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RE: st: left censoring in discrete-time duration model


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: left censoring in discrete-time duration model
Date   Thu, 16 Nov 2006 18:37:30 -0000

> -----Original Message-----
> From: Austin Nichols [mailto:austinnichols@gmail.com] 
> Sent: 16 November 2006 17:00
> To: statalist@hsphsun2.harvard.edu; Daniel Simon
> Subject: Re: st: left censoring in discrete-time duration model
> 
> 
> Daniel Simon--
> It seems to me that your estimates can only apply to introductions
> ("failures") after 1996, since you cannot distinguish pre-1996 and
> 1996 introductions, and you should drop firms (in all years) that
had
> websites in 1996, while keeping data on all other firms from 1996,
> though I would be interested to hear from someone who actually runs
> these sorts of models, e.g. Stephen Jenkins.
 

I am not clear about what the event is, nor about how the 'length of
time exposed to the risk of the event' is defined.

If the event is introduction of a website, when did a firm first
become at risk of introducing one?  The later of either the year web
technology became available or the year when the firm itself was
established?

Supposing you know the answer to this second question, then the
problem appears to be one of left truncation rather than left
censoring. (Left truncation is also known as delayed entry.)   The
correct likelihood involves conditioning on the probability of
surviving from t=0 to t at which first observed.

For discrete time survival models (as you appear to have), this is
easy to implement -- e.g. see my website materials -- as long as there
is not unobserved heterogeneity ('frailty'). In this case, the 'easy
estimation' methods for left-truncated data do not work; you have to
write your own program.    [My -hshaz- estimates discrete PH hazard
models with discrete mass point heterogeneity.]



Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk  
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/ 
Downloadable papers and software: http://ideas.repec.org/e/pje7.html

> On 11/16/06, Daniel Simon <dhs29@cornell.edu> wrote:
> > Hi - I'm using -hshaz- to estimate a discrete-time hazard 
> model. I have
> > some left censoring that I'm not sure how to deal with. I 
> am looking at
> > firms establishing websites. I can only observe the introduction
of
> > websites from 1996 onwards.  However, I know that some 
> firms established
> > websites prior to 1996, but I'm not sure which ones. 
> Currently, I have
> > tried three approaches: (1) Treat all firms that had a 
> website in 1996 as
> > if they adopted in 1996 (the first year of the sample 
> period), whether they
> > adopted in 1996 or adopted earlier; (2) Exclude 1996 from 
> the sample (begin
> > the analysis with 1997); (3) Drop all observations from 
> 1996 for firms that
> > had websites.
> > All three approaches give me quite similar results, so it 
> does not appear
> > that the censoring is a major issue. But, I'm wondering if 
> there is a
> > better way to deal with it. Thanks. Daniel
 


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