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

 From Joseph Coveney <[email protected]> To Statalist <[email protected]> Subject Re: st: Modelling two binary outcomes that are not mutually exclusive Date Sun, 28 Nov 2004 01:31:11 +0900

```Ron�n Conroy wrote:

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?

--------------------------------------------------------------------------------

Would -biprobit- (along the lines of Mark Schaffer's suggestion), or -xtprobit-
lend any help?

As an alternative, would formally modeling as a bivariate binomial regression
using -gllamm- (two random effects, one for each outcome, � la Van
Houwelingen's bivariate approach to meta-analysis) help?

Joseph Coveney

clear
set more off
drawnorm y1 x1 x2, mean(0 0 0) ///
sd(1 1 1) corr(1 0.7 0.7 \ 0.7 1 0.7 \ 0.7 0.7 1) ///
n(200) seed(`=date("2004-11-28", "ymd")')
generate byte y0 = uniform() > 0.5 // y0, Anxiety
replace y1 = y1 > 0  // y1, Depression
compress
pwcorr
biprobit y0 y1 x1 x2
// It shows that y1 is predicted and not y0
generate int pid = _n
reshape long y, i(pid) j(dep)
xi: xtprobit y i.dep*x1 i.dep*x2, i(pid) re
// The dependent-variable-by-predictor interaction terms
// indicate that one is predicted and not the other (given the
// necessary assumptions)
exit

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