[19220] in s-news-athena
Re[2]: [S] binary responses
daemon@ATHENA.MIT.EDU (jlongmate@smtplink.coh.org)
Tue Sep 14 14:10:00 1999
From: jlongmate@smtplink.coh.org
Message-Id: <9909149373.AA937324992@smtplink.coh.org>
Date: Tue, 14 Sep 1999 11:03:43 -0500
To: <ripley@stats.ox.ac.uk>, <s-news@wubios.wustl.edu>
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On 11 Sep 1999, Prof Brian D Ripley wrote:
> However, I don't think gee is really about repeated measures at all. It
> is about correlated outcomes, in this case Bernoulli, and indeed with
> specified correlation structure. Correlations are not the most natural
> way to handle dependence in binary variables. Repeated measures designs
> are to my mind most naturally handled by random effects, that is GLMMs
> here. With other distributions (normal, binomial, Poisson) the natural
> models give marginal distributions that are not (normal, binomial,
> Poisson), and it is the marginal distributions that gee models. This is
> not a problem with Bernoulli, though, as mixtures of Bernoulli are
> Bernoulli.
But if we indulge in any model simplification, we can easily be left with
the binomial, rather than Bernoulli case -- see below.
> There are simpler approaches to repeated measures. If the interest is in
> the two treatments, I would start by fitting a logistic regression
> with a per-subject factor, and look for differences in the response
> patterns by group. Something like
>
> glm(success ~ factor(subject) + time*treatment, family=binomial, ...)
>
> assumming treatment and time (the three times of response) are factors.
> and see if the treatment x time and treatment terms are (practically)
> significant.
>
> This is just like in the normal case using a fixed-effect randomized
> block analysis for treatment differences, even though the model is of
> random effects for blocks.
>
> [I would need a lot more details on the experiment before actually doing
> things like this, though, and suggest you talk to the local statistical
> consultant.]
I think one more caveat is in order, namely that the latitude suggested by
"something like" does not include dropping time from the model, at least
not without some accomodation of overdispersion.
If time had no effect, a more apt analogy might be to randomized blocks with
within-cell replication. In the normal case, one would ordinarily use
treatment-by-block interaction to estimate error, but glm() would calculate
standard errors from the variance function, somewhat analogous to using
within-cell error.
The device of including a subject factor within glm() needs to be used with
care, or glm() may very well present the user with underestimated standard
errors, while gee() would apply the sandwich variance estimator, which is
one reasonable way of accomodating overdispersion. Of course it is not too
difficult to inflate the standard errors from glm (e.g. Finney's correction
might do), but it is up to the user to do so.
I hope I'm not too far off subject in pointing out difficulties with something
that wasn't actually suggested, but this seems a bit of a slippery slope, and I
think gee has some merits here.
Jeffrey A. Longmate, Ph.D. Phone: 626-359-8111 ext.2478
Department of Biostatistics Fax: 626-301-8802
City of Hope National Medical Center E-mail: jlongmat@coh.org
and Beckman Research Institute
1500 East Duarte Road
Duarte CA, USA 91010-3000
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