Analysis of Ordered Categorical Data Using the Sas® System

In this talk we describe a method for combining a measure of association from several 2xC contingency tables. The columns in the 2xC tables are assumed to be ordered and the method uses the weighted least squares methodology of Grizzle, Starmer and Koch (1969). The method uses a transformation of the gamma statistic, a statistic proposed for the analysis of ordered contingency tables by Goodman. The procedure gives an estimate of the overall gamma statistic and a test for association. The CATMOD procedure of SAS can be used to calculate the estimate and the test statistic. In this talk we describe an SAS macro which integrates the results of this method into the usual output from the FREQ procedure. An example from the health sciences is presented as an illustration. INTRODUCTION In this paper we will present one method for describing the relationship between two ordered categorical variables after controlling for a third categorical variable. For example, it is often desirable to describe the relationship between disease and exposure after controlling for a confounding variable. For a single level of the confounding variable the disease-exposure table might look like this: Exposure Disease Low High Absent nIl .. . n1j ... n1c Present n21 .. . n2j ... n2c The main objective of this paper is to show how statistics derived from Goodman and Kruskal's (1954) gamma may be used to describe the relationship between disease and exposure after controlling for a confounding variable. The methods presented here can be used with any rxc tables where the rows and columns can be ordered but we are unable to assign scores to the levels of the row and column variables. This presentation will concentrate on the situation where several 2xC tables are analyzed. We will use the notation of Brown and Benedetti (1977) in the following discussion. Let the number of individuals in "agreement" with the (i,j) cell be Ai· = L L nkl + L L nkl J . I. k>i l>j k<l <J and let the number who Hdisagree be 957 2 c Then P = I: I: n· .A .. is equal to twice the number of i=l i=l IJ IJ 2 C concordant pairs and Q = I: I: n .. D .. is equal to twice i=l j=t IJ IJ the number of discordant pairs. In the population let ne be the proportion of randomly selected concordant pairs and let nn be the proportion of discordant pairs. The population version of gamma is The sample version of gamma