discrete survival time and marginal effects

[Oliver Winkler]

Dear statalisters,

I was wondering, whether it is reasonable to estimate AME after survival models using discrete time. With discrete time models, I mean models described here: http://www.stata.com/manuals13/stdiscrete.pdf

Since stata 12 was introduced, marginal effects can be computed after streg and stcox (http://www.stata.com/stata12/survival-data/). Those commands work for continuous time (off topic: I am a little confused by a comment stating that "there is no meaningful marginal effect" for the Cox-Model - see here: http://www.stata.com/statalist/archi.../msg01214.html ; can someone clarify?).

Technically, nothing would stop me from calculating an AME after a discrete survival time model, e.g.:
logit _d ib1._t i.x
margins, dydx(_all)

My question concerning the appropriateness emerged after finding a study that involves this practice: Göhlmann, S., Schmidt, C. M., & Tauchmann, H. (2010). Smoking initiation in Germany: the role of intergenerational transmission. Health Economics, 19(2), 227-242. (http://onlinelibrary.wiley.com/doi/1....1470/abstract)
In their study, the marginal effects are relatively low in the covariates but suspiciously higher in the dummy variables for the duration time.

A similar question was posed on statalist with a comment by Stephen Jenkins, he argued, that it is possible, yet, arguably, not very interesting in particular cases (http://www.stata.com/statalist/archi.../msg00069.html)

Thanks in advance!

[Maarten Buis]

I am a little confused by a comment stating that "there is no meaningful marginal effect" for the Cox-Model - see here: http://www.stata.com/statalist/archi.../msg01214.html ; can someone clarify?

The logic behind Cox regression is that you can calculate hazard ratios without specifying the baseline hazard function. This is a good thing in that you cannot make an error in a function you do not specify, but this robustness comes at a price: you can only interpret the hazard ratios and not any additional statistics that depend on the baseline hazard function, which includes marginal effects. There are ways around that, but then you are estimating the baseline hazard, and not doing so was the very advantage of using a Cox model to begin with. So, I would say that if you think hazard ratios are not enough for your research question (and that is very well possible, though I am not so convinced about marginal effects in this case), then Cox regression is not for you. You could consider the model that can be estimated with stpm2 (see: ssc descr stpm2) instead.

[Maarten Buis]

I was wondering, whether it is reasonable to estimate AME after survival models using discrete time. My question concerning the appropriateness emerged after finding a study that involves this practice: Göhlmann, S., Schmidt, C. M., & Tauchmann, H. (2010). Smoking initiation in Germany: the role of intergenerational transmission. Health Economics, 19(2), 227-242. (http://onlinelibrary.wiley.com/doi/1....1470/abstract) In their study, the marginal effects are relatively low in the covariates but suspiciously higher in the dummy variables for the duration time.

That result does not surprise, this study is about when young people start smoking and time is age. That the highest probability of starting to smoke is about 16 years old seems perfectly reasonable, and that the effect of age is much larger than most of the other effects also seems perfectly plausible to me.

However, as always, you should keep in mind what marginal effect you are trying to estimate. In survival analysis the probability of surviving a year is the only interesting outcome. So, be careful.