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st: correlated Competing Risks

From   "Stephen P. Jenkins" <>
To   <>
Subject   st: correlated Competing Risks
Date   Thu, 17 Apr 2008 11:16:31 +0100

Date: Wed, 16 Apr 2008 12:21:05 +0200
From: "Chiara Mussida" <>
Subject: st: correlated Competing Risks

Hi guys,
is there a specific command to estimate Seemeengly Unrelated Piecewise
constant hazard model?
more precisely, I have a CR framework that already gave me almost
satisfactory results with piecewise constant hazard rate models
estmations. Anyway, this modelisation is employed with the underlying
assumption of independence of CR. If I want to verify the existence of
correlation between my residuals (coming from different model
estimates), how can I proceed in terms of stata command?
thanks a lot

There is no canned Stata module in the public domain to estimate these
models that I am aware of.  To /test/ whether there are correlated
random effects, there are probably Lagrange Multiplier tests available
that do not require estimation of a full joint correlated hazard
model. Do a literature search.  Alternatively, to use a likelihood
ratio test, you would need to fit the correlated CR hazard model as
well as the ICR one, i.e. model the hazards jointly. This is a
non-trivial task -- see chapter 8 of my Survival Analysis manuscript
at the URL below.  See also the encyclopaedic survey paper by G van
der Berg on "Duration Models", ch 55, in Handboook of Econometrics Vol
5, JJ Heckman & E Leamer (eds), 2001, Elsevier.

The answer to your question may also depend on whether you are
treating survival times as continuous or interval-censored (a.k.a.
"grouped" or "discrete").  "Piecewise constant" refers to the shape of
the baseline hazard typically, and can occur in both continuous and
interval-censored models.

It is not immediately obvious to me that application of -suest-, as
suggested by Maarten Buis, is appropriate for such tests because of
the nature of the likelihoods involved. There's one case where it
/might/ be, though. It can be shown that, for interval censored data,
the likelihood for a CR model can be approximated by a multinomial
logit type likelihood. (And if intervals are narrow / interval hazards
'small', the approximation is usually quite good.)  See Chapter 8 op.
cit.  In this particular case, an independent CR model can be fitted
using -mlogit-, and a test for correlated unobservables is similar to
the standard IIA test for MNL models.  And the latter is something
that is discussed under [R] -suest-.  Note too the discussion of a MNL
model with correlated random intercepts by Haan & Uhlendorff in Stata
Journal 2006, 6(2).    Whether the MNL-based approach is suitable is
something you have to assess yourself.

Professor Stephen P. Jenkins <>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.  
Survival Analysis using Stata: 
Downloadable papers and software:

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