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Re: st: multiple state surv. analysis


From   Jenkins S P <stephenj@essex.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: multiple state surv. analysis
Date   Sat, 22 Nov 2003 17:43:33 +0000 (GMT)

On Sat, 22 Nov 2003, Maryah Fram wrote:

> Hi -- I'm a new stata user, and trying to do an analysis in stata for
> which I have syntax in R, as follows:
> coxph(Surv(DUR,UNC)~B+J+Q16+strata(STRT)+cluster(ID)).
> I'm looking at transitions between unemployment and work status during a
> two-year study, where DUR is time between transitions, UNC indicates
> final status is censored, B, J and Q16 are covariates, ID is the
> individual's id number, and STRT is a 4-level stratification variable
> indicating the type of transition (job to job, no job to job, etc.).  I
> can't figure out how to handle the STRT in Stata.  Could someone point
> me to the correct place in the manual? Or give any advice?

You have multi-state transition information for each person (ID). There
are a number of transition types, and each person may contribute multiple
spells relating to each type (complete or censored). IMHO it is misleading
to refer to your STRT variable as a "stratification" variable (in the
complex survey sense). Nor should you simply pool transitions of the
different types (as you appear to do -- though I admit that I do not know
R).

Standard survival models -- those available in Stata (and all other
packages that I know of) -- assume that there is one potential transition
type ("single risk" models) and also that each person contributes a single
spell ("single spell" analysis). If there were no unobserved
characteristics affecting transitions, then it would be ok to pool spells
for each person, and model each transition type separately -- but this
assumption is typically implausible. (Ceteris paribus, persons prone to
exit quickly from a spell of unemployment are also likely to be those who
are slow to re-enter unemployment if they have a job, and so on.)
Researchers have implemented this strategy, nonetheless, though often they
have adjusted standard errors to take account of the repeated observations
on the same individual (as if you clustered on ID in your case) -- see the
clear discussion of analysis of multiple spells by e.g. Allison PA (1984)
Event History Analysis, Sage.

To estimate multi-state transition models in a more sophisticated manner
takes you into advanced econometrics/stats (and advanced programming --
there are no easily accessible canned routines that I am aware of).  The
models are discussed in T Lancaster's 1990 monograph on the econometrics
of transition data. You should see also the survey by Gerard van den Berg
which is a chapter in a recent Handbook of Econometrics (Elsevier).
(Gerard and his co-authors are probably the leading experts on these sorts
of models, and have published many papers which discuss estimates of
them.) You might also search using Google or similar on "mixed
proportional hazard models".

good luck
Stephen
=============================================
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester CO4 3SQ, UK
Phone: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
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