# AFT model with time varying independent variables

I am a newbie in survival analysis and I would like to pose some simple questions, after reading numerous posts regarding how to perform survival analysis in R.

So, what I would like to know is:

Can survreg function of survival package handle combination of time - varying and fixed time independent variables?

Which are the mathematical formulations behind the following R commands:

Model 1: survreg(Time,Event) ~ Independent, dist = "w") and Model 2: survreg(log(Time),Event) ~ Independent, dist = "extreme")

Which of the above models can be considered as an AFT model?

In case anybody has tried fitting both models using a panel - like dataset, can easily understand that the coefficients are identical, though,

Model 2 tends to perform larger Mc Fadden's R - squared value. Why is this happening?

In response to this part of the question:

Can survreg function of survival package handle combination of time - varying and fixed time independent variables?

the answer is no. However, both the flexsurvreg from the flexsurv package and the aftreg function from the eha can do this, and the syntax is very similar to that of the survival::surv function.

The discussion on this question may be useful.

Well, as long as I remember, the ''feature'' of an AFT model is that it is the logarithm of the time that is on the left-hand side. The thing is that in this case hazard rate depends on exponent of regressors as well, which literally accelerate it.

And note that by changing distribution of u', you have just different AFT model. If you assume that errors have extreme value distribution, it might lead to higher R^2 just by construction (say, it's more flexible than Weibull, so it fits better). However, we need a formal proof to see if it's always the case.

I have done a little with survival models in R and I remember I had a feeling that ''KMsurv'' can be better to use than `survival'', but I am not sure. I also have a feeling that survival models are more straightforward to estimate in STATA, if you have it.

• To start with, thank you very much for your immidiate response. Consequently, I need not insert time in logarithmic transformation along with extreme value distribution for residuals. However the two models perform identical coefficients, value of log likelihood is different. Do you have in mind a reference explaining the mathematical formulation of the models in my previous post? Thanks again a lot. – nikolaos Oct 1 '14 at 21:11
• Well, you can try Cameron & Trivedi (2006) Microeconometrics, Ch.17, could be very useful. Also, there is a quite good lecture notes. – Alekz112 Oct 1 '14 at 21:47
• The point about different models is that AFT model (with log time) where you assume EV-dist differs from AFT where you assume Weibull – Alekz112 Oct 1 '14 at 21:49