# [R] survit function and cox model with frailty

gc4@duke.edu gc4 at duke.edu
Tue May 20 18:24:54 CEST 2003

```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

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

On Tue, 20 May 2003, Thomas Lumley wrote:

> 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
>
>

```