Fits Proportional excess hazards model with fixed offsets

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Description

Fits proportional excess hazards model. The Sasieni proportional excess risk model.

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

Usage

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pe.sasieni(formula=formula(data),data=sys.parent(),
id=NULL,start.time=0,max.time=NULL,offsets=0,Nit=50,detail=0,n.sim=500)

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.

id

gives the number of individuals.

start.time

starting time for considered time-period.

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.

offsets

fixed offsets giving the mortality.

Nit

number of itterations.

detail

if detail is one, prints iteration details.

n.sim

number of simulations, 0 for no simulations.

Details

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 "pe.sasieni". With the following arguments:

cum

baseline of Cox model excess risk.

var.cum

pointwise variance estimates for estimated cumulatives.

gamma

estimate of relative risk terms of model.

var.gamma

variance estimates for gamma.

Ut

score process for Cox part of model.

D2linv

The inverse of the second derivative.

score

final score

test.Prop

re-sampled absolute supremum values.

pval.Prop

p-value based on resampling.

Author(s)

Thomas Scheike

References

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

Sasieni, P.D., Proportional excess hazards, Biometrika (1996), 127–41.

Cortese, G. and Scheike, T.H., Dynamic regression hazards models for relative survival (2007), submitted.

Examples

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data(mela.pop)
out<-pe.sasieni(Surv(start,stop,status==1)~age+sex,mela.pop,
id=1:205,Nit=10,max.time=7,offsets=mela.pop$rate,detail=0,n.sim=100)
summary(out)

ul<-out$cum[,2]+1.96*out$var.cum[,2]^.5
ll<-out$cum[,2]-1.96*out$var.cum[,2]^.5
plot(out$cum,type="s",ylim=range(ul,ll))
lines(out$cum[,1],ul,type="s"); lines(out$cum[,1],ll,type="s")
# see also prop.excess function

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