Likelihood Ratio Tests With Three-Way Tables

• 成果类型: Article
• 署名作者: Cheng, Philip E.; Liou, Michelle; Aston, John A. D.
• 署名单位: Academia Sinica - Taiwan; University of Warwick
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09061
• 发表日期: 2010
• 页码: 740-749
• 关键词: common relative risk; contingency-tables; odds ratio; partial association; maximum-likelihood; binary response; estimators; models; combination; homogeneity

摘要

Likelihood ratio (LR) tests for association and for interaction are examined for three-way contingency tables, particularly the widely used 2 x 2 x K table. Mutual information identities are used to characterize the information decomposition and the logical relationship between the omnibus LR test for conditional independence across K strata and its two independent components. LR tests for interaction and for uniform association. The latter two tests are logically connected to formulating a natural two-step test for conditional independence. The proposed two-step test with reduced nominal levels is suggested instead of the Breslow-Day test and the Cochran-Mantel-Haenszel test. This yields efficient interval estimation for both the interaction parameter and the common odds ratio compared with using the Mantel-Haenszel estimate. This allows the development of power analysis for testing general hypotheses of varied interactions, using an invariant Pythagorean law of relative entropy.