A referee keeps asking: Predictive margin for hazard ratios after a Cox model is respect to what?

[Jukka Ollgren]

I have a problem. A referee keeps asking what is the reference category for the predictive margin for the hazard ratio in the Cox model for a categorical variable X having a value b which is not zero. The baseline hazard is defined to have all the covariates as zero in the parametric exponential part of the Cox model. It is said that in Stata this predictive hazard ratio is respect to baseline. Can one somehow say that predictive margins is PARTLY respect to X=0 or do you think that it is enough to say that it is respect to baseline like the hazard ratio is defined usually in the Cox model. What if the referee disagrees and rejects the paper?

[Tiago Pereira]

Hi, Jukka.

Would it possible to share with us the syntax you have used? It will be easier to help with detailed information on the commands.

[Maarten Buis]

A Cox model is not the best case for using margins. The main strength of a Cox model is that on can estimate hazard ratios without estimating the baseline hazard. That is what makes it a semi-parametric model. As is so often the case, the strength of a model is also its weakness. Anything that requires the baseline hazard is just not a good fit for this model. A lot of things that margins tries to estimate require the baseline function. You can kinda make it work, but it defeats the very purpose of a Cox model.

Cox models are great if you just want to interpret the hazard ratios (exponentiated coefficients, i.e. not using margins). That is the problem this model is designed to solve. If you want to use margins, then that is a sign that the Cox model is probably the wrong model for what you want to do (or there is something wrong with what you think you want to do).

[Jukka Ollgren]

hi, due to proportional hazards assumption (if valid) in many ratios, this baseline cancels out. Stata manual gives predictive margin for hazard ratio and it does not contain baseline at all. So is it so that there is a major bug in Stata and it has been there 20 years?

I have a model which contain a lot of interactions and in the graph I needed more compact result so this predictive hazard ratio seems to be ok. In predictive margin there is a mean (or ratios of them) when variable X is b (or =0) and other variables have their original values. Even if you use hazards (and then ratio) or exp()-part, you will get the same result if the proportional hazard assumption is valid.

margins tartuntareittiL_typistetty , at(posthiv==0 )

I noticed that in some old stata forums messages, it is said that it is respect to baseline, which cancels out in any case, or am I wrong?

[Jukka Ollgren]

See statalist.org/forums/forum/general-stata-discussion/general/1394383-predictive-margins-by-age-category-after-stcox-seem-intuitively-correct-but-are-they-statistically-correct.

There Clyde Schechter:


"If you notice, the -margins- output gives you relative hazards, so it is not dependent on the baseline hazard. It's perfectly reasonable to use these.

However, I don't understand the -if firstobs- clause in your -margins- command. What does firstobs mean, and why do you want to restrict the calculation to that subset? Also, your -margins- command probably be better written as:

Code:
margins rdiabe#scworkj, at(ragey_6cat = (1 2 3 4 5 6))". So was Clyde wrong?

[Maarten Buis]

At this point I have no idea anymore what you are asking and what you want to know. There are just too many loose comments floating around and I am not sure who those comments are aimed at. I strongly suspect that there is also a lot of terminological confusion going on. Especially around the term baseline. My suspicion is that you and the reviewer talk about different things. As long as we cannot resolve that, we cannot help you.

So take a step back, and figure out the one (and only one) question you want answered. Give us the information we need to answer that. That is one the one hand obvious, and on the other hand extremely difficult because if you knew the information needed for the answer then you would probably already know the answer. Tiago already gave you an indication: we need the exact (emphasis on exact) syntax you used. We also need the exact (again, emphasis on exact) wording the reviewer used. This includes the context, the sentences before and after the sentence you are confused about. Than we need to know what it is in that sentence that you do not understand.

[Jukka Ollgren]

hi, ok! Probably the problem is a terminological confusion ! We are trying to find some kind of solution with the referee. Thanks a lot!