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
________________________________________
From: [email protected] [[email protected]] On Behalf Of Clyde Schechter [[email protected]]
Sent: Saturday, November 14, 2009 4:01 PM
To: [email protected]
Subject: st: baseline adjustment in mixed models
I hesitate to disagree with Martin Buis, but perhaps I have interpreted
your question differently.
I suppose you have an outcome y observed on each participant at each time,
a variable group (coded 0 for control, 1 for intervention), a participant
identifier variable, id, and a variable, time, which might be actual times
of observation, or just a sequence 0 through N, whatever). If your time
variable is not coded as baseline = 0, it will make life simpler if you
transform it so that is the case.w
In the example below I will assume that you plan to model y as a linear
function of time, because that is the simplest from a coding perspective.
If you need a more complicated representation with dummies for different
times, or a spline, etc., you can modify accordingly. Again, life is
simplest if the baseline measurement corresponds to time = 0 (or the
omitted time category if dummies are used) in your coding.
If you want to test whether the intervention has modified the response
trajectory over time, the key is to test for the group X time interaction.
gen groupXtime = group * time
xtmixed y group time groupXtime || id:
gives you a random intercept model. The coefficient of group represents
the mean difference of y between intervention and control groups when time
= 0. That is, this model does incorporate, and in a useful sense,
"adjusts for" the baseline difference between the groups. The coefficient
of groupXtime represents the difference in the slopes of the y-time lines
between groups.
Now, you might want to make this more sophisticated if you anticipate that
individuals, within each group, might have different individual y-time
slopes, in which case a random slopes model might be better:
xtmixed y group time groupXtime || id: time
Again, baseline differences in y are satisfactorily accounted for in this
model, and are even directly estimated by the coefficient of group.
Again, the key inference is based on the coefficient of the interaction
term.
With either of these models you should get good, serviceable estimates of
the group difference in average y-time slope. Note that this approach is
different from adjusting for baseline response by excluding the time 0
observations from the model and including time 0 response as a covariate
in an ANCOVA like analysis.
Hope this helps.
Clyde Schechter
Associate Professor of Family & Social Medicine
Albert Einstein College of Medicine, Bronx, NY, USA
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