timereg (version 1.8.6)

two.stage: Fit Clayton-Oakes-Glidden Two-Stage model

Description

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 $$\theta_{k} = Q_{k}^T \nu$$. 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 $$\lambda_{ki}(t) = Y_{ki}(t) ( X_{ki}^T(t) \alpha(t) ) \exp(Z_{ki}^T \beta )$$

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 survival package. Only for right censored survival data.

Usage

two.stage(margsurv,data=sys.parent(),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)

Arguments

margsurv

fit of marginal survival cox.aalen model with residuals=2, and resample.iid=1 to get fully correct standard errors. See notaylor below.

data

a data.frame with the variables.

start.time

start of observation period where estimates are computed.

max.time

end of observation period where estimates are computed. Estimates thus computed from [start.time, max.time]. Default is max of data.

id

For timevarying covariates the variable must associate each record with the id of a subject.

clusters

cluster variable for computation of robust variances.

robust

if 0 then totally omits computation of standard errors.

Nit

number of iterations for Newton-Raphson algorithm.

detail

if 0 no details is printed during iterations, if 1 details are given.

theta

starting values for the frailty variance (default=0.1).

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.

var.link

default "0" is that the regression design on the variances is without a link, and "1" uses the link function exp.

step

step size for Newton-Raphson.

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.

se.clusters

cluster variable for sandwich estimator of variance.

Value

• returns an object of type "two.stage". With the following arguments:
• cum
  cumulative timevarying regression coefficient estimates are computed within the estimation interval.
• var.cum
  the martingale based pointwise variance estimates.
• robvar.cum
  robust pointwise variances estimates.
• gamma
  estimate of parametric components of model.
• var.gamma
  variance for gamma.
• robvar.gamma
  robust variance for gamma.
• D2linv
  inverse of the derivative of the score function from marginal model.
• score
  value of score for final estimates.
• theta
  estimate of Gamma variance for frailty.
• var.theta
  estimate of variance of theta.
• SthetaInv
  inverse of derivative of score of theta.
• theta.score
  score for theta parameters.

Details

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.

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).

Examples

library(timereg)
data(diabetes)
# Marginal Cox model  with treat as covariate
marg <- cox.aalen(Surv(time,status)~prop(treat)+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)