twostage: Fits Clayton-Oakes or bivariate Plackett models for bivariate...
In mets: Analysis of Multivariate Event Times

Description Usage Arguments Author(s) References Examples

The reported standard errors are based on the estimated information from the likelihood assuming that the marginals are known.

twostage(margsurv, data = sys.parent(), score.method = "nlminb", Nit = 60,
  detail = 0, clusters = NULL, silent = 1, weights = NULL,
  control = list(), theta = NULL, theta.des = NULL, var.link = 1,
  iid = 1, step = 0.5, notaylor = 0, model = "plackett",
  marginal.trunc = NULL, marginal.survival = NULL, marginal.status = NULL,
  strata = NULL, se.clusters = NULL, max.clust = NULL, numDeriv = 1)

`margsurv`	Marginal model
`data`	data frame
`score.method`	Scoring method
`Nit`	Number of iterations
`detail`	Detail
`clusters`	Cluster variable
`silent`	Debug information
`weights`	Weights
`control`	Optimization arguments
`theta`	Starting values for variance components
`theta.des`	Variance component design
`var.link`	Link function for variance
`iid`	Calculate i.i.d. decomposition
`step`	Step size
`notaylor`	Taylor expansion
`model`	model
`marginal.trunc`	marginal left truncation probabilities
`marginal.survival`	optional vector of marginal survival probabilities
`marginal.status`	related to marginal survival probabilities
`strata`	strata for fitting, see example
`se.clusters`	for clusters for se calculation with iid
`max.clust`	max se.clusters for se calculation with iid
`numDeriv`	to get numDeriv version of second derivative, otherwise uses sum of squared score

Thomas Scheike

Clayton-Oakes and Plackett bivariate survival distributions,

data(diabetes)

# Marginal Cox model  with treat as covariate
margph <- coxph(Surv(time,status)~treat,data=diabetes)
### Clayton-Oakes, from timereg
fitco1<-two.stage(margph,data=diabetes,theta=1.0,detail=0,Nit=40,clusters=diabetes$id)
summary(fitco1)
### Plackett model
fitp<-twostage(margph,data=diabetes,theta=3.0,Nit=40,
               clusters=diabetes$id,var.link=1)
summary(fitp)
### Clayton-Oakes
fitco2<-twostage(margph,data=diabetes,theta=0.0,detail=0,
                 clusters=diabetes$id,var.link=1,model="clayton.oakes")
summary(fitco2)
fitco3<-twostage(margph,data=diabetes,theta=1.0,detail=0,
                 clusters=diabetes$id,var.link=0,model="clayton.oakes")
summary(fitco3)

### without covariates using Aalen for marginals
marg <- aalen(Surv(time,status)~+1,data=diabetes,n.sim=0,max.clust=NULL,robust=0)
fitpa<-twostage(marg,data=diabetes,theta=1.0,detail=0,Nit=40,
                clusters=diabetes$id,score.method="optimize")
summary(fitpa)

fitcoa<-twostage(marg,data=diabetes,theta=1.0,detail=0,Nit=40,clusters=diabetes$id,
                 var.link=1,model="clayton.oakes")
summary(fitcoa)

### Piecewise constant cross hazards ratio modelling
########################################################

d <- subset(simClaytonOakes(2000,2,0.5,0,stoptime=2,left=0),!truncated)
udp <- piecewise.twostage(c(0,0.5,2),data=d,score.method="optimize",
                          id="cluster",timevar="time",
                          status="status",model="clayton.oakes",silent=0)
summary(udp)


### Same model using the strata option, a bit slower
########################################################
## makes the survival pieces for different areas in the plane
##ud1=surv.boxarea(c(0,0),c(0.5,0.5),data=d,id="cluster",timevar="time",status="status")
##ud2=surv.boxarea(c(0,0.5),c(0.5,2),data=d,id="cluster",timevar="time",status="status")
##ud3=surv.boxarea(c(0.5,0),c(2,0.5),data=d,id="cluster",timevar="time",status="status")
##ud4=surv.boxarea(c(0.5,0.5),c(2,2),data=d,id="cluster",timevar="time",status="status")

## everything done in one call
ud <- piecewise.data(c(0,0.5,2),data=d,timevar="time",status="status",id="cluster")
ud$strata <- factor(ud$strata);
ud$intstrata <- factor(ud$intstrata)

## makes strata specific id variable to identify pairs within strata
## se's computed based on the id variable across strata "cluster"
ud$idstrata <- ud$id+(as.numeric(ud$strata)-1)*2000

marg2 <- aalen(Surv(boxtime,status)~-1+factor(num):factor(intstrata),
               data=ud,n.sim=0,robust=0)
tdes <- model.matrix(~-1+factor(strata),data=ud)
fitp2<-twostage(marg2,data=ud,se.clusters=ud$cluster,clusters=ud$idstrata,
                score.method="fisher.scoring",model="clayton.oakes",
                theta.des=tdes,step=0.5)
summary(fitp2)

### now fitting the model with symmetry, i.e. strata 2 and 3 same effect
ud$stratas <- ud$strata;
ud$stratas[ud$strata=="0.5-2,0-0.5"] <- "0-0.5,0.5-2"
tdes2 <- model.matrix(~-1+factor(stratas),data=ud)
fitp3<-twostage(marg2,data=ud,clusters=ud$idstrata,se.cluster=ud$cluster,
                score.method="fisher.scoring",model="clayton.oakes",
                theta.des=tdes2,step=0.5)
summary(fitp3)

### same model using strata option, a bit slower
fitp4<-twostage(marg2,data=ud,clusters=ud$cluster,se.cluster=ud$cluster,
                score.method="fisher.scoring",model="clayton.oakes",
                theta.des=tdes2,step=0.5,strata=ud$strata)
summary(fitp4)