R: Fit Clayton-Oakes-Glidden Two-Stage model

two.stage {timereg} | R Documentation

## 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.

### 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.
`Nit` | number of iterations for Newton-Raphson algorithm.
`detail` | if 0 no details is printed during iterations, if 1 details are given.
`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.
`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.

### Details

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

θ_{k} = Q_{k}^T ν

. 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

λ_{ki}(t) = Y_{ki}(t) ( X_{ki}^T(t) α(t) ) \exp(Z_{ki}^T β )

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.

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.

### 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.

### Author(s)

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).

### 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)

[Package timereg version 1.9.4 Index]