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

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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 const(), and cluster variables (for computing robust variances) by the wrapper cluster().

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 λ_0(t) = \exp(α_0(t)) or the "breslow" version where the baseline is parametrised as λ_0(t).

degree

gives the degree of the local linear smoothing, that is local smoothing. Possible values are 1 or 2.

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.

Value

Returns an object of type "timecox". 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.

residuals

list with residuals. Estimated martingale increments (dM) and corresponding time vector (time).

obs.testBeq0

observed absolute value of supremum of cumulative components scaled with the variance.

pval.testBeq0

p-value for covariate effects based on supremum test.

sim.testBeq0

resampled supremum values.

obs.testBeqC

observed absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect.

pval.testBeqC

p-value based on resampling.

sim.testBeqC

resampled supremum values.

obs.testBeqC.is

observed integrated squared differences between observed cumulative and estimate under null of constant effect.

pval.testBeqC.is

p-value based on resampling.

sim.testBeqC.is

resampled supremum values.

conf.band

resampling based constant to construct robust 95% uniform confidence bands.

test.procBeqC

observed test-process of difference between observed cumulative process and estimate under null of constant effect over time.

sim.test.procBeqC

list of 50 random realizations of test-processes under null based on resampling.

schoenfeld.residuals

Schoenfeld residuals are returned for "breslow" parametrisation.

Author(s)

Thomas Scheike

References

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

Examples

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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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