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# st: Re: Test for homogeneity of odds ratios with ordinal data (r x 2)?

 From "Joseph Coveney" To Subject st: Re: Test for homogeneity of odds ratios with ordinal data (r x 2)? Date Wed, 20 May 2009 22:20:34 +0900

```Mike Schmitt wrote:

I'm somewhat familiar with the Mantel-Haenszel test for homogeneity of
odds ratios for a 2 x 2 structure, however I'm currently working on a
project that is part of a randomized control trial, although the
outcome I'm looking at was not specifically targeted by the
intervention.  I want to ensure/check that the intervention did not
have an unexpected effect.  I have intervention(=1) and control(=0)
groups, an ordinal outcome measure(0 through 4), and several
dichotomous predictor variables.

For a 2 x 2, I could use:

"mhodds dep_var predict_var, by(intervention)"

However, I'm running into a wall with the ordinal dependent/outcome
measure.  I've found a few papers that speak of extending the
principles behind the MH test and another method using a proportional
odds model, however I do not possess the skill set to understand how
to implement this in Stata.  Does anyone have any pointers or possible
avenues for exploring this issue?  Thanks,

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

I'm not familiar with the literature that you're alluding to, but fitting a
proportional odds model is straightforward in Stata using the official command,
-ologit-.  Inasmuch as Mantel-Haenszel testing of homogeneity of odds ratios is
equivalent to testing the predictor-by-stratification variable interaction term
in logistic regression, I would expect that you could do an analogous test with
-ologit-, e.g.,

generate byte iXp = intervention * predictor
ologit outcome intervention predictor iXp, or
test iXp

This assumes that the dichotomous predictor variable is coded 0/1 just as you
show for the intervention variable.  You can also perform a likelihood ratio
test via the official -lrtest-, and there is a user-written command, -testomit-,
that allows a score test.

Plotting the data might be more beneficial than testing.  There is user-written
command, -distplot-, that comes in handy for ordered-categorical response data.
Syntax for it in your circumstances would be something like:

distplot outcome, over(intervention) by(predictor) [other options, such as
-midpoint-]

With these plots, you're often looking for rightward or leftward shifts of the
curves (the curves roughly parallel).  For that, it's sometimes helpful to put
in a visual reference line using the option -yline(0.5)-.  You're concerned
about heterogeneous odds ratios, and so I suggest looking whether there are
dramatic differences in the spread between control and experimental treatment
group curves between predictor groups, or even transposition of the treatment
group curves between predictor group categories.   Comparison of slopes and
shapes of the lines can give insight into model assumptions.

Joseph Coveney

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