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The generalization of the odds ratio, risk ratio and risk difference to r × k tables
Author(s) -
Edwardes Michael D. deB.,
Baltzan Marc
Publication year - 2000
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 - 10.1002/1097-0258(20000730)19:14<1901::aid-sim514>3.0.co;2-v
Subject(s) - odds ratio , confidence interval , statistics , pooling , generalization , statistic , mathematics , relative risk , standard error , diagnostic odds ratio , odds , absolute risk reduction , type i and type ii errors , econometrics , computer science , logistic regression , artificial intelligence , mathematical analysis
A Correction has been published for this article in Statisitcs in Medicine 2000; 19(21): 3017. Familiar measures of association for 2 × 2 tables are the odds ratio, the risk ratio and the risk difference. Analagous measures of outcome–exposure association are desirable when there are several degrees of severity of both exposure and disease outcome. One such measure ( α ), which we label the general odds ratio (OR G ), was proposed by Agresti. Convenient methods are given for calculation of both standard error and 95 per cent confidence intervals for OR G . Other approaches to generalizing the odds ratio entail fitting statistical models which might not fit the data, and cannot handle some zero frequencies. We propose a generalization of the risk ratio (RR G ) following the statistical approaches of Agresti, Goodman and Kruskal. A method of calculating the standard error and 95 per cent confidence interval for RR G is provided. A known statistic, Somers' d , fulfils the characteristics necessary for a generalized risk difference (RD G ). These measures have straightforward interpretations, are easily computed, are at least as precise as other methods and do not require fitting statistical models to the data. We also examine the pooling of such measures as in, for example, meta‐analysis. Copyright © 2000 John Wiley & Sons, Ltd.