluster after cluster.index call to deal with characters
if (inherits(margsurv,"coxph")) {
if (is.null(se.clusters) & is.null(secluster) ) secluster <- clusters;
antsecluster <- length(unique(secluster))
if (is.numeric(secluster)) secluster <- sindex.prodlim(unique(secluster),secluster)-1 else {
clusters <- as.integer(factor(clusters, labels = 1:antsecluster))-1
}
}
if (length(clusters)!=length(secluster)) stop("length of se.clusters not consistent with cluster length\n");
if (sum(abs(start))>0) lefttrunk <- 1 else lefttrunk <- 0;
cumhazleft <- 0;
RR <- rep(1,antpers);
update <- 1;
if (update==0) { ## {{{
if ((attr(margsurv,"residuals")!=2) || (lefttrunk==1)) { ### compute cum hazards in time point infty;
nn <- nrow(margsurv$cum)
cum <- Cpred(margsurv$cum,time2)[,-1]
if (npar==TRUE) cumhaz <- apply(cum*X,1,sum)
if (npar==FALSE) cumhaz <- apply(cum*X,1,sum)*exp( Z %*% margsurv$gamma)
if (lefttrunk==1) {
cum <- Cpred(margsurv$cum,start)[,-1]
cumhazleft <- apply(cum*X,1,sum)
if (npar==TRUE) cumhazleft <- cumhazleft
if (npar==FALSE) cumhazleft <- cumhazleft * exp( Z %*% margsurv$gamma)
}
} else { residuals<-margsurv$residuals$dM; cumhaz<-status-residuals; }
} ## }}}
if (update==1)
if (inherits(margsurv,c("aalen","cox.aalen"))) { ## {{{
if ((attr(margsurv,"residuals")!=2) || (lefttrunk==1)) {
resi <- residualsTimereg(margsurv,data=data)
residuals <- resi$residuals;
cumhaz <- resi$cumhaz;
cumhazleft <- resi$cumhazleft;
RR <- resi$RR
} else { residuals <- margsurv$residuals$dM;
cumhaz <- status-residuals;
if (inherits(margsurv,"cox.aalen")) RR <- exp( Z %*% margsurv$gamma)
}
}
else if (inherits(margsurv,"coxph")) {
notaylor <- 1
residuals <- residuals(margsurv)
cumhaz <- status-residuals
cumhazleft <- rep(0,antpers)
RR<- exp(margsurv$linear.predictors-sum(margsurv$means*coef(margsurv)))
if ((lefttrunk==1)) {
### baseout <- basehaz(margsurv,centered=FALSE);
sfit <- survfit(margsurv, se.fit=FALSE)
zcoef <- ifelse(is.na(coef(margsurv)), 0, coef(margsurv))
offset <- sum(margsurv$means * zcoef)
chaz <- sfit$cumhaz * exp(-offset)
cum <- cbind(sfit$time,chaz)
cum <- Cpred(cum,start)[,2]
cumhazleft <- cum * RR
}
} ## }}}
### print(head(cbind(residuals,cumhaz,RR,time2,status)))
ratesim<-rate.sim;
inverse<-var.link
pxz <- px + pz;
times<-c(start.time,time2[status==1]);
times<-sort(times);
if (is.null(max.time)==TRUE) maxtimes<-max(times)+0.1 else maxtimes<-max.time;
times<-times[times<maxtimes]
Ntimes <- sum(status[time2<maxtimes])+1;
Biid<-c(); gamma.iid <- 0;
if (is.null(margsurv$B.iid)) notaylor <- 1;
if (notaylor==0) {
nBiid <- length(margsurv$B.iid)
if (nBiid!=antsecluster) stop("Number of clusters for marginal models must be consistent with se.cluster for standard error sandwich\n");
for (i in 1:nBiid) Biid<-cbind(Biid,margsurv$B.iid[[i]]);
if (!is.null(margsurv$gamma.iid)) gamma.iid<-margsurv$gamma.iid;
if (is.null(margsurv$time.sim.resolution)) {
time.group <- (1:nrow(Biid))-1;
maxtimesim <- nrow(Biid);
timereso <- margsurv$cum[,1]
}
else {
timereso <- margsurv$time.sim.resolution
qqc <- cut(times, breaks = margsurv$time.sim.resolution, include.lowest = TRUE)
time.group <- as.integer(factor(qqc, labels = 1:(nrow(Biid)-1)))
maxtimesim <- nrow(Biid);
}
if (inherits(margsurv,"cox.aalen")) {
times <- margsurv$time.sim.resolution
Ntimes <-length(times)
}
} else {time.group <- 1; maxtimesim <- 1; timereso <- 1}
if (is.null(theta.des)==TRUE) ptheta<-1;
if (is.null(theta.des)==TRUE) theta.des<-matrix(1,antpers,ptheta) else
theta.des<-as.matrix(theta.des);
ptheta<-ncol(theta.des);
if (nrow(theta.des)!=antpers) stop("Theta design does not have correct dim");
if (is.null(theta)==TRUE) {
if (var.link==1) theta<- rep(-1,ptheta);
if (var.link==0) theta<- rep(exp(-5),ptheta);
}
if (length(theta)!=ptheta) theta<-rep(theta[1],ptheta);
theta.score<-rep(0,ptheta);Stheta<-var.theta<-matrix(0,ptheta,ptheta);
if (maxclust==1) stop("No clusters !, maxclust size=1\n");
theta.iid <- matrix(0,antsecluster,ptheta)
## }}}
### print(ant.clust)
### print(dim(idiclust))
### print(sum(is.na(idiclust)))
### print(table(clusters))
### print(table(secluster))
DUbeta <- matrix(0,pz,ptheta);
nparout <- .C("twostagereg",
as.double(times), as.integer(Ntimes), as.double(X),
as.integer(antpers), as.integer(px), as.double(Z),
as.integer(antpers), as.integer(pz), as.integer(antpers), ## 9
as.double(start),as.double(time2), as.integer(Nit),
as.integer(detail), as.integer(id), as.integer(status), ## 15
as.integer(ratesim), as.integer(robust), as.integer(clusters),
as.integer(antclust), as.integer(beta.fixed), as.double(theta),
as.double(var.theta), as.double(theta.score), as.integer(inverse),
as.integer(cluster.size), ## 25
as.double(theta.des), as.integer(ptheta), as.double(Stheta),
as.double(step), as.integer(idiclust), as.integer(notaylor),
as.double(gamma.iid),as.double(Biid),as.integer(semi), as.double(cumhaz) ,
as.double(cumhazleft),as.integer(lefttrunk),as.double(RR),
as.integer(maxtimesim),as.integer(time.group),as.integer(secluster),
as.integer(antsecluster),as.double(theta.iid), as.double(timereso),as.double(DUbeta),PACKAGE = "timereg")
## {{{ handling output
gamma <- margsurv$gamma
Varbeta <- margsurv$var.gamma; RVarbeta <- margsurv$robvar.gamma;
score <- margsurv$score; Iinv <- margsurv$D2linv;
cumint <- margsurv$cum; vcum <- margsurv$var.cum; Rvcu <- margsurv$robvar.cum;
theta<-matrix(nparout[[21]],ptheta,1);
var.theta<-matrix(nparout[[22]],ptheta,ptheta);
theta.score<-nparout[[23]];
SthetaI<-matrix(nparout[[28]],ptheta,ptheta);
theta.iid <- matrix(nparout[[43]],antsecluster,ptheta);
theta.iid <- theta.iid %*% SthetaI
### DUbeta <- matrix(nparout[[45]],pz,ptheta);
### if (is.null(call.secluster) & is.null(max.clust)) rownames(theta.iid) <- unique(cluster.call) else rownames(theta.iid) <- unique(se.clusters)
ud <- list(cum = cumint, var.cum = vcum, robvar.cum = Rvcu,
gamma = gamma, var.gamma = Varbeta, robvar.gamma = RVarbeta,
D2linv = Iinv, score = score, theta=theta,var.theta=var.theta,
SthetaInv=SthetaI,theta.score=theta.score,theta.iid=theta.iid)
ptheta<-length(ud$theta);
if (ptheta>1) {
rownames(ud$theta)<-colnames(theta.des);
names(ud$theta.score)<-colnames(theta.des); } else {
names(ud$theta.score)<- rownames(ud$theta)<-"intercept" }
attr(ud,"Call")<- match.call();
class(ud)<-"two.stage"
attr(ud,"Formula")<-formula;
attr(ud,"id")<-id;
attr(ud,"cluster")<-clusters;
attr(ud,"cluster.call")<-cluster.call;
attr(ud,"secluster")<-secluster;
attr(ud,"start")<-start;
attr(ud,"time2")<-time2;
attr(ud,"var.link")<-var.link
attr(ud,"beta.fixed")<-beta.fixed
attr(ud,"marg.model")<-class(margsurv)
### attr(ud,"DUbeta")<-DUbeta
return(ud)
## }}}
} ## }}}
##' @export
summary.two.stage<-function (object,digits=3,...) { ## {{{
if (!(inherits(object, 'two.stage') )) stop("Must be a Two-Stage object")
prop<-TRUE;
if (is.null(object$prop.odds)==TRUE) p.o<-FALSE else p.o<-TRUE
var.link<-attr(object,"var.link");
cat("Dependence parameter for Clayton-Oakes-Glidden model\n");
if (sum(abs(object$theta.score)>0.000001) )
cat("Variance parameters did not converge, allow more iterations\n\n");
resdep <- coef.two.stage(object,...)
prmatrix(resdep[,1:6,drop=FALSE]); cat(" \n");
prmatrix(resdep[,7:9,drop=FALSE]); cat(" \n");
if (attr(object,"marg.model")!="coxph")
if (attr(object,"beta.fixed")==0) { ## {{{
### cat("Marginal Cox-Aalen model fit\n\n");
if (sum(abs(object$score)>0.000001) && sum(object$gamma)!=0)
cat("Marginal model did not converge, allow more iterations\n\n");
### if (prop) {
### if (p.o==FALSE) cat("Proportional Cox terms : \n") else cat("Covariate effects \n")
###
### out=coef.two.stage(object,digits=digits);
### out=signif(out,digits=digits)
### print(out)
###
### }
} ## }}}
### cat(" \n"); cat(" Call: \n"); dput(attr(object, "Call"));
cat("\n");
} ## }}}
##' @export
print.two.stage <- function (x,digits = 3,...) { ## {{{
summary.two.stage(x,digits=digits,...)
### if (!(inherits(x, 'two.stage') )) stop("Must be a Two-Stage object")
### cat(" Two-stage estimation for Clayton-Oakes-Glidden model\n");
### cat(" Marginals of Cox-Aalen form, dependence by variance of Gamma distribution\n\n");
### object <- x; rm(x);
###
### cat(" Nonparametric components : ");
### cat(colnames(object$cum)[-1]); cat(" \n");
### if (!is.null(object$gamma)) {
### cat(" Parametric components : "); cat(rownames(object$gamma));
### cat(" \n");
### }
### cat(" \n");
###
### cat(" Call: \n");
### print(attr(object,'Call'))
} ## }}}
##' @export
vcov.two.stage <- function(object, ...) {
rv <- object$robvar.gamma
if (!identical(rv, matrix(0, nrow = 1L, ncol = 1L))) rv # else return NULL
}
##' @export
coef.two.stage<-function(object,digits=3,d2logl=1,alpha=0.05,...) { ## {{{
if (!(inherits(object, 'two.stage') )) stop("Must be a Two-Stage object")
var.link <- attr(object,"var.link")
ptheta<-nrow(object$theta)
sdtheta<-diag(object$var.theta)^.5
if (var.link==0) {
vari<-object$theta
sdvar<-diag(object$var.theta)^.5
upper <- object$theta-qnorm(alpha/2)*sdvar
lower <- object$theta+qnorm(alpha/2)*sdvar
}
else {
vari<-exp(object$theta)
sdvar<-vari*diag(object$var.theta)^.5
upper <- exp(object$theta-qnorm(alpha/2)*sdtheta)
lower <- exp(object$theta+qnorm(alpha/2)*sdtheta)
}
dep<-cbind(object$theta[,1],sdtheta)
walddep<-object$theta[,1]/sdtheta;
waldpdep<-(1-pnorm(abs(walddep)))*2
kendall<-1/(1+2/vari)
kendall.ll<-1/(1+2/(object$theta+qnorm(alpha/2)*sdvar))
kendall.ul<-1/(1+2/(object$theta-qnorm(alpha/2)*sdvar))
if (var.link==0) resdep<-signif(as.matrix(cbind(dep,lower,upper,walddep,waldpdep,kendall,kendall.ll,kendall.ul)),digits)
else resdep<-signif(as.matrix(cbind(dep,lower,upper,walddep,waldpdep,vari,sdvar,kendall,kendall.ll,kendall.ul)),digits);
slower <- paste("lower",signif(100*alpha/2,2),"%",sep="")
supper <- paste("upper",signif(100*(1-alpha/2),3),"%",sep="")
if (var.link==0) colnames(resdep) <- c("Variance","SE",slower,supper,"z","P-val","Kendall's tau",slower,supper)
else colnames(resdep)<-c("log(Variance)","SE",slower,supper,"z","P-val","Variance","SE Var.","Kendall's tau",slower,supper)
### prmatrix(resdep); cat(" \n");
return(resdep)
} ## }}}
##' @export
plot.two.stage<-function(x,pointwise.ci=1,robust=0,specific.comps=FALSE,
level=0.05,
start.time=0,stop.time=0,add.to.plot=FALSE,mains=TRUE,
xlab="Time",ylab ="Cumulative regression function",...)
{ ## {{{
if (!(inherits(x, 'two.stage'))) stop("Must be a Two-Stage object")
object <- x; rm(x);
B<-object$cum; V<-object$var.cum; p<-dim(B)[[2]];
if (robust>=1) V<-object$robvar.cum;
if (sum(specific.comps)==FALSE) comp<-2:p else comp<-specific.comps+1
if (stop.time==0) stop.time<-max(B[,1]);
med<-B[,1]<=stop.time & B[,1]>=start.time
B<-B[med,]; Bs<-B[1,]; B<-t(t(B)-Bs); B[,1]<-B[,1]+Bs[1];
V<-V[med,]; Vs<-V[1,]; V<-t( t(V)-Vs);
Vrob<-object$robvar.cum;
Vrob<-Vrob[med,]; Vrobs<-Vrob[1,]; Vrob<-t( t(Vrob)-Vrobs);
c.alpha<- qnorm(1-level/2)
for (v in comp) {
c.alpha<- qnorm(1-level/2)
est<-B[,v];ul<-B[,v]+c.alpha*V[,v]^.5;nl<-B[,v]-c.alpha*V[,v]^.5;
if (add.to.plot==FALSE)
{
plot(B[,1],est,ylim=1.05*range(ul,nl),type="s",xlab=xlab,ylab=ylab)
if (mains==TRUE) title(main=colnames(B)[v]); }
else lines(B[,1],est,type="s");
if (pointwise.ci>=1) {
lines(B[,1],ul,lty=pointwise.ci,type="s");
lines(B[,1],nl,lty=pointwise.ci,type="s"); }
if (robust>=1) {
lines(B[,1],ul,lty=robust,type="s");
lines(B[,1],nl,lty=robust,type="s"); }
abline(h=0);
}
} ## }}}
##' @export
predict.two.stage <- function(object,X=NULL,Z=NULL,times=NULL,times2=NULL,X2=NULL,Z2=NULL,
theta=NULL,theta.des=NULL,diag=TRUE,...)
{ ## {{{
time.coef <- data.frame(object$cum)
if (!is.null(times)) cum <- Cpred(object$cum,times) else cum <- object$cum;
if (!is.null(times2)) cum2 <- Cpred(object$cum,times2) else cum2 <- object$cum;
if (is.null(Z) & (!is.null(object$gamma))) Z <- matrix(0,1,nrow(object$gamma));
if (is.null(X) & (!is.null(Z))) { Z <- as.matrix(Z); X <- matrix(1,nrow(Z),1)}
if (is.null(Z) & (!is.null(X))) {X <- as.matrix(X); Z <- matrix(0,nrow(X),1); gamma <- 0}
if (is.null(X)) X <- 1;
X2 <- X;
Z2 <- Z2;
if (diag==FALSE) {
time.part <- X %*% t(cum[,-1])
time.part2 <- X2 %*% t(cum2[,-1])
if (!is.null(object$gamma)) {
gamma <- object$gamma
RR <- exp( Z %*% gamma );
RR2 <- exp( Z2 %*% gamma );
cumhaz <- t( t(time.part) * RR ); cumhaz2 <- t( t(time.part2) * RR2 )}
else { cumhaz <- time.part; cumhaz2 <- time.part2; }
} else {
time.part <- apply(as.matrix(X*cum[,-1]),1,sum)
time.part2 <- apply(as.matrix(X2*cum2[,-1]),1,sum)
}
if (!is.null(object$gamma)) {
RR<- exp(Z%*%object$gamma);
RR2 <- exp(Z2 %*%object$gamma);
cumhaz <- c((time.part) * RR) ;
cumhaz2 <- c((time.part2) * RR2);
} else {
cumhaz <- c(time.part); cumhaz2 <- c(time.part2);
}
S1 <- pmin(1,exp(-cumhaz)); S2 <- pmin(1,exp(-cumhaz2))
###print(length(S1))
###print(length(S2))
if (is.null(theta)) theta <- object$theta
if (!is.null(theta.des)) theta <- c(theta.des %*% theta)
if (attr(object,"var.link")==1) theta <- exp(theta)
### theta is variance
if (diag==FALSE) St1t2<- (outer(c(S1)^{-(theta)},c(S2)^{-(theta)},FUN="+") - 1)^(-(1/theta)) else
St1t2<- ((S1^{-(theta)}+S2^{-(theta)})-1)^(-(1/theta))
###St1t2<- ((S1^{-(1/theta)}+S2^{-(1/theta)})-1)^(-(theta))
out=list(St1t2=St1t2,S1=S1,S2=S2,times=times,times2=times2,theta=theta)
return(out)
} ## }}}
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