Mixed Proportional Hazards Model

[Ng Luke]

I have not done Cox Regression Models before.

I am currently looking at how benefit sanctions for unemployment insurance affect individual's re-entry into the workforce. As the benefit sanctions are "treated" at different points in time for some individuals (i.e., time-varying treatment covariate for selected individuals), I realised that the standard cox regression is unable to handle this. Is there any manual on Stata that I can refer to analyse the effect of the benefit sanctions on the individual's re-entry into the workforce (event)?

Thank you.

[Stephen Jenkins]

the standard cox regression is unable to handle this

It would help if you were to make a clear(er) distinction between (a) survival time (elapsed time at risk of experiencing the event of interest since first at risk), and (b) calendar time.

Why do you think the standard Cox regression is unable to account for time-varying covariates -- whether varying by survival time or by calendar time? Have a good look through the help-files and manual. Parametric models, such as those fitted by streg can also deal with these.

It's also unclear to me why your post title refers to "mixed" PH models. Do you mean models incorporating unobserved heterogeneity (a.k.a. 'frailty')? On these, help-files and the manuals are relevant resources.

[Ng Luke]

Why do you think the standard Cox regression is unable to account for time-varying covariates -- whether varying by survival time or by calendar time? Have a good look through the help-files and manual. Parametric models, such as those fitted by streg can also deal with these.

Hi Stephen,

Thank you for the reply. I am looking at survival time. My time is from the time to first unemployment to employment. Lets say there are 10 individuals. Only 5 of them are treated (i.e., given a benefit sanction) at different points in their survival time. I would like to see the effect of this treatment on the transition to employment from unemployment. I have read the manual earlier on the standard Cox regressions on Stata for time-varying covariates. Their suggestion was to 'stratify' them into different groups. However, I do not think this would work for my case. Correct me if I am wrong.

It's also unclear to me why your post title refers to "mixed" PH models. Do you mean models incorporating unobserved heterogeneity (a.k.a. 'frailty')? On these, help-files and the manuals are relevant resources.

Yes. Noted, with thanks.

[Paul Dickman]

There's an example in the manual (example 3 in https://www.stata.com/manuals13/ststcox.pdf) that seems to be very similar (if not identical). In the Stanford heart transplant data, the treatment is a heart transplant, but the design is similar to yours in that the treatment happens at different times in the follow-up for each individual. The standard approach for such data is to split the person-time (e.g., using the stsplit command) for those individuals who received the treatment into two observations,one for the time up to treatment and one for the time post treatment. The data in that example have already been split, but you can look at the help for stsplit to see how to do that.

As Stephen said, it's not obvious to me from your description why you need to incorporate frailty. There may be some aspect of your study that makes it necessary, but if your individuals are independent and you only observe them from unemployment to re-entry into the workforce once then I don't see any reason to incorporate frailty.

[Ng Luke]

There's an example in the manual (example 3 in https://www.stata.com/manuals13/ststcox.pdf) that seems to be very similar (if not identical). In the Stanford heart transplant data, the treatment is a heart transplant, but the design is similar to yours in that the treatment happens at different times in the follow-up for each individual. The standard approach for such data is to split the person-time (e.g., using the stsplit command) for those individuals who received the treatment into two observations,one for the time up to treatment and one for the time post treatment. The data in that example have already been split, but you can look at the help for stsplit to see how to do that.

Hi Paul,

Thank you for the reply. And yes I did refer to the example as well prior. However, I was unsure about the data structure and approach. Your explanation was very helpful. Thank you again. Could I go one step further to ask, what if I have two variations of the treatment - a 6 months grace period and a 3 months grace period? Do I still stsplit the individuals who received the treatment into two observations,one for the time up to treatment and one for the time post treatment? After which, I use a categorical variable instead of a dummy variable to classify the type of treatment - a value of 0 for no treatment, a value of 1 for 3 months treatment and a value of 2 for 6 months treatment?

Thank you again.

Noted on your frailty reply. I will take a look at my dataset and problem statements again to verify.

[Paul Dickman]

Glad I could help. I don't fully understand the two variations of treatment, and since there's a time dimension to them I'm reluctant to express myself conclusively. I'll get back to that topic.

Let's assume instead that your two treatments were an intensive program (e.g., including daily in-person meetings with a case officer) and a low-intensity treatment with a lower level of support. Then one would absolutely do as you suggested. An individual who was treated would contribute 2 observations, 1 where the treatment variable was 0 (for the untreated time) and one observation where the treatment variable was 1 if the treatment was moderate and 2 if it was intensive. In such a design I would hope the treatment would be allocated randomly; if the treatment is allocated based on the predicted probability of success than the problem becomes more difficult. That is, you don't want the individuals who were thought to need more help to get more help.

Could you you explain your design in more details (I work in biomedicine so this is not my area of expertise). If the individuals in your study are receiving the exact same treatment but some are getting it after 3 months of being unemployed and others are getting it after 6 months of being employed then this is a slightly different design to the one I mentioned above (where there were two different treatments). If individuals are getting the same treatment, but at different times, then I would not suggest 3 values of the treatment variable.

Alternatively, if the 3 and 6 months are the planned treatment duration then this would involve different considerations.

[Ng Luke]

Glad I could help. I don't fully understand the two variations of treatment, and since there's a time dimension to them I'm reluctant to express myself conclusively. I'll get back to that topic.

Let's assume instead that your two treatments were an intensive program (e.g., including daily in-person meetings with a case officer) and a low-intensity treatment with a lower level of support. Then one would absolutely do as you suggested. An individual who was treated would contribute 2 observations, 1 where the treatment variable was 0 (for the untreated time) and one observation where the treatment variable was 1 if the treatment was moderate and 2 if it was intensive. In such a design I would hope the treatment would be allocated randomly; if the treatment is allocated based on the predicted probability of success than the problem becomes more difficult. That is, you don't want the individuals who were thought to need more help to get more help.

Could you you explain your design in more details (I work in biomedicine so this is not my area of expertise). If the individuals in your study are receiving the exact same treatment but some are getting it after 3 months of being unemployed and others are getting it after 6 months of being employed then this is a slightly different design to the one I mentioned above (where there were two different treatments). If individuals are getting the same treatment, but at different times, then I would not suggest 3 values of the treatment variable.

Alternatively, if the 3 and 6 months are the planned treatment duration then this would involve different considerations.

Hi Paul,

Thank you so much for the explanation. Apologies as I am new to Cox regressions so I may be asking very rudimentary questions. Yes, we are planning to randomise the treatment of the individuals. I will be working on another Cox regression and may seek your guidance again. Thank you again for your patience.