title: Unconditional efficient one-sided confidence limits for the odds ratio based on conditional likelihood.
abstract: We compare various one-sided confidence limits for the odds ratio in a 2 x 2 table. The first group of limits relies on first-order asymptotic approximations and includes limits based on the (signed) likelihood ratio, score and Wald statistics. The second group of limits is based on the conditional tilted hypergeometric distribution, with and without mid-P correction. All these limits have poor unconditional coverage properties and so we apply the general transformation of Buehler (J. Am. Statist. Assoc. 1957; 52:482-493) to obtain limits which are unconditionally exact. The performance of these competing exact limits is assessed across a range of sample sizes and parameter values by looking at their mean size. The results indicate that Buehler limits generated from the conditional likelihood have the best performance, with a slight preference for the mid-P version. This confidence limit has not been proposed before and is recommended for general use, especially when the underlying probabilities are not extreme.
authors: Melbourne Business School, Carlton 3053, Australia. c.lloyd@mbs.edu
authors: Chris J
authors: CJ
authors: Lloyd
authors: Max V
authors: MV
authors: Moldovan
mesh_terms: D000818:Animals; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D004195:Disease Models, Animal; D016013:Likelihood Functions; D051379:Mice; D009374:Neoplasms, Experimental / Q000139:chemically induced; D016017:Odds Ratio; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D018401:Sample Size; D012906:Smoke / Q000009:adverse effects; D014026:Nicotiana / Q000009:adverse effects
chemical_list: D012906:Smoke