[R] Two ways to deal with age in Cox model

[Peter Dalgaard]

John Sorkin wrote:
> I hope one and all will allow a stats question:
>
> When running a cox proportional hazards model ,there are two ways to
> deal with age, 
> including age as a covariate, or to include age as part of the
> follow-up time, viz,
>
> Age as a covariate:
>
> tetest1 <- list(time=  c(4, 3,1,1,2,2,3),
>                      status=c(1,NA,1,0,1,1,0),
>                      age= c(0, 2,1,1,1,0,0),
>                      riskfactor=   c(0, 0,0,0,1,1,1))
>  fitagecovariate<-coxph( Surv(time, status) ~ age +riskfactor, test1) 
>  fitagecovariate
>
> Age included as part of follow-up time:
>
>  test2<-test1
>  test2$timeplusage<-test2$time+test2$age
>  fitagefollowup<-coxph( Surv(timeplusage, status) ~ riskfactor, test2)
>  fitagefollowup
>
> I would appreciate any thoughts about the differences in the
> interpretation of the two models.
> One obvious difference is that in the first model (fitagecovariate) one
> can make inferences about age and in the second one cannot. I think a
> second
> difference may be that in the first model the riskfactor is assumed to
> have values measured at the values of age where as in the second model
> riskfactor is assumed to have given values throughout the subject's
> life.
>
>   
Model2 is plainly wrong, unless your times can be negative it represents
long stretches of immortality (more obvious if all ages are about
80...)! Presumably, age is the age at entry, so a delayed-entry model
could be appropriate (Surv(age,timeplusage,status)). If this
modification is made, the main difference is that the time-since-entry
scale can not (easily) have a separate effect in the delayed-entry
model. If time is really is time since diagnosis or operation, then that
could be badly wrong.

> Your thoughts please.
>
> Thanks,
> John
>
> R 2.1.1
> windows XP
>
> John Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> Baltimore VA Medical Center GRECC,
> University of Maryland School of Medicine Claude D. Pepper OAIC,
> University of Maryland Clinical Nutrition Research Unit, and
> Baltimore VA Center Stroke of Excellence
>
> University of Maryland School of Medicine
> Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
>
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
> jsorkin at grecc.umaryland.edu
>
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-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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