The generalization of the odds ratio, risk ratio and risk difference to r x k tables

Familiar measures of association for 2 x 2 tables are the odds ratio, the r isk ratio and the risk difference. Analagous measures of outcome-exposure a ssociation are desirable when there are several degrees of severity of both exposure and disease outcome. One such measure (alpha), which we label the general odds ratio (ORG), was proposed by Agresti. Convenient methods are given for calculation of both standard error and 95 per cent confidence int ervals for ORG. Other approaches to generalizing the odds ratio entail fitt ing statistical models which might not fit the data, and cannot handle some zero frequencies. We propose a generalization of the risk ratio (RRG) foll owing the statistical approaches of Agresti, Goodman and Kruskal. A method of calculating the standard error and 95 per cent confidence interval for R RG is provided. A known statistic, Somers' d, fulfils the characteristics n ecessary for a generalized risk difference (RDG). These measures have strai ghtforward interpretations, are easily computed, are at least as precise as other methods and do not require fitting statistical models to the data. W e also examine the pooling of such measures as in, for example, metaanalysi s. Copyright (C) 2000 John Wiley & Sons, Ltd.