SAS Phreg with time dependent covariate

[sasstats]

Hello,

we have a question concerning the interpretation of the hazard ratio of a time dependent covariate.

We used the syntax of the following example of SAS

PROC PHREG: Model Using Time-Dependent Explanatory Variables :: SAS/STAT(R) 9.3 User's Guide

time = survival time, Status=1=death, Waittime = Waiting time until transplantation 

proc phreg data= Heart;
   model Time*Status(0)= XStatus XAge XScore;
   where NotTyped ^= 'y';
   if (WaitTime = . or Time < WaitTime) then do;
      XStatus=0.;
      XAge=0.;
      XScore= 0.;
   end;
   else do;
      XStatus= 1.0;
      XAge= Xpl_Age;
      XScore= Mismatch;
   end;
run;

The hazard ration for xstatus is equal 0.935.

What does this mean in case of time dependency?

Does is it mean that the risk to die is lower (-6.5%) in case of status gets one, i.e. the patients gets a transplant where the time dependence is taken into account ?

Best regards,

statstats

[FreelanceReinh · Accepted solution]

Hello @sasstats,

First, note that the hazard ratio 0.935 for XStatus resulted from the model

model Time*Status(0)= XStatus Acc_Age;

The corresponding p-value 0.8261 indicates that the true hazard ratio might well be 1  (i.e., no difference in hazard rates due to XStatus; see the 95% confidence interval [0.513, 1.703]).

But let's assume that the model accurately describes the population, so the hazard ratio is "real." Then we would conclude that a patient with XStatus=1 (i.e., who has received a transplant) is slightly less likely to die (by a factor 0.935) than a patient

• of the same Acc_Age
• who has not received a transplant yet (XStatus=0)
• in the corresponding time interval (with that hazard ratio being effective, in particular: before the second patient receives their transplant).

Or in other words: Comparing two sufficiently and equally large subpopulations "XStatus=0" vs. "XStatus=1" with the same distribution of variable Acc_Age, we might see 1000 deaths in the first group within a certain period of time and would expect only about 935 deaths in the parallel group of transplant recipients.