Comparing the effects of two treatments on two ordinal outcome variables

Abstract

When evaluating whether the effect of one treatment is larger than that of another the first step in the comparison is to decide what should be understood by the statement that one patient has achieved a greater effect than has another patient. When the outcome variable is quantitative, measured on a ratio scale, absolute or relative effects are the most commonly used effect measures; however, such effects are usually not meaningful for ordinal outcome variables. In order to answer the question whether one of two treatments acts more effectively on one of two outcome variables and the other treatment more efficiently on the other we shall present a method of comparing the treatment effects of patients that is based on pair-wise comparisons between patients in analogy with many non-parametrical methods. These comparisons use only the ordinal properties of the outcome variables. We shall even define a measure of the difference between the treatment effects and demonstrate how confidence intervals can be constructed.