Application of Goodman-Kruskal's Gamma for Ordinal Data,in Comparing Several Ordered Treatments: A Different Approach

A commonly used measure of ordinal association in two-way contingency tables is Goodman and Kruskal's gamma. In a randomized clinical trial setting, the row variable may consist of increasing doses of a drug and placebo (i.e., treatments) and the column variable may be an ordinal response variable (e.g., physician's global evaluation of treatment effectiveness). Typically, patients are randomly assigned to treatments (rows) such that the row totals are fixed and the rows form a product-multinomial sample of the ordinal response variable. For the above situation, we provide the asymptotic variance of gamma using the delta method. The population version of gamma and its standard error can be estimated by their sample counterparts, enabling us to construct approximate tests and confidence intervals using the normal distribution.