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December 2021 Non-inferiority marginal symmetry model and its decomposition for ordinal square contingency tables
Mana Aizawa, Shuji Ando, Kouji Tahata, Sadao Tomizawa
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SUT J. Math. 57(2): 147-165 (December 2021). DOI: 10.55937/sut/1641859466

Abstract

The marginal homogeneity (MH) model is well-known for analyzing ordinal square contingency tables. This study proposes a non-inferiority marginal symmetry (NiMS) model, which has a different marginal symmetry structure than the MH model. In the NiMS model, the probability of an observation falling in row category $i$ or below and column category $i$ or above is equal to the probability of an observation falling in row category $i$ or above and column category $i$ or below. Additionally, two kinds of extended NiMS models are proposed. These extended NiMS models constantly hold when the NiMS model holds. However, the converse is not necessarily true. This study examines what a model should be necessary, in addition to the extended NiMS model, to satisfy the NiMS model.

Acknowledgments

The authors thank the editor and the anonymous referee for the valuable comments.

Citation

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Mana Aizawa. Shuji Ando. Kouji Tahata. Sadao Tomizawa. "Non-inferiority marginal symmetry model and its decomposition for ordinal square contingency tables." SUT J. Math. 57 (2) 147 - 165, December 2021. https://doi.org/10.55937/sut/1641859466

Information

Received: 14 April 2021; Published: December 2021
First available in Project Euclid: 21 April 2022

Digital Object Identifier: 10.55937/sut/1641859466

Subjects:
Primary: 62H17

Keywords: asymmetry , clinical study , generalized marginal symmetry , marginal homogeneity , ordered category , relationships among models

Rights: Copyright © 2021 Tokyo University of Science

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Vol.57 • No. 2 • December 2021
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