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Re: st: discrete-time survival analysis and continuous-time analogues


From   "Jesper B. Sorensen" <sorensen@mit.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: discrete-time survival analysis and continuous-time analogues
Date   Mon, 02 Jun 2003 15:05:10 -0400

For both of your questions I think a useful place to go is Paul Allison's 1984 Event History Analysis book from Sage (one of the little green ones).

Per pp.24-25 your specifications for the Weibull and Gompertz are correct.

Also, the reviewer is obviously wrong. There are purists who distinguish between continuous-time and discrete-time event history, and will not allow those practising discrete-time methods to call what they do event-history, but that seems silly. In principle the difference comes down to whether the event could in theory happen at any time (in which case it is a continuous time process) or whether it could only happen at discrete points. The latter type is very rare in most social science applications, but from an estimation standpoint it usually doesn't matter much. How much it matters depends on the rate relative to the observation interval. Trond Petersen has a paper on this. But just because you do not have data on exact timing does not mean its not event history.

Hope this helps.

//Jesper


At 01:40 PM 6/2/2003 -0500, you wrote:

Dear all,

I am estimating discrete time hazard models using cloglog. The data are
structured as organization-years (similar to person-months) and many of
the covariates are time-varying, i.e. change with each organization-year.
I know only the year in which the failure / event occurred, not the
specific moment or date. I also have many tied events / many failures in
the same year. These characteristics of the data have led me to
discrete-time models.

My question is whether I'm specifying the time variables correctly to
check out different functional forms of the hazard. I want to compare a
constant hazard, a linear increase in the hazard, and a piece-wise
constant exponential model. I have been referring to Stephen Jenkins'
terrific lectures and lessons and found explicit confirmation on how to
write a piece-wise exponential model for discrete-time data, but I'd like
to run the other specifications by you all too.

ALSO a reviewer saw these models and said "but you're not really doing
event-history analyses." Any suggestions for quick explanations of why
discrete-time methods are legitimate and actually more appropriate for
these data? I'd be especially happy to cite recent sociology or political
science articles that use discrete-time analyses, so let me know if you
have an empirical example for me to review and possibly cite.


Back to the first question, here's what I've been running:

Exponential analogue:
cloglog depvar ind1 ind2 ind3...
        * model has no covariate that is explicit measure of time / year *

Piece-wise constant exponential analogue:
cloglog depvar years6-15 years16-30 ind3 ind4...
        * model has dummy intervals marking certain years (with intervals
defined by theoretical / historical claims) and omits one dummy
period; allows me to investigate disjunctures in hazard associated with
changes in public policies (or other historical events) *

Gompertz analogue:
cloglog depvar year ind2 ind3...
        * model has year in it, assume linear increase in risk over time *

Weibull analogue:
cloglog depvar lnyear ind2 ind3...
        * model has ln(year) in it, coefficient is about .6 corresponding
to increase over time that levels off slowly *

Look OK?


Many thanks.

Erin Kelly

Assistant Professor of Sociology
University of Minnesota

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jesper B. Sørensen
Richard S. Leghorn (1939) Associate Professor of Strategic Management
Sloan School of Management
Massachusetts Institute of Technology
E52-581
Cambridge, MA 02142
http://web.mit.edu/sorensen/www/
(617) 253 7945  -- voice
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