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

[Thomas Lumley]

On Mon, 5 Feb 2007, John Sorkin wrote:

> 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,
<snip>
> 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.

There are even more possibilities (a nice example and discussion is in 
Breslow & Day, the example being occupational exposure to nickel and 
later cancer).

The Cox model works by comparing covariates for the observation that 
failed and other observations at risk at the same time, so the comparisons 
are entirely within time-point.

If you use time since start of study you are comparing people with 
different covariates at the same time since start of study.

If you use calendar time you are comparing people with different 
covariates at the same calendar time

If you use age you are comparing people with different covariates at the 
same age.


In an observational study it often is more important to control for age or 
for calendar time than for time since the study started, so these might be 
better time scales.  A disadvantage in some studies with longitudinal data 
is that on the study time scale everyone may have measurements at the same 
time but on other time scales everyone may have measurements at different 
times.


 	-thomas