Dear Marteen,
I am using the population averaged Cox model in my analysis of clustered data form a trial: stcox with the option-cluster ().
Not being in possession of the book you advised, I thought that I could ask you another question.
The marginal (Cox) model uses the sandwich estimator to obtain standard errors. It seems that with a total number of clusters below 40 as it is my case, one has to correct the confidence interval as with less than 40 clusters the sandwich estimator is biased downwards.
I am not sure about how to correct for the confidence intervals in general and in Stata in particular. How do I do that in Stata?
I came across an article suggesting theoretical approaches (use of a t distribution or jacknife standard errors) to do the correction, but it does not really tell how to implement the suggested approaches in a package.
What about the following ways of implementing the approaches below?
1- Using the t distribution instead of the Z distribution to derive CI: Would the derivation of the confidence interval using the robust SE on the log scale and the value of the t distribution with n-2 degree of freedom instead of the usual 1.96 value, where n is the total number of clusters randomised, be a sensible approach? I would then do and exponentiation of the CI limits to have the corrected standard errors. I am thinking of something like this: Estimates ± t30 x robust SE on the log scale. Does that sounds like a sensible application of this correction.
2- Using a jacknife estimator instead of the sandwich estimator:
xi: jacknife: stcox i.randomgp, cluster(clinic)
What do you think? I hope that I am not completely off track
Many thanks
Justin B.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Justin B Echouffo Tcheugui
Sent: 16 March 2009 16:17
To: [email protected]
Subject: RE: st: Multilevel modelling of survival data
Dear Marteen,
I tried the command stcox with the option -shared () as you advised. As
you can see below I am not having the desired output
xi: stcox i.randomgp, shared(clinic)
i.randomgp _Irandomgp_0-1 (naturally coded; _Irandomgp_0 omitted)
failure _d: event
analysis time _t: followup_time
Fitting comparison Cox model:
Estimating frailty variance:
numerical derivatives are approximate flat or discontinuous region
encountered
Iteration 0: log profile likelihood = -2482.4152
could not calculate numerical derivatives flat or discontinuous region
encountered r (430);
I tried adding the option - difficult, hoping that it will help but it
did not
xi: stcox i.randomgp, shared(practice) difficult
i.randomgp _Irandomgp_0-1 (naturally coded; _Irandomgp_0
omitted)
failure _d: event
analysis time _t: followup_time
Fitting comparison Cox model:
Estimating frailty variance:
numerical derivatives are approximate flat or discontinuous region
encountered
Iteration 0: log profile likelihood = -2482.4152
could not calculate numerical derivatives flat or discontinuous region
encountered r(430);
Could you please advise on this?
Many thanks
Justin B.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Maarten buis
Sent: 16 March 2009 10:58
To: stata list
Subject: RE: st: Multilevel modelling of survival data
--- On Mon, 16/3/09, Justin B Echouffo Tcheugui wrote:
> > in this case the option - cluster() in this case does
> > not fit the clinic into the model as a random
> > intercept
--- On Mon, 16/3/09, Maarten buis wrote:
> That is correct.
A point on terminology again: When discussing the
distrinction between these models, the models estimated
with the -cluster()- option are sometimes known as
population averaged models, while the random intercept
models are sometimes known as individual specific models.
-- Maarten
-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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