I am new to survival analysis and now trying to learn counting process input style. I am using the same dataset, but when using proc phreg, the couting process input and regular input is very different. Here is my first several lines in the dataset:

The regular one:

enter image description here

Here is the counting process input style, these 2 are basically the same enter image description here

here is the code:

Proc phreg data=ds; class covar; model followup*event(0)=covar / entry=delay_entry; run;

proc phreg data=ds; class covar; model (start, end)*event(0)=covar; run;

Why the results are so different? Any idea would be appreciated. Thank you!

  • $\begingroup$ try proc phreg data=ds; class covar; model (delay_entry,followup)*event(0) =covar; run; $\endgroup$ – user158565 Jul 22 '19 at 22:27
  • $\begingroup$ Wow, that works! Thank you So much!!!Would you mind to explain to me why this is happening? the interval of (delay_entry,followup) and (Start, end) are the same, what's the story behind this issue? $\endgroup$ – Z.Gary Jul 23 '19 at 15:59

In Cox proportional hazard model, there is unspecified baseline hazard function $\lambda_0(t)$. It is not constant and is the function of time. For subject id=11, the first table says the subject went through from $t_1 = 62$ to $t_2=243$. So the subject should has the hazard $\lambda_0(t)exp(X\beta)$, for $ t=62 \text{ to } 243$. From table 2, the subject has the hazard $\lambda_0(t)exp(X\beta)$, for $ t=0 \text{ to } 181$.

Because $\lambda_0(t)$ is not a constant, so in this case $\lambda_0(0) \ne \lambda_0(62)$. Therefore, your two statements fit two different models.

In SAS, model t2*event(0)=X / entry=t1; and model (t1, t2)*event(0)=X are the exact same if you use them on the same dataset. If you replace the first model by Proc phreg data=ds; class covar; model end*event(0)=covar / entry=end; run;, you will get the same results generated by your second model.

  • $\begingroup$ Thank you So much. This is really helpful. I was shifting all the timelines by transforming data to the second table, and eventually create a different study. Thanks again! $\endgroup$ – Z.Gary Jul 23 '19 at 16:30

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