st: Survival analysis: competing risks models with fraility [Was: Fwd: Request for your papers]

["Stephen P. Jenkins" <stephenj@essex.ac.uk>]

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Date: Sun, 16 May 2010 19:30:23 -0400
From: Sridhar Telidevara <sridhar.telidevara@gmail.com>
Subject: st: Fwd: Request for your papers

I ran two log-logistic competing risks models, one with and
another without gamma heterogeneity (mean 1 and variance
1/theta). There is a huge difference between the two likelihoods
(likelihood-ratio test
holds), but the estimate for the variance term (1/theta) is
pretty close to zero and also insignificant.
I know that if the estimate of the variance parameter for gamma
heterogeneity is zero then the model should
converge to the model without heterogeneity (independent risks)
and the likelihood ratios of
the two models should pretty much be the same. I am not sure how
to interpret the results.
I highly appreciate your input in this regard.
Thank you,
Regards,
Sridhar Telidevara
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(1) please use properly informative "Subject:" headers in your
posts

(2) You'll need to provide more details about the models you
think you've estimated and/or give a precise reference to an
article or book which describes the model. 

It sounds like you have used -streg <...>, dist(weibull)
frailty(gamma)- twice, once for each risk. If this is the case,
then the "competing risks" model that you estimated is rather
weird. Put another way, you are assuming unobserved gamma
variability in each of the two marginal distributions for the
latent hazards, but are assuming zero correlation between them --
which is unrealistic.  The 'proper' way to incorporate unobserved
heterogeneity in a competing risk model is to use a multivariate
distribution for the heterogeneity, allowing for correlation. If
you assume a continuous frailty distribution, then assuming
multivariate normality is the easiest way to go. Alternatively,
assume a multivariate discrete distribution (a series of mass
points with associated probabilities). Either way, you'll likely
have to program your own likelihood function using -ml-.

Stephen
-------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester CO4 3SQ, UK
Tel: +44(0)1206 873374. Fax: +44(0)1206 873151
http://www.iser.essex.ac.uk 
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/survival-analysis  
Downloadable papers and software:
http://ideas.repec.org/e/pje7.html 


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