Cox proportional hazard model and the PH assumption

[Tim Hartmann]

Hello everybody,

im am running a cox regression in order to assess whether individuals return to the labour market earlier after some legislation change. My treatment group is consisting of individuals in the year after the new law and the control group of individuals before the law change. The treated variable takes on value 1 if individuals are in the treatment group and 0 otherwise. Now, estimation results show that individuals respond to the law and return earlier but the treated variable does not survive the proportinality assumption test. (Which in my view is logic because whether you get into the treatment group depends on the timing of the law, or am i mistaken?)

My question now:

(1) when I interact time and treated to a new variable (interact=treated*_t), does the interpretation of the estimate stay the same? the treated hazard ratio was 1.3 meaning a higher chance to face the failure event. The interact estimate is 1.02 still meaning that the failure event is more likely for the treatment group?! , although there is a big drop in the effect.

(2) do i have to include both variables then, treated and interact?

If I need to clarify anything further, pls tell me

Kind regards
Tim

[Andrea Discacciati]

Use the tvc() option to specify a time-dependent coefficient for the treatment variable in your Cox model. The approach you're suggesting (creating an interaction variable interact=treated*_t) is wrong (unless you first split the dataset using -stsplit-).

[Tim Hartmann]

Hi Andrea,

thanks for your remark. I used the tvc option already but then stata told me that the command

estat phtest, detail

to test for the ph assumptions of all the covariates in my model is not possbile anymore.
The interaction variable and the variable on treated via the tvc option produce the same coefficient, which is why I assumed that the interaction term is implented by stata through the tvc option and that by doing it manually, the

estat phtest, detail

becomes feasible again.

Anyone else who can give guidance on this topic?

Greetings
Tim

[Marcos Almeida]

[...]in order to assess whether individuals return to the labour market earlier after some legislation change

That seems, theoretically speaking, more "familiar" to the realm of time-series analysis.