An 'unconditional-like' structure for the conditional estimator of odds ratio from 2 x 2 tables.
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.
Hanley
James A
JA
Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montreal, Quebec, Canada. James.Hanley@McGill.CA
Miettinen
Olli S
OS
D000465:Algorithms; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D016013:Likelihood Functions; D016015:Logistic Models; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D016017:Odds Ratio; D016016:Proportional Hazards Models; D012044:Regression Analysis