Section 49
Chapter 48,222

An 'unconditional-like' structure for the conditional estimator of odds ratio from 2 x 2 tables

Hanley, J.A.; Miettinen, O.S.

Biometrical Journal. Biometrische Zeitschrift 48(1): 23-34


ISSN/ISBN: 0323-3847
PMID: 16544810
DOI: 10.1002/bimj.200510167
Accession: 048221373

In the estimation of the odds ratio (OR), the conditional maximum-likelihood estimate (cMLE) is preferred to the more readily computed unconditional one (uMLE). However, the exact cMLE does not have a closed form to help divine it from the uMLE or to understand in what circumstances the difference between the two is appreciable. Here, the cMLE is shown to have the same 'ratio of cross-products' structure as its unconditional counterpart, but with two of the cell frequencies augmented, so as to shrink the unconditional estimator towards unity. The augmentation involves a factor, similar to the finite population correction, derived from the minimum of the marginal totals.

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