timereg (version 1.8.6)

prop.excess: Fits Proportional excess hazards model

Description

Fits proportional excess hazards model.

The models are written using the survival modelling given in the survival package.

Usage

prop.excess(formula=formula(data),data=sys.parent(),excess=1
,tol=0.0001,max.time=NULL,n.sim=1000,alpha=1,frac=1)

Arguments

formula

a formula object, with the response on the left of a `~' operator, and the terms on the right. The response must be a survival object as returned by the `Surv' function.

data

a data.frame with the variables.

excess

specifies for which of the subjects the excess term is present. Default is that the term is present for all subjects.

tol

tolerance for numerical procedure.

max.time

stopping considered time-period if different from 0. Estimates thus computed from [0,max.time] if max.time>0. Default is max of data.

n.sim

number of simulations in re-sampling.

alpha

tuning paramter in Newton-Raphson procedure. Value smaller than one may give more stable convergence.

frac

number between 0 and 1. Is used in supremum test where observed jump times t1, ..., tk is replaced by t1, ..., tl with l=round(frac*k).

Value

• Returns an object of type "prop.excess". With the following arguments:
• cum
  estimated cumulative regression functions. First column contains the jump times, then follows the estimated components of additive part of model and finally the excess cumulative baseline.
• var.cum
  robust pointwise variance estimates for estimated cumulatives.
• gamma
  estimate of parametric components of model.
• var.gamma
  robust variance estimate for gamma.
• pval
  p-value of Kolmogorov-Smirnov test (variance weighted) for excess baseline and Aalen terms, H: B(t)=0.
• pval.HW
  p-value of supremum test (corresponding to Hall-Wellner band) for excess baseline and Aalen terms, H: B(t)=0. Reported in summary.
• pval.CM
  p-value of Cramer von Mises test for excess baseline and Aalen terms, H: B(t)=0.
• quant
  95 percent quantile in distribution of resampled Kolmogorov-Smirnov test statistics for excess baseline and Aalen terms. Used to construct 95 percent simulation band.
• quant95HW
  95 percent quantile in distribution of resampled supremum test statistics corresponding to Hall-Wellner band for excess baseline and Aalen terms. Used to construct 95 percent Hall-Wellner band.
• simScoreProp
  observed scoreprocess and 50 resampled scoreprocesses (under model). List with 51 elements.

Details

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 Verlag (2006).

Examples

data(melanoma)
lt<-log(melanoma$thick)          # log-thickness 
excess<-(melanoma$thick>=210)    # excess risk for thick tumors

# Fits Proportional Excess hazards model 
fit<-prop.excess(Surv(days/365,status==1)~sex+ulc+cox(sex)+
                 cox(ulc)+cox(lt),melanoma,excess=excess,n.sim=100)
summary(fit)
par(mfrow=c(2,3))
plot(fit)