I'm investigating a discrete time survival problem (the units are months and exit times range from month 1 to 36). From looking around so far, it seems like there are a few different types of model that I could apply:
A Cox proportional hazards model with "exact" tie resolution, a.k.a a conditional logistic regression with the strata being the set of subjects alive at each month. This would not automatically give me an estimate of the baseline hazard, but I understand that I could recover one later.
A standard logistic regression with one data point per subject-month, with time represented as a categorical variable (edit: or as Alexis points out I could use some functional form as well). This amounts to a proportional-odds model, or proportional hazards if I use a cloglog link.
A mixed-effects model--like the above, but considering time as a random effect rather than a dummified categorical variable.
I'm interested in predicting the entire survival function for all of my data points, not just understanding the direction and magnitude of covariate effects. I have on the order of 100k subjects and 100 covariates, so I can easily afford the extra 35 parameters for a dummy variable/mixed-effects model.
It seems to me that I should expect these models all to output similar results. In general, when should I prefer one over the other? (Or are there other types of models that I'm missing?)
EDIT: I've preliminarily tried fitting some of them in R and have run into various random segfaults/stack-overflows in the exact Cox model and computational difficulties with a previous mixed-effects model. So I may end up going simply with whichever one doesn't explode on my data! Still, I'd appreciate other considerations.