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

[Peter Dalgaard]

John Sorkin wrote:
> Peter,
> Many thanks for your prompt reply.
>
> I think you may have been too quick to dismiss model2; there is no need for time to be negative. The time parameter is Surv represents survival, i.e. follow-up time. We usually start the follow-up clock at the time a subject is enrolled into a study, but this is not the only measure of survival time. One might argue that the clock should start at birth because the subject has survived to birth to plus the time represented by the ususal follow-up clock. 
>   

Yes, but your subjects logically cannot die before their recorded age if
I understand the setup correctly. I.e. you have left truncation --
people who die before enrolment are not recorded at all. This is at odds
with the proportional hazards assumption and it is a source of
(potential) grave error if the length of the "immortal" period is
related to the presence of the risk factor.

> John
>
> 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
>
>   
>>>> Peter Dalgaard <P.Dalgaard at biostat.ku.dk> 2/5/2007 9:16 AM >>>
>>>>         
> 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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>>   
>>     
>
>
>   


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