survit function and cox model with frailty

Hi:

Special thanks to Thomas B. and Thomas L.

The question that arises is whether it is statistically legitimate to
estimate survival probabilities after fitting a cox model with a frailty
term.

In this regard, I offer a brief clarification on what I'm attempting to
do.

The example I submitted is a simplified working example I am using to make
sure I am able to make the code work. My assumption is that if it does not
work on something simple, it will not work on something more complicated.

I am estimating a model measuring the survival of political leaders in
office in a sample of 1992 leaders from 166 countries from 1919 to 1999.
My interest in on the effect of victory and defeat in war on leaders'
survival in office. I include variables measuring economic conditions,
domestic political institutions, domestic unrest, leaders' age and
previous times in office, and war participation and war outcomes. I also
include a country-level frailty term on the assumption that my covariates
only partially capture the range of country-specific conditions affecting
leaders' political survival.

If I interpret a frailty term as a latent effect that enters
multiplicatively into the specification of the hazard function, I can
consider it as an additional covariate associated with a hidden
coefficient of 1. Then, for example, I would ask what the survival
probabilities are given a covariate path for a political leader in a high
frailty country or in a low frailty country.

And if this is statistically legitimate, can the survfit function
accommodate a frailty term?

Thanks again to you all.
giacomo

I don't actually understand what the intent is (and why the multiple time
periods with identical covariates), but it isn't going to be at all
straightforward to do a proper prediction for a single new case: the
survival curve should be the survival distribution with the frailty
integrated out, which is hard.

It should be possible to do a prediction setting the frailty to 1, but it
isn't.  Given that coxph will fit user-defined penalised likelihoods
survfit would have to be fairly clever to guess what it was supposed to do
in each circumstance.


	-thomas