title: Weighted profile likelihood-based confidence interval for the difference between two proportions with paired binomial data.
abstract: Inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations. Tang et al. (2010, Statistics in Medicine) discussed six methods to construct confidence intervals (henceforth, we abbreviate it as CI) for the difference between two proportions in paired binomial setting using method of variance estimates recovery. In this article, we propose weighted profile likelihood-based CIs for the difference between proportions of a paired binomial distribution. However, instead of the usual likelihood, we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 × 2 table in the spirit of Agresti and Min (2005, Statistics in Medicine). We then conduct numerical studies to compare the performances of the proposed CIs with that of Tang et al. and Agresti and Min in terms of coverage probabilities and expected lengths. Our numerical study clearly indicates that the weighted profile likelihood-based intervals and Jeffreys interval (cf. Tang et al.) are superior in terms of achieving the nominal level, and in terms of expected lengths, they are competitive. Finally, we illustrate the use of the proposed CIs with real-life examples.
authors.affiliation: Pfizer Inc., 200 Cambridge Park Drive, Cambridge, MA 02140, U.S.A.
authors.forename: Vivek
authors.initials: V
authors.lastname: Pradhan
authors.forename: Krishna K
authors.initials: KK
authors.lastname: Saha
authors.forename: Tathagata
authors.initials: T
authors.lastname: Banerjee
authors.forename: John C
authors.initials: JC
authors.lastname: Evans
mesh_terms: D002759:Adenoma, Bile Duct / Q000175:diagnosis; D016010:Binomial Distribution; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D016099:Endoscopy, Gastrointestinal / Q000379:methods; D005260:Female; D005833:Genital Neoplasms, Female / Q000473:pathology; D006801:Humans; D016013:Likelihood Functions; D009716:Numerical Analysis, Computer-Assisted; D059408:Pain Management / Q000379:methods
keywords: bivariate copula; confidence interval; paired binomial distribution; profile likelihood; variance estimate recovery