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

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

1 2 | ```
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)
``` |

`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. |

The program assumes that there are no ties, and if such are present random noise is added to break the ties.

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. |

Thomas Scheike

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.

1 2 3 4 5 6 7 8 9 10 | ```
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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