Solved – Cox regression – Hazard and Survival Estimates

I have a couple questions about Cox survival regression:

1) Is it true that the hazard function h(t) is not available (even WITHOUT time dependent covariates)- and if not, is it because the baseline hazard is not defined (only the cumulative hazard is and you cant go from the cumulative hazard to the hazard)?

2) When you have time dependent covariates is it not possible to estimate the survival curve for a chosen set of covariate values (I'd like to plot prototypical values)? Can anyone explain why not?

1) Yes that's correct. There is no intercept in the CoxPH – it is one of the reasons why it's usually complemented by Kaplan-Meier or cumulative incidence curves

2) I've had some efforts into looking into time dependant covariates and it seems to be a mine-field, I've summarised most of the things I've learned in my previous question. If you leave the cox regression then you could try poisson regression or the Laplace regression (quantile regression) that might be easier to work with. One important part is that even though the PH might be violated it might not be important unless there is a clear trend in your data. What you get is an average and that might be good enough – T. Thernaugh mentions in his book that it's not always that you have to address this issue.

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