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timereg (version 1.8.6)

timecox: Fit Cox model with partly timevarying effects.

Description

Fits proportional hazards model with some effects time-varying and some effects constant. Time dependent variables and counting process data (multiple events per subject) are possible.

Resampling is used for computing p-values for tests of timevarying effects.

The modelling formula uses the standard survival modelling given in the survival package.

Usage

timecox(formula=formula(data),data=sys.parent(),
start.time=0,max.time=NULL,id=NULL,clusters=NULL,n.sim=1000,
residuals=0,robust=1,Nit=20,bandwidth=0.5,method="basic",
weighted.test=0,degree=1,covariance=0)

Arguments

formula
a formula object with the response on the left of a '~' operator, and the independent terms on the right as regressors. The response must be a survival object as returned by the `Surv' function. Time-invariant regressors are specified by the wrapper
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.
robust
to compute robust variances and construct processes for resampling. May be set to 0 to save memory.
id
For timevarying covariates the variable must associate each record with the id of a subject.
clusters
cluster variable for computation of robust variances.
n.sim
number of simulations in resampling.
weighted.test
to compute a variance weighted version of the test-processes used for testing time-varying effects.
residuals
to returns residuals that can be used for model validation in the function cum.residuals
covariance
to compute covariance estimates for nonparametric terms rather than just the variances.
Nit
number of iterations for score equations.
bandwidth
bandwidth for local iterations. Default is 50 % of the range of the considered observation period.
method
Method for estimation. This refers to different parametrisations of the baseline of the model. Options are "basic" where the baseline is written as $\lambda_0(t) = \exp(\alpha_0(t))$ or the "breslow" version where the baseline is parametrised as $\lambda
degree
gives the degree of the local linear smoothing, that is local smoothing. Possible values are 1 or 2.

Value

  • Returns an object of type "timecox". With the following arguments:
  • cumcumulative timevarying regression coefficient estimates are computed within the estimation interval.
  • var.cumthe martingale based pointwise variance estimates.
  • robvar.cumrobust pointwise variances estimates.
  • gammaestimate of parametric components of model.
  • var.gammavariance for gamma.
  • robvar.gammarobust variance for gamma.
  • residualslist with residuals. Estimated martingale increments (dM) and corresponding time vector (time).
  • obs.testBeq0observed absolute value of supremum of cumulative components scaled with the variance.
  • pval.testBeq0p-value for covariate effects based on supremum test.
  • sim.testBeq0resampled supremum values.
  • obs.testBeqCobserved absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect.
  • pval.testBeqCp-value based on resampling.
  • sim.testBeqCresampled supremum values.
  • obs.testBeqC.isobserved integrated squared differences between observed cumulative and estimate under null of constant effect.
  • pval.testBeqC.isp-value based on resampling.
  • sim.testBeqC.isresampled supremum values.
  • conf.bandresampling based constant to construct robust 95% uniform confidence bands.
  • test.procBeqCobserved test-process of difference between observed cumulative process and estimate under null of constant effect over time.
  • sim.test.procBeqClist of 50 random realizations of test-processes under null based on resampling.
  • schoenfeld.residualsSchoenfeld residuals are returned for "breslow" parametrisation.

Details

The data for a subject is presented as multiple rows or 'observations', each of which applies to an interval of observation (start, stop]. When counting process data with the )start,stop] notation is used the 'id' variable is needed to identify the records for each subject. The program assumes that there are no ties, and if such are present random noise is added to break the ties.

References

Martinussen and Scheike, Dynamic Regression Models for Survival Data, Springer (2006).

Examples

Run this code
library(survival)
data(sTRACE)
# Fits time-varying Cox model 
out<-timecox(Surv(time/365,status==9)~age+sex+diabetes+chf+vf,
data=sTRACE,max.time=7,n.sim=100)

summary(out)
par(mfrow=c(2,3))
plot(out)
par(mfrow=c(2,3))
plot(out,score=TRUE)

# Fits semi-parametric time-varying Cox model
out<-timecox(Surv(time/365,status==9)~const(age)+const(sex)+
const(diabetes)+chf+vf,data=sTRACE,max.time=7,n.sim=100)

summary(out)
par(mfrow=c(2,3))
plot(out)

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