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Asymptotic distributions of kappa statistics and their differences with many raters, many rating categories and two conditions
Author(s) -
Grassano Luca,
Pagana Guido,
Daperno Marco,
Bibbona Enrico,
Gasparini Mauro
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201700016
Subject(s) - kappa , categorical variable , cohen's kappa , mathematics , statistics , statistic , reliability (semiconductor) , complement (music) , econometrics , medicine , power (physics) , physics , geometry , biochemistry , chemistry , quantum mechanics , complementation , gene , phenotype
In clinical research and in more general classification problems, a frequent concern is the reliability of a rating system. In the absence of a gold standard, agreement may be considered as an indication of reliability. When dealing with categorical data, the well‐known kappa statistic is often used to measure agreement. The aim of this paper is to obtain a theoretical result about the asymptotic distribution of the kappa statistic with multiple items, multiple raters, multiple conditions, and multiple rating categories (more than two), based on recent work. The result settles a long lasting quest for the asymptotic variance of the kappa statistic in this situation and allows for the construction of asymptotic confidence intervals. A recent application to clinical endoscopy and to the diagnosis of inflammatory bowel diseases (IBDs) is shortly presented to complement the theoretical perspective.