Date: Wed, 1 Sep 2010 13:53:22 -0700
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: cross sectional design and difference of differences model
In-Reply-To: <0D6BED2F7A98414697EA36B4EC1E3C1601601E9BE8@URMCMS9.urmc-sh.rochester.edu>
Content-Type: text/plain; charset=us-ascii
Yes, the parameter for the interaction is exactly the effect
you wish to estimate. Your model has the following design:
Intervention/Control
Baseline/ control intervention
follow-up |------------------------|------------------------|
| bhat(baseline) + | bhat(baseline) + |
B | bhat(control) + | 0 + |
| bhat(baseline,control) | 0 |
|------------------------|------------------------|
| 0 + | 0 + |
F | bhat(control) + | 0 + |
| 0 | 0 |
|------------------------|------------------------|
In each cell, the three parameter estimates for the effects
of time (top row in each cell), intervention arm (middle row
in each cell), and the interaction of treatment arm with time
(bottom row in each cell) are shown (assuming a fixed age
effect which is the same for all cells). Now, the difference
of means between intervention and control at baseline and at
follow-up are:
Diff(B) = bhat(baseline) -
(bhat(baseline) + bhat(control) + bhat(baseline,control))
= -bhat(control) - bhat(baseline,control)
Diff(F) = 0 - bhat(control)
= - bhat(control)
and the difference of differences is
Diff(F) - Diff(B) = -bhat(control) -
(-bhat(control) - bhat(baseline,control)
= bhat(baseline,control)
So, the interaction effect is exactly the effect of interest.
Note that I am assuming that you have quite a few more observations
than the 33 which you show. The 33 observations shown have a very
limited range of response values for BMI. These appear to be the
first 33 records in a data set which has been ordered by BMI.
If these 33 records are the complete data set, then your response
cannot be assumed to be normally distributed. The point estimate
of the intervention effect (the difference of differences) is
OK regardless of the distribution. However, inferences about
the intervention effect could be markedly wrong.
Dale
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@NO_SPAMfhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------
--- On Wed, 9/1/10, Thevenet-Morrison, Kelly <Kelly_Thevenet-morrison@URMC.ROCHESTER.EDU> wrote:
> From: Thevenet-Morrison, Kelly <Kelly_Thevenet-morrison@URMC.ROCHESTER.EDU>
> Subject: cross sectional design and difference of differences model
> To: SAS-L@LISTSERV.UGA.EDU
> Date: Wednesday, September 1, 2010, 7:08 AM
> I am trying to set up the data for
> the mixed modeling to look at differences of differences
> model where I am interested in the difference of the
> intervention and control between baseline and follow-up
> measures. We are using a cross-sectional design with
> different people for baseline and follow-up, so subtracting
> baseline from follow-up doesn't make sense since there are
> different people.
>
> My data looks like this:
> Study_ID baseline_followup Intervention_control BMI age
> 001 B intervention 16 .
> 002 B intervention 17 50
> 003 F control 18 27
> 004 F intervention 18 42
> 005 F control 18 .
> 006 F intervention 18 45
> 007 F control 18 55
> 008 B control 18 38
> 009 B control 18 28
> 010 B intervention 18 49
> 011 F intervention 18 .
> 012 B control 19 51
> 013 B control 19 37
> 014 B intervention 19 48
> 015 B intervention 19 29
> 016 F intervention 19 28
> 017 B intervention 19 52
> 018 B control 19 59
> 019 B intervention 19 48
> 020 B control 19 50
> 021 B intervention 19 38
> 022 B intervention 19 52
> 023 B control 19 .
> 024 F intervention 19 46
> 025 F intervention 19 53
> 026 B control 19 45
> 027 F intervention 19 55
> 028 B intervention 19 57
> 029 B intervention 19 50
> 030 B control 19 30
> 031 B intervention 19 49
> 032 B control 19 40
> 033 B control 19 44
>
>
> Could I set up baseline_followup and intervention_control
> as my class variables and do the following:
>
> Proc mixed data=mydata;
> Class baseline_followup intervention_control;
> Model bmi=baseline_followup intervention_control
> baseline_followup*intervention_control age;
> Run;
>
> Would this give me the differences in baseline and
> follow-up and intervention and control for BMI test?
>
> Kelly
>
> Kelly Thevenet-Morrison
> e-mail: kelly_thevenet-morrison@urmc.rochester.edu
>
