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Re: st: Competing Cause Mortality


From   "Anthony Gichangi" <anthony@stat.sdu.dk>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Competing Cause Mortality
Date   Wed, 2 Jun 2004 23:49:18 +0200

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
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

*
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