Survival analysis with time-dependent covariates - model specification

chris2377 — Fri, 01 Mar 2024 11:26:01 GMT

Hi,

I want to asses how some specific regulatory intervention (e.g. tax relief) affects time to firms' defaults using survival analysis. I have around 130 thousand firms, around 6% default cases.

Each firm can receive treatment (regulatory intervention) in a different moment of time and more than once, so I use time‐dependent covariates approach as in this paper and reshape my original dataset to the "counting process style".

In my model I want to control also for the industry in which each firm operates as the treatment is somehow linked to this.

So, following the paper linked above, I use the following code:

PROC PHREG DATA = my_data;
CLASS industry_code;
MODEL (tstart, tstop)*endpt(0) = treatment_variable industry_code/ TIES = EFRON RL;
RUN;

where:

- tstart and tstop are the boundaries of time periods created in accordance with "counting process style"

- endpt(0) - shows if each period ends in default or not

- industry_code - a 4-digit NACE code of the industry

Now I have two questions:

1. Is it correct to use NACE industry code both in the class and model statement? It's just a set of digits with no interpretation - should I transform it and create a set of dummies instead?

2. As regards the treatment_variable: one way of specyfing this variable is the value of treatment in a given tstart-tstop period. What about specyfing it as a dummy showing whether the firm was at all subject to treatment or not? This would not be time-variant but time-fixed. Can I include it in the model with counting process setup? This dummy would be created as follows:

firm 1: was subject to regulatory intervention twice, in 2010Q4 and 2011Q1, and did not default -> treatment dummy = 1
firm 2: was not subject to regulatory intervention and did not default -> treatment dummy = 0
firm 3: was subject to regulatory intervention once in 2010Q3 and went into default in 2011Q4 -> treatment dummy = 1
firm 4: was not subject to regulatory intervention and went into default in 2012Q1 -> treatment dummy = 0

Re: Survival analysis with time-dependent covariates - model specification

Mike_N — Mon, 04 Mar 2024 16:25:13 GMT

Answering your questions in order:

1. Yes, the industry code variable should be included in the class statement. You do not need to create dummy variables yourself.

2. If you know that your treatment variable actually is time-varying, I recommend modeling it that way.

topic Survival analysis with time-dependent covariates - model specification in Statistical Procedures

Survival analysis with time-dependent covariates - model specification

Re: Survival analysis with time-dependent covariates - model specification