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R: st: Survival analysis: repeated spells


From   "Carlo Lazzaro" <carlo.lazzaro@tin.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   R: st: Survival analysis: repeated spells
Date   Sat, 26 Sep 2009 20:44:11 +0200

Vinicio might want to run -stcox- with -cluster(id)- standard error to get
some evidences about the differences between the non-parametric regresion
models he is interested in comparing.

Kind Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di V.Martini
Inviato: sabato 26 settembre 2009 16.58
A: statalist@hsphsun2.harvard.edu
Oggetto: 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
>> *
>> *   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/
>>
>
> -- 
> 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
> epw@mail.med.upenn.edu
> *
> *   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/
>

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