Cox proportional hazards model with time varying covariates where PH assumption was violated.

[Ali Baykus]

Hi,

"Follow_up" (between 1 and 24 months) is the time variable. "Status" (0=IN, 1=OUT) is the failure variable. Independent variables are age (groups), gender, sector, province, gross minimum monthly wage range (groups).

Gender (female, male), Age_groups (<25, 25-34, 35-44, >=45), Sectors (government, private), Province (10 of them), GMMWR (GM, GM-3GM, 3GM-5GM, >5GM)

I have conducted a cox regression model and checked for PH assumption. Realized that "except province" all my independent variables violated the assumption. A time ago, for another data, as a solution to this, i used stratified cox regression models. At that time, only one of the variables violated the assumption, so it was an "fairly" easy task. But in this situation, 4 variables violating the PH assumption, stratified cox regression modeling would be a bit "tricky" (i guess!!).

So as a solution i am willing and trying to conduct "Extended" Cox regression model with time varying covariates.

I have several questions about this procedure.

1) Is choosing "Extended cox regression model with time varying covariates" rather than "stratified models" correct, or practical at least?

If so;

2) My initial model codes are as follows;

stset Follow_up, failure(Status==1)

stcox i.Gender i.Age_groups i.Sector i.Province i.GMMWR, nohr

So at this stage, how do i insert the time varying variables. I have seen both of the following methods on different sources.

a) stcox i.Gender i.Age_groups i.Sector i.Province i.GMMWR, tvc(i.Gender i.Age_groups i.Sector i.GMMWR) texp(_t) nohr
b) stcox i.Province, tvc(i.Gender i.Age_groups i.Sector i.GMMWR) texp(_t) nohr

Which one is correct? And also, should i use _t or ln(_t)?

3) If "a" is the right choice; how do i interpret the estimates since i have 2 for each variable. For example for gender and age results are as follows;

Thank you for your answers.

[Clyde Schechter]

Yes, using time varying coefficients is both practical and sensible.

Code b) is correct; a) is wrong.

As for the use of t or ln(t), that depends on how you think the hazard ratio for those effects varies with time. It's a substantive question, not a statistical question. Only somebody with expertise in your content area can advise you.

[Bree Shi]

Yes, using time varying coefficients is both practical and sensible.

Code b) is correct; a) is wrong.

As for the use of t or ln(t), that depends on how you think the hazard ratio for those effects varies with time. It's a substantive question, not a statistical question. Only somebody with expertise in your content area can advise you.

Hi Clyde,

Your answer is different to Maarten Buis' in post https://www.statalist.org/forums/for...fter-using-tvc which concludes that code (a) is correct and the effect should be interpreted as time-varying instead of one single number. Would you be able to further explain?

Thank you in advance!

Kind Regards,
Bree

[Clyde Schechter]

I don't actually see in the post you link to where Maarten Buis indicates how he would code the model with time varying coefficients.

Be that as it may, my earlier response was incorrect. a) is the correct way to code the model when age group, gender, sector and GMMWR violate proportional hazards. The variables should appear both in the original varlist and in the -tvc()- option unless you wish to constrain the effect at time zero to be null (which is seldom going to be true in the real world).