Testing equality of generalized treatment effects

Recently, the concept of generalized treatment effect, defined as P(X > Y) where X and Y denote continuous outcome variables for treatment arm and control arm, respectively, has been proposed as an appropriate measure of treatment effect in clinical trials with parallel design. Compared to the mean difference, the generalized treatment effect has many advantages; for example, it is a scaleless measure and it does not change under monotonic transformations. This article investigates the problem of testing equality of generalized treatment effects among several clinical trials. The proposed approach follows the same vein as the generalized variable method for testing equality of several log-normal means proposed by Li (2009). Numerical study demonstrates that the proposed test has excellent type I error control for clinical trials with small to medium sample sizes. Robustness study shows that the proposed method performs reasonably for categorical data.