timecox: Fit Cox model with partly timevarying effects.

In scheike/timereg: Flexible Regression Models for Survival Data

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.

Usage

timecox(
  formula = formula(data),
  data,
  weights,
  subset,
  na.action,
  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.
weights	for analysis
subset	to subset
na.action	to have na.action
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.
n.sim	number of simulations in resampling.
residuals	to returns residuals that can be used for model validation in the function cum.residuals
robust	to compute robust variances and construct processes for resampling. May be set to 0 to save memory.
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).
weighted.test	to compute a variance weighted version of the test-processes used for testing time-varying effects.
degree	gives the degree of the local linear smoothing, that is local smoothing. Possible values are 1 or 2.
covariance	to compute covariance estimates for nonparametric terms rather than just the variances.

Details

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.

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

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)

scheike/timereg documentation built on Jan. 25, 2023, 3:43 p.m.