[R] FW: Age as time-scale in survival analysis

[Eleni Rapsomaniki]

Dear R users,

My question is more methodology related rather than specific to R usage.
Using time on study as time in a cox model, eg:

library(Design)
stanf.cph1=cph(Surv(time, status) ~ t5+id+age, data=stanford2, surv=T)

#In this case the 1000-day survival probability would be:
stanf.surv1=survest(stanf.cph1, times=1000)

#Age in this case is a covariate. 

#I now want to compare the above estimate to the 1000-day survival
probability I get using age at entry and exit as my time-scale:
stanf.cph2=cph(Surv(age,age+time, status) ~ t5+id, data=stanford2,
surv=T)
stanf.surv2=survest(stanf.cph2, times=1000)

summary(stanf.surv1$surv)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.1131  0.3370  0.4669  0.4538  0.5633  0.7480 27.0000 
> summary(stanf.surv2$surv)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
 0.07387  0.23240  0.35770  0.35370  0.46820  0.60650 27.00000 

These are obviously out-of sync, so there must be some way I can adjust
them to mean the same thing. The first means the probability of
surviving a 1000 days since they started being followed up while the
second means the probability of surviving up to starting age+1000 days.
How do I get the equivalent risks from the two models?

Any tips greatly appreciated!!

(FYI A related entry to my question can be found at:
http://tolstoy.newcastle.edu.au/R/e2/help/07/02/9831.html)

Eleni Rapsomaniki
 
Research Associate
Department of Public Health and Primary Care
University of Cambridge