Re: compare 2 odds ratios

Marc Schwartz wrote:
[...] I
spent some time doing a Google and Medline search, looking for pointers
to studies where a gold standard was being compared to two alternative
tests, where the primary efficacy measure is dichotomous.

What appears to be "typical" in this situation, is the use of Cochran's
Q Test, which is a generalization of the McNemar test to >2 strata. This
test provides insight into whether or not there are differences across
the multiple strata relative to marginal homogeneity.

Cochran's Q Test can then be followed by multiple pairwise comparisons
performed with the standard McNemar test, giving due consideration to
multiple comparisons correction approaches. Thus, in this case,
performing GS vs T1, GS vs T2 and T1 vs T2.
[...]

If I understand the data layout correctly -- n Subjects x k+1 Tests,
scored 0/1, with one of the Tests being "correct" -- Cochran's test
misses the point. The null hypothesis it tests is that the k+1 Tests
have the same discovery rate, which is almost irrelevant. More to the
point would be to subtract each subject's "correct" Test score from
his k other Test scores and then do a Cochran test on the squared
values in the resulting n x k matrix. This would test the null hypo-
thesis that the k Tests have the same error rate. Pairwise comparisons
would be McNemar tests on the k(k-1)/2 pairs, with some correction for
multiplicity.

.

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