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Re: st: Survival analysis: repeated spells
Thank you very much for your reply!
My question was, in a sense, much more basic. When I say "repeated
spells", I simply mean multiple records per unit (under no subject
event dependence).
Therefore, putting it differently, my question is the following:
Compare
stset t
stcox X
with
stset t, id(var)
stcox X
Does the introduction of the option id() change the likelihood
function in stcox? Or it simply allows stata to cluster the standard
error by "var"?
Concerning the way I wrote the likelihood, maybe I'm wrong, but I
still think it is correct (notice that h is the hazard, not the
failure function)
Many thanks,
Vinicio
Il giorno 25/set/2009, alle ore 19.25, E. Paul Wileyto ha scritto:
You have some choices to make for modeling recurrent events. Stata
has many utilities for structuring the risk-set for survival
modeling, especially for multiple record data. Best thing is to go
to the survival manual for Stata, and look up the methods and
formulas section in STREG. Here is how you stated the log-
likelihood...
ln L(i)= c log h(t)+log S(t)
This should actually be
ln L(i)= c log h(t)+ (1-c) log S(t)
The manual adds one more term to make likelihood conditional on time
of entry into the risk set.
ln L(i)= c log h(t)+ (1-c) log S(t) - S(t0)
You will have to make a choice about how to represent time. For
models like Anderson-Gill, the only time=0 is when you enter the
cohort at the beginning. The time for your first event becomes the
entry time for the second event, and so on. Gap time models reset
the clock back to zero after each event, so t for later events
becomes (ti-t0), and the S(t0) term in the likelihood goes away.
Beyond that, you will have to adjust at least the standard errors,
either by some sort of clustering approach (vce(cluster) or
bootstrap), or using shared frailty.
I will say that STSET is unfriendly to certain types of multiple
record data. I have had bad luck trying to STSET data for gap time,
and usually have to do something heroic that side-steps STSET's
"idiot proofing." That is, I either have to create my multiple
records with an Anderson-Gill type structure, and then subtract out
the t0 values, or I have to treat it as single record data... STSET
only generates the risk-set representation of the data, and
clustering or shared frailty will work without giving the IDs to
STSET.
Paul
V. Martini wrote:
Hello,
this is maybe a trivial question for some of you:
how does stata account for the presence of repeated spells?
I know that, in order to account for different spells that refers
to the same unit, stata requires to specify the id( ) option when
the data are stset-ted. But my question is about how stata deals
with this problem in the estimation.
For instance, suppose the contribution to the loglikelihood (with
right censoring) is given by:
L(i)= c log h(t)+log S(t)
where c is a censoring variable (c=1 if spell is complete), h is
the hazard function and S the survival function.
How the contribution to the likelihood changes when unit i has
repeated spells? In my case this is relevant because I have to
program the likelihood function by myself.
Many thanks,
Vinicio
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--
E. Paul Wileyto, Ph.D.
Assistant Professor of Biostatistics
Tobacco Use Research Center
School of Medicine, U. of Pennsylvania
3535 Market Street, Suite 4100
Philadelphia, PA 19104-3309
215-746-7147
Fax: 215-746-7140
[email protected]
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*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/