timereg (version 1.3-0)

aalen.test: Fit additive hazards model

Description

Fits both the additive hazards model of Aalen and the semi-parametric additive hazards model of McKeague and Sasieni. Estimates are un-weighted. Time dependent variables and counting process data (multiple events per subject) are possible.

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

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

Usage

aalen.test(formula,data=sys.parent(),start.time=0,max.time=NULL,robust=1,
id=NULL,clusters=NULL,residuals=0,n.sim=1000,weighted.test=0,
covariance=0,resample.iid=0,weights=0,offsets=0,fix.gam=0,pseudo.score=0,
approx = "dt", gamma = 0,silent=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 w

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.

resample.iid

to return i.i.d. representation for nonparametric and parametric terms.

offsets

fixed intensity only works for semiparametric, model but fully non-parametric model can be fitted by using fix.gam option, see also example.

weights

weights for estimation.

fix.gam

keep gamma parameter fixed.

pseudo.score

number of simulation for pseudo-score test. If pseudo.score=0 it is not computed. The pseudo-score test for fixed effects appears to be superior to other tests computed.

The semiparametric model is given as $$\lambda(t) = Y_i(t) ( X_i^t \beta(t) + Z_i

approx

describes how the integrals are approximated, "dt" is default and uses a piececonstant approximation for all time points both censoring and event tiems, "death-times" uses only the event times for the approximation.

gamma

values for potential fixed gamma coefficients.

silent

set to 1 to avoid printing of warnings for non-inverible design-matrices for different timepoints, default is 0.

Value

• returns an object of type "aalen". With the following arguments:
• cum
  cumulative timevarying regression coefficient estimates are computed within the estimation interval.
• var.cum
  the martingale based pointwise variance estimates for cumulatives.
• robvar.cum
  robust pointwise variances estimates for cumulatives.
• 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.
• covariance
  covariances for nonparametric terms of model.
• B.iid
  Resample processes for nonparametric terms of model.
• gamma.iid
  Resample processes for parametric terms of model.
• deviance
  Two components : first component "likelihood" equivalent to partial likelihood for Cox's model, second component sum of least squares of increments.
• intZHZ
  computes the integral int ZHZ dt.
• intZHdN
  computes the integral int ZH dN.
• obs.pscore
  pseudo score test value.
• pscore.iid
  iid decomposition of pseudo-score test.
• intZHZt
  computes the integral int ZHZ dt over time.
• pstest.pval
  pseudo-score p-value.
• sup.pscore
  simulated supremum values for pseudo-score test.

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. 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).

Martinussen and Scheike (200.), Tests for time-varying effects within Aalen's additive hazards model,

Examples

library(survival)
data(mela.pop)
# Fits Aalen model  with offsets 
dummy<-rnorm(nrow(mela.pop)); 

out<-aalen.test(Surv(start,stop,status==1)~age+sex+const(dummy),
mela.pop,max.time=7,n.sim=100,offsets=mela.pop$rate,id=mela.pop$id,
fix.gam=1)

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

# Fits semi-parametric additive hazards model  with offsets 
out<-aalen.test(Surv(start,stop,status==1)~age+const(sex),
mela.pop,max.time=7,n.sim=100,offsets=mela.pop$rate,id=mela.pop$id)

summary(out)
plot(out)

################################################################
# Computes pseudo.score tests for fixed effects 
data(sTRACE)
out<-aalen.test(Surv(time,status==9)~const(age)+const(sex)+const(diabetes)+
chf+vf,sTRACE,max.time=7,n.sim=100,pseudo.score=100)

summary(out)