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Weighted profile likelihood‐based confidence interval for the difference between two proportions with paired binomial data
Author(s) -
Pradhan Vivek,
Saha Krishna K.,
Banerjee Tathagata,
Evans John C.
Publication year - 2014
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6130
Subject(s) - statistics , mathematics , confidence interval , negative binomial distribution , binomial (polynomial) , binomial proportion confidence interval , binomial distribution , continuity correction , coverage probability , inference , maximum likelihood , quasi likelihood , medical statistics , variance (accounting) , interval (graph theory) , beta binomial distribution , combinatorics , computer science , poisson distribution , artificial intelligence , accounting , business
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. Copyright © 2014 John Wiley & Sons, Ltd.