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Re: st: conditional logistic


From   Ricardo Ovaldia <ovaldia@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: conditional logistic
Date   Thu, 25 Oct 2007 05:22:26 -0700 (PDT)

Dear all,

I posted this under a different header and did not get
a reply. So let me ask the question better.

What is the difference between conditional logistic
regression grouping on clinic and unconditional
logistic regression including clinic as a dummy
(indicator) variable? Tha is, what is the difference
in model assumptions and parameter estimates?

Thank you,
Ricardo.

--- Ricardo Ovaldia <ovaldia@yahoo.com> wrote:

> Thank you Dr. Gould for a thorough and clear
> explanation. 
> 
> I have a similar problem related to conditional
> logistic regression. I have data from a multi-center
> (7 clinics) study. I analyzed the data using
> conditional logistic grouping on clinic. I was asked
> to defend my method, because previous analyses on
> these data were performed using indicator variables
> or
> simply using a robust variance estimator. 
> 
> I am planning on using the explanation from Dr.
> Gould
> post, however, the argument that I would use for
> conditional logistic is the same as that presented
> for
> the indicator variables (dummies) . So I am missing
> something, what is the difference? By the way, the
> results I obtained using conditional logistic and
> dummies are very similar.
> 
> Thank you,
> Ricardo
> 
> 
> 
> 
> --- "William Gould, StataCorp LP" <wgould@stata.com>
> wrote:
> 
> > Daniel Koralek <dkoralek@unc.edu> writes about
> using
> > -stcox- on individual
> > data where each individual was recruited from one
> of
> > ten centers.  He is
> > concerned that which center may influence survival
> > because "different foods
> > eaten in different regions may influence
> nutrients".
> > 
> > He considers three ways of dealing with this
> > problem,
> > 
> >        . stcox ..., vce(cluster center)           
>  
> >   (1)
> > 
> >        . xi:  stcox ... i.center                  
>  
> >   (2)
> > 
> >        . stcox ..., stratify(center)              
>  
> >   (3)
> > 
> > and, of course, he could ignore center altogether
> > 
> >        . stcox ... [center completely omitted]    
>  
> >   (0)
> > 
> > As a matter of notation, let's assume the other
> > covariates in the 
> > models (the ... part) are x1 and x2.
> > 
> > My comments are as follows:
> > 
> > Re solution (0):
> > 
> >      This solution assumes center has no effect
> and
> > Daniel has already
> >      raised concerns that it does, so the solution
> > is inappropriate.
> > 
> > Re solution (1):
> > 
> >      This solution also assumes center has no
> > effect; it instead 
> >      conservatively handles the situation where
> the
> > individual patients
> >      are overly homogeneous, which is to say, not
> > independent draws.
> >      Actually, I didn't say that exactly right for
> > the Cox model, but
> >      what I said implies what what I should have
> > said, which is that
> >      selection of the failures from the risk pools
> > at each failure time 
> >      are not independent.
> > 
> >      Daniel tried solution (1) and found that the
> > standard errors changed, 
> >      but the reported coefficients did not. 
> > Exactly.  Under solution (1),
> >      because center has no effect, the
> coefficients
> > estimated the standard
> >      way are fine, although perhaps inefficient. 
> > The lack of independence,
> >      however, means standard errors usually will
> be
> > understated and
> >      -vce(cluster center)- handles that.
> > 
> > Re solution (2):
> > 
> >      This solution assumes that center does have a
> > direct effect on 
> >      survival, and it constrains the effect to be
> a
> > multiplicative 
> >      shift in the the baseline hazard function. 
> The
> > baseline hazard 
> >      function ho(t) is a function of time, such as
> > 
> >             ho(t)
> >               |             .
> >               | .         .   .
> >               |. .       .
> >               |   .    .
> >               |     . .
> >               |
> >               +-------------------  time
> > 
> >       FYI, the baseline survival function So(t) is
> > the integral of 
> >       ho(t), negated and exponentiated.  There's
> > nothing deep there; 
> >       that's just the mathematical formula for
> > calculating one one 
> >       from the other.  I switchd to hazard
> > functions, however, 
> >       because the hazard function is the natural
> > metric for the Cox model.
> >       The hazard rate for a particular individual
> in
> > the data at a particular
> >       time is just ho(t)*exp(X_i*b), where X_i are
> > the individual's covariates
> >       at time t.  That's why I said solution (2)
> > constrains each center's
> >       effect to be a multiplicative shift of
> ho(t).
> > 
> >       Concerning our use of dummy variables for
> the
> > centers, 
> >       we would like to think that we chose this
> > particular functional form
> >       because it is truly representative of how
> the
> > different 
> >       foods served in the different centers
> > influence the hazard, but 
> >       the fact is that we choose this functional
> > form because it is 
> >       convenient; the effect of each center is
> > wrapped up in just a 
> >       single coefficient.
> > 
> >       This is not a bad approach.  
> > 
> > Re solution (2.5):
> > 
> >       Alright, I admit that Daniel did not include
> a
> > solution (2.5), but 
> >       I want to add it; it will help to understand
> > solution (2), and 
> >       is often useful in and of itself.
> > 
> >       Solution (2) was 
> > 
> >        . xi:  stcox ... i.center                  
>  
> >   (2)
> > 
> >       Solution 2.5 is 
> > 
> >        . xi:  stcox ... i.center i.center*x1      
>  
> >   (2.5)
> > 
> >       In this solution, we assume that center does
> > not merely shift 
> >       the hazard function in a multiplicative way,
> > we assume that 
> >       center modifies the effect of x1.
> > 
> >       Actually, there are a lot of solution
> (2.5)'s.
> >  I could have chosen 
> >       x2 rather than x1, 
> >       
> >        . xi:  stcox ... i.center i.center*x2
> > 
> 
=== message truncated ===


Ricardo Ovaldia, MS
Statistician 
Oklahoma City, OK

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