[R] Problem of COX model with time dependent covariate

Terry Therneau therneau at mayo.edu
Wed Dec 28 16:50:20 CET 2011

```I'll add just a little to what David said.
The normal meaning of a "time dependent covariate" is a covariate that
changes with time.  For instance in a model that included x="most recent
available blood pressure" the value of x will change at each patient
visit.  You obviously can't get those new values as x=baseline + c*time
unless you are willing to assume a very odd biology for the patient.  I
would think the same about glomular filtration rate (GFR).

A different question is a time dependent coefficient.  That is, the
variable stays the same but it's effect changes over time.  Now in this
case a model that beta(t) = a + bt has some possible merit, but in my
optinion the biology it implies is still quite odd.  So I don't find
that model very interesting, even though some packages impliment it.  In
R there is a more useful approach:
fit <- coxph(Surv(time, outcome) ~ eGFR.base, ori.data)
zfit <- cox.zph(fit)
plot(zfit)

This produces a smoothing spline estimate of beta(t) with confidence
bands.  You can look at the plot and begin to understand the data, not
just create p-values.

Terry T.

On Dec 26, 2011, at 3:02 AM, JiangGZ wrote:

>
> Hi all,
>
>
> I am trying to detect association between a covariate and a disease
> outcome using R. This covariate shows time-varying effect, I add a
> time-covariate interaction item to build Cox model as follows:
> COX <- coxph(as.formula("Surv(TIME,outcome)~eGFR_BASE
> +eGFR_BASE:TIME"),ori.data);
>
>
>                           coef   exp(coef)   e(coef)        z   p
> eGFR_BASE                 6.40     603.5133     0.3702    17.3   0
> eGFR_BASE:TIME -3.41      0.0329     0.0772   -44.2   0
>
>
> But the result seems very different from that got by SPSS:

```