Date:         Wed, 19 Dec 2007 12:43:46 -0800
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: Deviance Test?
In-Reply-To:  <89a194fe-f094-4bd3-9384-f8fc52e18b3b@v4g2000hsf.googlegroups.com>
Content-Type: text/plain; charset=iso-8859-1

> > Well, yes, that would be the correct approach.  In a group
> randomized
> > trial with a non-Gaussian response, one might use the GLIMMIX
> > procedure and with CLASS, MODEL, and RANDOM statements such as
> >
> >     class group trt <covariates>;
> >     model y = trt <covariates> / s;
> >     random intercept / subject=group(trt);
> >
> > In the above code, groups are nested within treatment.  This has
> > consequence both for the appropriate denominator as well as df
> > for an F-test examining the treatment effect.
> >
>
> Thank you.
>
> Dale, I'm curious. What if you incorporated time as measured by weeks
> into the model? How would that look? Would you need a nested variable
> within an interaction term?
>
> Thanks again,
>
> Ryan
>

In a group randomized trial with groups observed at multiple time
points, subjects are always the groups.  And the groups are nested
within treatment, not within treatment by time.

The group randomized trial with multiple observation periods can
get a little difficult, especially with a non-Gaussian response.
You actually have a within-group correlation structure over time
as well as within-individual correlation structure over time to
contend with.  It is probably not unreasonable to assume that
the between-group variance is the same at times i and j.  Ignoring
for the moment within-person correlations over time, I would code
the following:

    class group trt time <covariates>;
    model y = trt|time <covariates> / s;
    random time / subject=group(trt) type=cs;  /* or type=ar(1) */

Note that I have suggested the type=cs or type=ar(1) covariance
structures because they give the same variance at all time points.
Other covariance structures could be used, but one of these two would
probably be reasonable in most situations.

Now, if the response were Gaussian and we were using the MIXED
procedure, then I would add a repeated statement which models
the within-individual covariance structure.  Code would then be
something like

    class group trt time person <covariates>;
    model y = trt|time <covariates> / s;
    random time / subject=group(trt) type=cs;       /* or type=ar(1) */
    repeated time / subject=person(group) type=cs;  /* or type=ar(1) */

Code similar to this can be written for the generalized linear
mixed models.  But there is no repeated statement in the GLIMMIX
procedure.  In the GLIMMIX procedure, we might write

    class group trt time person <covariates>;
    model y = trt|time <covariates> / s;
    random time / subject=group(trt) type=cs;       /* or type=ar(1) */
    random time / subject=person(group) type=cs residual;

You may wish to constrain the person variance estimates to 1 if you
do not want a multiplicative overdispersion parameter included in
the model.  The subject of overdispersion parameters is beyond where
I wish to go with this response.  You can look at the GLIMMIX
documentation for much more on the subject of overdispersion
parameters.

Dale


---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@NO_SPAMfhcrc.org
Ph:  (206) 667-2926
Fax: (206) 667-5977
---------------------------------------


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