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st: Comparing overlapping groups


From   Fred Wolfe <fwolfe@arthritis-research.org>
To   statalist@hsphsun2.harvard.edu
Subject   st: Comparing overlapping groups
Date   Tue, 2 Oct 2012 09:06:31 -0500

Dear Statalisters,

I am analyzing a medical condition (FM) that has 4 different
definitions for the same condition. A person can be in 1 or more of
four definition defined groups (FM1, FM2, FM3, FM4). There are 2442
observations.

I am interested the value of a dependent variable, phq_sss, according
to each group definition.

For the first two definitions, I get these results

. regress phq_sss i.wsp

      Source |       SS       df       MS              Number of obs =    2442
-------------+------------------------------           F(  1,  2440) =  605.51
       Model |  7621.27967     1  7621.27967           Prob > F      =  0.0000
    Residual |  30711.1417  2440  12.5865335           R-squared     =  0.1988
-------------+------------------------------           Adj R-squared =  0.1985
       Total |  38332.4214  2441  15.7035729           Root MSE      =  3.5478

------------------------------------------------------------------------------
     phq_sss |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.wsp |   6.247731   .2538992    24.61   0.000      5.74985    6.745611
       _cons |   2.728905   .0751615    36.31   0.000     2.581518    2.876292
------------------------------------------------------------------------------

. regress phq_sss i.mwsp

      Source |       SS       df       MS              Number of obs =    2442
-------------+------------------------------           F(  1,  2440) =  229.25
       Model |  3292.19831     1  3292.19831           Prob > F      =  0.0000
    Residual |  35040.2231  2440  14.3607472           R-squared     =  0.0859
-------------+------------------------------           Adj R-squared =  0.0855
       Total |  38332.4214  2441  15.7035729           Root MSE      =  3.7896

------------------------------------------------------------------------------
     phq_sss |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      1.mwsp |   10.37138   .6849863    15.14   0.000     9.028161    11.71459
       _cons |   3.144753   .0771774    40.75   0.000     2.993413    3.296093
------------------------------------------------------------------------------

There are two additions definitions that are not shown.

So the difference for group members as opposed to none groups members
in the two analyses above is:
wsp  6.2
mwsp 10.4
(there will be 2 other groups).

My question is, how do i tell if the results are statistically
different between the 4 groups, given the overlapping membership in
the groups. I have a feeling that some sort of permutation test is the
way to get such an answer. I'd appreciate suggestions.

Thanks,

Fred


Fred Wolfe
National Data Bank for Rheumatic Diseases
Wichita, Kansas
NDB Office +1 316 263 2125 Ext 0
Research Office +1 316 686 9195
fwolfe@arthritis-research.org
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