timereg (version 1.8.6)

aalen: 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(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,deltaweight=1,silent=1,weights=NULL,
max.clust=1000, gamma=NULL, offsets=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.

deltaweight

uses weights to estimate semiparametric model, under construction, default=1 is standard least squares estimates

silent

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

weights

weights for estimating equations.

max.clust

sets the total number of i.i.d. terms in i.i.d. decompostition. This can limit the amount of memory used by coarsening the clusters. When NULL then all clusters are used. Default is 1000 to save memory and time.

gamma

fixes gamme at this value for estimation.

offsets

offsets for the additive model, to make excess risk modelling.

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
  Least squares of increments.

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).

Examples

data(sTRACE)
# Fits Aalen model 
out<-aalen(Surv(time,status==9)~age+sex+diabetes+chf+vf,
sTRACE,max.time=7,n.sim=100)

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

# Fits semi-parametric additive hazards model 
out<-aalen(Surv(time,status==9)~const(age)+const(sex)+const(diabetes)+chf+vf,
sTRACE,max.time=7,n.sim=100)

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

## Excess risk additive modelling 
data(mela.pop)
dummy<-rnorm(nrow(mela.pop));

# Fits Aalen model  with offsets 
out<-aalen(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,
gamma=0)
summary(out)
par(mfrow=c(2,3))
plot(out,main="Additive excess riks model")

# Fits semi-parametric additive hazards model  with offsets 
out<-aalen(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,main="Additive excess riks model")