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Re: st: equivalence of log-logistic survival estimation with gllamm


From   Karen Ruckman <ruckman@sfu.ca>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: equivalence of log-logistic survival estimation with gllamm
Date   Tue, 26 Mar 2013 13:01:52 -0700 (PDT)

thanks guys for the information.  i see that the loglog link is not the same thing as the loglog distribution in survival analysis.  (even though the loglog link is not actually listed anywhere...i digress.)  i most definitely was not looking to run a cloglog.  that was suggested by someone else.  i do not have a discrete dependent variable, so cloglog is not appropriate.

tricking -gllamm- to use poisson was exactly what i was after.  in the gllamm manual on p.80, the authors give two commands, both the equivalent of each other:
streg secondp after decl, dist(exp)
poisson unceni secondp after decl, offset(lny) irr

they do not show it but claim they would produce identical results.  i would use the same (although in the -gllamm- command) except the problem is my underlying survival analysis hazard rate doesn't have an exponential structure. i use a log-logistic structure but log-normal would be fine too.  i am unsure how to get this to work in -poisson- or in -gllamm-.



----- Original Message -----
From: "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To: statalist@hsphsun2.harvard.edu
Sent: Tuesday, March 26, 2013 12:42:30 PM
Subject: Re: st: equivalence of log-logistic survival estimation with gllamm

On Tue, Mar 26, 2013 at 2:43 PM, Nick Cox <njcoxstata@gmail.com> wrote:

>
> The loglog and cloglog link functions have no application to survival
> times whatsoever. They are relevant _only_ to mean responses bounded
> by 0 and 1.

I'm with Nick. It's pretty clear there's some confusion going on.

However, there are discrete time proportional hazards survival models
that involve the cloglog link, and maybe that's what the original
poster wanted? I just checked Multilevel and Logitudinal Modeling
Using Stata, Volume II: Categorical Responses, Counts, and Survival,
Third Edition, S. Rabe-Hesketh and A. Skrondal, 2012, Stata Press.
They give an example using -xtcloglog- on p. 783, and discuss how this
could be fit using -gllamm-.

For a continuous time parametric survival model, I'm guessing that
some kind of censored normal model on the log-transformed time would
be necessary. That would be the lognormal model, not the log-logistic.
Out of my area, but I wonder if it would be possible to trick -gllamm-
to use the same basic "Poisson" likelihood discussed here, but with
censoring?

http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/
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