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st: RE: baseline adjustment in mixed models


From   Clyde Schechter <clyde.schechter@einstein.yu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: RE: baseline adjustment in mixed models
Date   Mon, 16 Nov 2009 09:48:56 -0800

Yes, in general.  One could concoct a data generating process in which the
baseline value y0 exerted some outsize influence over all subsequent
values (e.g., repeated measures in which the subject was fed back his/her
response at the baseline measurement shortly prior to each subsequent one
and asked to try to achieve consistency with that) that would necessitate
inclusion of y0 as a covariate as well.  But I can't think of any examples
that aren't really artificial. So, unless there is something about what
you are studying that specifically suggests y0 is needed as a covariate,
the standard growth model represented just by

xtmixed y group time groupXtime || id:

(or the corresponding random-slopes version) should do the trick. For most
situations it adequately accounts for any baseline group difference.

Again, as coded this model assumes that the y-time relationship is linear.
 If that is not the case, time needs to be transformed or recoded as
dummies or splines, etc., accordingly.  And again, since the coefficient
of group represents the mean group difference conditional on the other
model variables all being zero, life is simplest for this purpose if time
is coded so that it (or, more generally, all variables representing it) is
zero at baseline.

I've never really thought about using random slopes as a way of optimally
regressing extreme values to the mean.  It seems to me that the
distinction between a random intercept and random slopes model depends on
what the science says about the evolution of y over time.  If it is
credible that a single growth rate (coefficient of time) applies within
each group and that individual deviations from that reflect either
baseline differences being carried forward or simple random errors (e.g.
measurement error), then the random intercept model is a complete
specification.  If, however, it is more reasonable to suppose that, within
each group, subjects may differ not just in their baseline values but also
in the rate at which y varies over time, then a random slopes model is a
better specification.  If the science is not clear, one could test this
empirically by seeing whether the random slopes model turns up appreciable
variance for the slope(s) or not.

I don't think I understand your question regarding a model of choice with
respect to regression to the mean, so I won't say any more about it here.

Clyde Schechter



> Date: Sun, 15 Nov 2009 10:42:58 -0500
> From: "Visintainer PhD, Paul" <Paul.Visintainer@baystatehealth.org>
> Subject: st: RE: baseline adjustment in mixed models
>
> Clyde, thanks for the very clear explanation.  You're getting to the root
> of my question. So, if I understand you correctly, the following model is
> unnecessary:
>
> xtmixed y y0 group time groupXtime || id:
>
> or the random slope equivalent, because the group variable accounts for
> differences at Y0.  Two related questions:
>
> 1) You mentioned that coding baseline as Y0 makes life simpler.  Suppose
> time is coded as baseline plus time1 through time4.  Is there any utility
> to the model:
>
> xtmixed y baseline group time groupXtime || id: , where the time variable
> does not include baseline Y0.
>
> 2)  Controlling for baseline attempts to account for group differences at
> the start of the trial, and also for control for those observations with
> extreme values (i.e., regression to the mean).  Am I correct in assuming
> that the random coefficient model is the model of choice for correcting
> regression to the mean? My logic (or illogic) here is that the more
> extreme the baseline values, the greater the effect of regression to the
> mean (i.e., an individual's slope is a composite of the group assignment
> plus the effect of regression to the mean depending on his initial value).
>
> Thanks, this has been really helpful.
>
> - -Paul


Clyde Schechter, MA MD
Associate Professor of Family & Social Medicine

Please note new e-mail address: clyde.schechter@einstein.yu.edu


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