Time dependent COX analysis interpretation

#1
I use SPSS 23 for windows. I run a survival analysis and one of the variables (a categorical variable with 3 levels) did not answer the proportionally assumption. So I run it again with a time-dependent covariant – time*variable. Now I have 4 HR, 2 for the original variable's levels (adjusted for the interaction) and 2 for the interaction itself, one for each level. Which one do I report? Do I report the original variable or the interaction?​
 

ondansetron

TS Contributor
#3
I think that Staassis may have provided an answer that is better suited for a different question (assuming that his or her reply is regarding your cov*time interactions).

If you've identified that the proportional hazards assumption is not reasonably satisfied in your case, you shouldn't be testing these corrective interactions with time (with the possibility of removing them) because you already determined the time*covariate interaction is needed.

You can report both in a table to show how much estimated coefficients changed with and without the remedy for non-proportional hazards. If they are very similar, you may want to consider putting the full model with interactions in a supplemental document. The idea being that the easily interpreted model is in your main text, and you refer the reader to the supplemental document so they can verify how little the estimates and conclusions change in this case when the remedy is applied. However, I would opt for trying to include both, side by side, in the main manuscript if space allows.

It may look like this:
A
B
T
A*T
B*T

**with a foot note explaining how to properly calculate the hazard ratio at time T for group A relative to the baseline group.

Just a thought, some other people may have different ideas, though.
 
#4
I think that Staassis may have provided an answer that is better suited for a different question (assuming that his or her reply is regarding your cov*time interactions).

If you've identified that the proportional hazards assumption is not reasonably satisfied in your case, you shouldn't be testing these corrective interactions with time (with the possibility of removing them) because you already determined the time*covariate interaction is needed.

You can report both in a table to show how much estimated coefficients changed with and without the remedy for non-proportional hazards. If they are very similar, you may want to consider putting the full model with interactions in a supplemental document. The idea being that the easily interpreted model is in your main text, and you refer the reader to the supplemental document so they can verify how little the estimates and conclusions change in this case when the remedy is applied. However, I would opt for trying to include both, side by side, in the main manuscript if space allows.

It may look like this:
A
B
T
A*T
B*T

**with a foot note explaining how to properly calculate the hazard ratio at time T for group A relative to the baseline group.

Just a thought, some other people may have different ideas, though.
Ondansetron, Thank you very much for your answer!

Let me see if I understood it correctly, you are saying that if the original covariate’s coefficients did not changed dramatically between the models (with and without the adjustment for the interaction with time) I should report them in the main manuscript?

Does the coefficients of the interaction with time (as a continuous variable) has any importance or it is just the method for correcting the original covariate’s coefficients?
 

ondansetron

TS Contributor
#5
Ondansetron, Thank you very much for your answer!

Let me see if I understood it correctly, you are saying that if the original covariate’s coefficients did not changed dramatically between the models (with and without the adjustment for the interaction with time) I should report them in the main manuscript?
In my opinion, you should report all analyses done to give full disclosure in the paper. In you situation, you'll be able to report that the PH assumption was violated for a some covariate. You can then show the original model coefficients with p-values and CI for the coefficients, and then you can also show these for the corrected model. In my mind this gives the reader some confidence in your reporting because you've given them all of your output and you're allowing them to see for themselves whether the change is small or big. If the change is big, you may see this in very different coefficients, p-values, or CIs. This would make me think it is most important that you've made the corrections using an interaction with time. I would report BOTH irrespective of whether the changes are big or small. Where it gets reported, though, may depend on the journal or your preference. In my opinion, I would try both in the main text, regardless of how big or small the changes are, but it wouldn't be unreasonable to put the corrected model in a supplemental document that you refer the reader to if the changes in estimates, p-values, and CIs are so small. That's just my opinion though. In direct response to your question: I would report both irrespective of the size difference. Here is a paper discussing the importance of the PH assumption and how a violation may effect CI coverage. His website on Vanderbilt said it was a preprint for a publication in Statistics in Medicine (if you need to find a reference).

Does the coefficients of the interaction with time (as a continuous variable) has any importance or it is just the method for correcting the original covariate’s coefficients?
It depends. If the interaction is A*T where T is time, and you had no interest in A before except to control for it, then you probably have little interest in it afterwards. If you were trying to make a decision or inference about A's relationship with the time to event, then it would still be important to you, so the A*T coefficient is needed to calculate the hazard ratio relating A to the outcome at a given point in time.