# Re: st: Modelling two binary outcomes that are not mutually exclusive

 From Mark Schaffer To statalist@hsphsun2.harvard.edu, Ronán Conroy Subject Re: st: Modelling two binary outcomes that are not mutually exclusive Date Sat, 27 Nov 2004 14:28:42 +0000 (GMT)

```Ronan,

Quoting Ronán Conroy <rconroy@rcsi.ie>:

> I have two binary outcomes, measured in a patient population (anxiety
> and depression). For various reasons, I suspect that a number of patient
> characteristics predict depression but not anxiety.
>
> If the two diagnoses were mutually exclusive, all would be well. I could
> use multinomial logistic regression and compare the coefficients.
> However, there is about a 20% overlap. Is this a Known Problem? I could
> model the overlap category as a third outcome, and show that the
> coefficients were similar to those for depression alone and different to
> those for anxiety alone, but this is slicing the sample a little thin -
> there are just 8 people with both disorders. (This approach actually
> works, sort of, given the small numbers, so I'm on the right track from
> the theory point of view.)
>
> Any suggestions out there?

Just to see if I understand the problem correctly, what's the difference
between your problem and seemingly-unrelated regression (sureg)?  That is,
if your outcomes were continuous instead of binary, would sureg be an
appropriate framework?

Say you have two dependent variables, anxiety and depression, and their
continuous ("degree of anxiety" or somesuch).  You have 3 covariates, x1, x2
and z1.  x1-x2 predict depression, x1-x2 & z1 predict anxiety.  You would
estimate

sureg (depression x1 x2) (anxiety x1 x2 z1)

and you could test equality of coeffs across equations and so forth.

If the question makes sense, then I suppose you're looking for something
like sureg for logistic.  Maybe suest after logistic estimation would allow
you to do what you want?

Of course, the question might not make sense!

Cheers,
Mark

>
> --
>
> Ronan M Conroy (rconroy@rcsi.ie)
> Senior Lecturer in Biostatistics
> Royal College of Surgeons
> Dublin 2, Ireland
> +353 1 402 2431 (fax 2764)
> --------------------
> Just say no to drug reps
> http://www.nofreelunch.org/
>
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>

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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