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Re: st: Need to Determine an Intervention Effect using xtmixed


From   Clyde B Schechter <clyde.schechter@einstein.yu.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Need to Determine an Intervention Effect using xtmixed
Date   Wed, 5 Sep 2012 14:50:39 +0000

Elizabeth Prezio wrote, in part:


I am using xtmixed to evaluate panel data. There are two groups. I have
repeated measures for my outcome of interest (hemoglobin A1c at baseline,
3,6,9, and 12 months). I can get adjusted means for HbA1c using margins, but
I am at a loss to calculate an "intervention effect". I need a between group
comparison. 


. xtmixed test i.patgrp##i.time duration blmeds medchange hba1_bl || id:

...

I need some sort of "intervention effect" comparing the adjusted HbA1c
(test) values over  12 months between the intervention and control groups. I
need 95% CI and a P-value.

####

Well, your -xtmixed- model doesn't specify any single intervention effect.  Because you have treated time as a nominal variable, there is a separate intervention effect at each time period.  These effects are represented by the coefficients of 1.patgrp#3.time, 1.patgrp#6.time, 1.patgrp#9.time, and 1.patgrp#`12.time.  [I'm assuming that patgrp is a 0/1 variable.  If there are several groups or it is differently coded, then the relevant coefficients will change accordingly.] You will find 95% CI's and p-values for these in the -xtmixed- output table. [Well, actually, one of these coefficients will not be there because it will refer to the reference category of time.]

If you want to test the hypothesis that at least one of these effects is not zero, then you can, after -xtmixed- run:

test 1.patgrp#3.time 1.patgrp#6.time 1.patgrp#9.time 1.patgrp#12.time

and you will get a Wald F-test of that joint null hypothesis.  But there will be no single summary statistic that is an effect size.

There can't be--because what if the effect is different at different times.  That is precisely what your model specifies: a separate effect at each time.  If theory suggests that there should be a single effect that applies uniformly across time, then you can test that theory by testing for equality of these coefficients.  And if you are satisfied that there is a single effect across time, you can re-do the modeling leaving out the time variables and the patgrp#time interactions, and just look at the effect of patgrp.

But you might actually be thinking of something different.  Perhaps you expect that people will follow a trajectory characterized by a slope of test over time.  And perhaps you expect that slope to be different in the two groups.  In that case you need to estimate a different model:

xtmixed test i.patgrp##c.time duration blmeds medchange hba1_bl || id:

Notice that in this case, time is treated as a "continuous" variable.  The output will include a 1.patgrp#c.time coefficient that then represents the unique effect of the intervention on slope of test over time, along with 95% CI and p-value in the regression table.

More subtle models are also possible: you may imagine that the treatment alters the slope for part of the observation period, but then things change (e.g. the intervention's effect dissipates).  In that case you would want to model time as a linear spline with "early" and "late" periods, and estimate corresponding "early" and "late" treatment effects.  Or perhaps things are curvilnear: think quadratic terms, or fractional polynomials or cubic splines.  It is also possible that when you think this through, you will find that it is better to include the baseline A1c as a separate observation with time = 0 than to include it as a covariate in the middle.  Anyway, the possibilities are manifold.  You might also find it convenient to center the covariates before entering them in the model.

The point is that the model you estimated, does not represent any single intervention effect.  You need to clarify exactly what kind of treatment effect(s) you are looking for and then specify your model in a way that will reflect and estimate it.  That's a matter of understanding the science behind your intervention and translating it into variable representations.

Best of luck.  Hope this helps.

Clyde Schechter
Dept. of Family & Social Medicine
Albert Einstein College of Medicine
Bronx, NY, USA



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