[R] Survival prediction

[Terry Therneau]

> Dear All,
>
> I have built a survival cox-model, which includes a covariate * time interaction. (non-proportionality detected)
> I am now wondering how could I most easily get survival predictions from my model.
>
> My model was specified:
> coxph(formula = Surv(event_time_mod, event_indicator_mod) ~ Sex +
>      ageC + HHcat_alt + Main_Branch + Acute_seizure + TreatmentType_binary +
>      ICH + IVH_dummy + IVH_dummy:log(event_time_mod)
>
> And now I was hoping to get a prediction using survfit and providing new.data for the combination of variables
> I am doing the predictions:
> 	  survfit(cox, new.data=new)

  Some comments:
     1. even though it is in the SAS manual and some literature, I have myself never used 
  "X * log(time)" as a fix for lack  of proportionality.  Is it really true that when you 
use
        fit <- coxph(Surv(event_time_mod, event_indicator_mod) ~ Sex +
             ageC + HHcat_alt + Main_Branch + Acute_seizure + TreatmentType_binary +
              ICH + IVH_dummy)
        zfit <- cox.zph(fit, transform="log")
        plot(zfit[8])

that the estimated function is linear?  I have not yet seen such a simple time effect
and would find it interesting.

     2. The code you wrote does not fit the time dependent model that you suppose; it 
treats event_time_mod as a fixed covariate.  To fit the model see the relevant vignette 
for the survival package.  Essentially the program has to build a large (start, stop) data 
set behind the scenes.  (SAS does the same thing).  Defining proper residuals for said 
data set is hard and the R code does not yet do this.  (Last I checked, SAS did the same 
thing.)

     3. The "survival curve" for a time dependent covariate is something that is not 
easily defined.  Read chapter 10.2.4 of the Therneau and Grambch book for a discussion of 
this (largely informed by the many mistakes I've myself made.)

Terry Therneau