Proc phreg counting syle process and PH verification

[chris2377]

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?

[Season]

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@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.

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@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?

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