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An ‘Unconditional‐like’ Structure for the Conditional Estimator of Odds Ratio from 2 × 2 Tables
Author(s) -
Hanley James A.,
Miettinen Olli S.
Publication year - 2006
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200510167
Subject(s) - mathematics , estimator , statistics , odds ratio , maximum likelihood , population , odds , econometrics , combinatorics , demography , sociology , logistic regression
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. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)