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 <[email protected]> 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" <[email protected]>
> wrote:
>
> > Daniel Koralek <[email protected]> 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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