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chris2377
Quartz | Level 8
Hi,
 
I want to asses how some specific regulatory intervention (e.g. tax relief) affects time to firms' defaults using survival analysis. Since my covariate of interest is time-dependent (different firms receive tax reliefs in different moments of time, sometimes more than once), I want to use counting process syntax in the following way (I control also for the industry, in which firm operates, by including NACE code):
 
PROC PHREG DATA = my_data
CLASS industry_code
MODEL (tstart, tstop)*endpt(0) = treatment_variable industry_code/ TIES = EFRON RL;
RUN;
 
I've read the "Survival Analysis using SAS. A Practical Guide" book by Paul D. Allison. According to the book when using time-dependent covariates the model is no longer a proportional hazard anymore, but it "creates no real problem for the partial likelihood estimation method".
 
My questions are as follows:
1. Do I understand correctly that I don't have to verify the PH assumption prior to estimating the model?
2. If the answer to the previous question is "yes", are there any other assumptions that I have to verify to make sure that I can estimate the model as shown above?
3. Are the ways to asses goodness of fit the same for models with time-dependent covariates and "standard" PH models? Can use the statistics produced by the phreg or I need to adjust them somehow to account for using counting process syntax?
1 REPLY 1
Season
Lapis Lazuli | Level 10

@chris2377 wrote:
My questions are as follows:
1. Do I understand correctly that I don't have to verify the PH assumption prior to estimating the model?

The answer to the first question is "No, you should verify the PH assumption". I am not sure of the underlying rationale of imposing a time-dependent variable on the Cox model. If you do not reject the PH assumption, then it is statistically plausible to get rid of the time-dependent variable.


@chris2377 wrote:
3. Are the ways to asses goodness of fit the same for models with time-dependent covariates and "standard" PH models? Can use the statistics produced by the phreg or I need to adjust them somehow to account for using counting process syntax?

See this dissertation for more details: Evaluation of Goodness-of-fit Tests for the Cox Proportional Hazards Model with Time-Varying Covaria....

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