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RE: st: trend in ORs across ordered levels of a 3rd variable


From   "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: trend in ORs across ordered levels of a 3rd variable
Date   Tue, 22 Apr 2008 08:41:53 -0700

Sometimes it helps in the interpretation if we look at the terms of the
logistic regression under the various conditions.
Suppose we have
logit death consec sex sex*consec
where sex is a 0-1 variable.
Then when sex is 0, we have the model
Logit(death)=A+B1*consec
When sex is 1 we have the model
Logit(death)=A+B1'*consec+B2+B3*consec=A+B2+(B1'+B3)*consec
So adding sex to the model can change the intercept and the slope.  If
we changing the intercept (without the interaction, i.e., B3=0)
corresponds to confounding.  If B3 is not equal to 0, we have effect
modification.


Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Visintainer,
Paul
Sent: Tuesday, April 22, 2008 7:02 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: trend in ORs across ordered levels of a 3rd variable

Thanks Maarten, Peter, and Berthold.  I arrived at a similar
conclusion--addressing the problem through logistic regression.  But,
I'm interested in Maarten's and Berthold's use of -suest-, which, from
what I gather, is the Chow test (or something like it), right?

Maarten, your model tested the interaction term in the logit.  Am I
right to assume that, in this situation, the Chow test and the logit
test of the interaction term are accomplishing similar goals?

Thanks,

-p

______________________________________
Paul F. Visintainer, PhD
Department of Epidemiology and Biostatistics
School of Public Health
New York Medical College
PH: (914) 594-4804
FX: (914) 594-4853
 
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: Tuesday, April 22, 2008 8:23 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: trend in ORs across ordered levels of a 3rd variable

--- Visintainer, Paul asked:
> What I wanted to know is whether we can detect a linear pattern of
> the ORs over levels of the confounder (which, to me, looks like a
> specific type of interaction)

--- Peter A. Lachenbruch answered:
> This sounds like a task for logistic regression using the confounder
> and the risk factor.  If you want to see if there's effect
> modification, use the product of the risk factor and confounder.  You
> may want to categorize these variables.

--- "Berthold Hoppe" responded:
> The problem seems to be similiar to one I am actually faced with.
> Have you tried an analyses like this:
> 
> logit death consc if sex==0
> est store A
> logit death consc if sex==1
> est store B
> suest A B
> test [A]consc=[B]consc

There is no need to use -suest-, this is just an interaction term:

*----------- begin example -------------------
sysuse nlsw88, clear
gen byte grade3 = cond(grade <  12, 1, ///
                  cond(grade == 12, 2, 3)) ///
                  if grade < .

gen southXgrade3 = south*grade3
logit marr south grade3 southXgrade3

logit marr grade3 if south == 1
est store A
logit marr grade3 if south == 0
est store B

suest A B
test [A]grade3=[B]grade3
*---------------- end example ----------------
(For more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )

However, the propper interpretation of these results is a very very
tricky issue regardless of whether you estimate this using an
interaction term or -suest- and you will want to take a good look at: 
http://www.stata-journal.com/article.html?article=st0063

There is also a second problem with this approach which is among others
discussed in this post:
http://www.stata.com/statalist/archive/2008-02/msg00892.html. 

Hope this helps,
Maarten


-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands



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