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RE: st: Competing Cause Mortality


From   "Stephen P Jenkins" <stephenj@essex.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Competing Cause Mortality
Date   Thu, 3 Jun 2004 14:57:18 +0100

Could someone please offer some clarification for me in this discussion
of competing risks models?  Is the key issue to do with whether one
assumes that the cause-specific hazard rates are independent or not?   

If they are independent, and survival times are continuous rather than
interval-censored then the likelihood function for CR model factors into
a set of terms each epending on each cause-specific hazard. Hence the
overall CR likelihood can be estimated via separate maximization of the
likelihood of models for each cause-specific hazard in which exits via
other causes are treated as censored.  In my view, the point that has
been made about censoring is to do with the way in which the model is
estimated, rather than about the model itself.

If competing risks are not independent, then economists typically assume
a "multivariate mixed proportional hazard model" (MMPHM), allowing for
dependence between the unobservable factors influencing each risk.
(Latent survival times are assumed independent conditional on the
observed and /unobserved/ variables, rather than independence
conditional on observed vbles as in the standard ICR model.) See e.g. GJ
van den Berg (2001) "Duration models: specification, identificaton, and
multiple durations", in JJ Heckman & E Leamer (eds.) Handbook of
Econometrics Volume 5, Elsevier, Amsterdam, especially section 8.2.1.
[See also a recent paper by Abbring and van den Berg in the JRSS about
identification of such models.]

Do these multivariate mixed proportional hazard models enable one to
address the issues that correspondents have raised?  If not, in what
senses are they seen to be deficient?

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   


> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Anthony Gichangi
> Sent: 02 June 2004 22:49
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Competing Cause Mortality
> 
> 
> I have read the article but the most important question is, 
> what problem does Lunn and McNeil solve ?. Kalbleisch and 
> Prentice new book (2002) describes similar model described by 
> Lunn and McNeil and they have indicated that it helps to 
> improve efficiency of the estimates when proportional risk 
> holds i.e when all cause specific hazards differ by a 
> constant throughout. Hower the methods in Lunn and McNeil and 
> the book may differ slighly, may be..I have never had time to 
> check them.
> 
> 
> The hazards that you deal with in competing risk are not the 
> same hazards that you deal with in ordinary survival data. 
> The cause-specific hazard are hazard of a particular cause in 
> the presence of other causes. They assume an arbitrary 
> dependence between the causes, which we do not worry about.  
> So by treating other causes as censoring you define the 
> cause-specific hazard function, however the people who failed 
> from other causes are treated as being at risk because 
> explicitly assume that the censoring and death from other 
> causes occurs after the cause of  interest. If we assume 
> otherwise, then we have to change the risk set in the 
> appropriate manner.
> 
> Furthermore, what Trevo say is being overestimated is not 
> what is being estimated. In ideal situation you want to 
> estimate the marginal hazard or the hazard of a particular 
> cause if that is the only cause acting in the population. But 
> since this is not true, therefore we estimate the 
> cause-specific hazard which¨ allows other causes and possible 
> dependence between the causes
> 
> With respect to Shawns problem, the question is which method 
> solves his problem.  To be able to look what is happening to 
> other cause, then it pays to look onto the cause-specific 
> hazard functions and the cumulative incidence functions 
> (Aalen Johansen estimator) or "derivatives" of such 
> functions. One interesting  function is "relative risk", 
> which compares the hazard of death from a particular cause 
> with the overall hazard, then you can see how the 
> contribution of individual causes vary over time and you can 
> compare between groups.
> 
> It is clear that, although we do not assume independence of 
> risk, it exist and there is almost no way of investigating 
> the dependence. Some authors have suggested using time 
> dependent covariates.  However if we restrict ourselves to 
> cause-specific hazard function then the dependence is not to 
> worry because the cause-specific hazard function is a 
> function of dependence itself.
> 
> 
> Regards
> Anthony
> 
> ----- Original Message ----- 
> From: "Tero T Kivela" <tekivela@cc.helsinki.fi>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Wednesday, June 02, 2004 9:09 PM
> Subject: Re: st: Competing Cause Mortality
> 
> 
> > Dear May,
> >
> > I have not yet read the paper you refer to but will do so. 
> Meanwhile:
> >
> > I wonder how the technique cited handles death as a competing risk. 
> > Shawn's question was on mortality. If death from competing 
> causes is 
> > handled as censored, Cox will not give the right answer. When a 
> > subject is censored from analysis, he or she is still 
> modeled as being 
> > at risk of the event of interest. However, if the patient 
> died, he or 
> > she will not be at risk of further events, and Cox normally 
> produces 
> > an overestimate of mortality.
> >
> > I other words, how does the result of this method compare 
> with the one 
> > obtained with competing risks proportional hazards regression, the 
> > competing risk equivalent of Cox regression.
> >
> > T Kivela
> >
> >
> > On Wed, 2 Jun 2004, May Boggess wrote:
> >
> > > On Wednesday, Shawn asked about competing risks analysis:
> > >
> > > > I am trying to do an analysis of competing-cause 
> mortality. I have 
> > > > a mortality dataset where I have death (yes/no) and among those 
> > > > who
> died,
> > > > whether it was a specific type of death (yes/no).
> > >
> > > > Initially, I used stset with any-cause death as my failure, then
> repeated
> > > > the analysis with type-specific death as failure. I've been told
> that's
> > > > incorrect, because it treats those who died from 
> another cause as 
> > > > just
> being
> > > > censored, and doesn't allow me to examine whether my exposure of
> interest
> > > > also increases the non-specific cause of death. I was 
> told I need 
> > > > to
> do
> > > > competing-cause mortality, to see how my exposure 
> impacts both the 
> > > > type-specific and the other causes of death.
> > >
> > > Tero Kivela gave the following suggestions:
> > > >
> > > > Enzo Coviello's very handy -stcompet- ado-file will solve your 
> > > > problem
> if
> > > > you need a Kaplan-Meire type analysis. If you need an 
> equivalent 
> > > > of Cox regression, Stata doen not help you (yet).
> > >
> > > It is possible to use Cox regression for competing risks 
> in Stata. 
> > > There is a very nice paper by Lunn and McNeil "Applying Cox 
> > > regression to competing risks" Biometrics 51, 524-532,
> June 1995.
> > > They go through a number of different methods, none of 
> which is the
> method
> > > mentioned in the multiple risk FAQ.
> > >
> > > Below is the example from a response to a Statalist 
> question I gave 
> > > a few weeks go.
> > >
> > > Here I will give examples of the different methods. I am going to 
> > > keep it relatively simple by sticking to non-repeated 
> failures, in 
> > > other words, each subject is either censored or suffers 
> one event, 
> > > which in this example will be one of two types.
> > >
> > > First I need to create an appropriate dataset. I will 
> begin with the
> > > following:
> > >
> > >  clear
> > >  sysuse cancer
> > >  set seed 12345
> > >  drop died
> > >  gen id=_n
> > >  move id st
> > >  gen death=int(uniform()*3)
> > >  list
> > >
> > > Here death=0 is censored and 1 and 2 are the competing events.
> > >
> > > For competing risks is that we need one record for each 
> failure type 
> > > for each subject. This is the "expanded" dataset. 
> Continuing where 
> > > we left
> > > off:
> > >
> > >  expand 2
> > >  bysort id : gen type = _n
> > >  gen status=(type==death)
> > >  recode type (1=0)(2=1)
> > >  list, sepby(id)
> > >  stset studytime, f(status)
> > >
> > > Now we have two records per subject and status is our failure 
> > > variable. For each subject, having two zeroes means censored. We 
> > > have the following choices for models:
> > >
> > >  * risk type as covariate with interactions (Lunn & 
> McNeal Method A)  
> > > gen aget=age*type  gen drugt=drug*type
> > >  stcox type drug age drugt aget, nolog nohr cluster(id)
> > >  estimates store methodA
> > >
> > >  * risk type as covariate with interactions only (Lunn & McNeal 
> > > Table 2)  stcox type  drugt aget, nolog nohr cluster(id)  
> estimates 
> > > store table2
> > >
> > >  * risk type as strata (as in FAQ)
> > >  stcox drug age, strata(type) nolog nohr cluster(id)  estimates 
> > > store faq
> > >
> > >  * risk type as strata with interactions (Lunn & McNeal 
> Method B)  
> > > stcox drug age drugt aget, strata(type) nolog nohr cluster(id)  
> > > estimates store methodB
> > >
> > >
> > > I have saved the estimates from each of the models so that if I 
> > > wanted to compare them I could do so as follows:
> > >
> > >  estimates table _all, stats(aic bic)
> > >
> > > -- May
> > > mmb@stata.com
> > >
> > > *
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> > >
> > *
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> 
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