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Statistical Methods for Ordered Categorical Data Based on a Constrained Odds Model
Author(s) -
Dark Roberta,
Bolland Kim,
Whitehead John
Publication year - 2003
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.200390025
Subject(s) - odds , categorical variable , statistics , odds ratio , sample size determination , mathematics , econometrics , statistical model , statistical hypothesis testing , computer science , logistic regression
The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann‐Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.