The statistical tests that are commonly used for detecting mean or median treatment effects suffer from low power when the two distribution functions differ only in the upper (or lower) tail, as in the assessment of the Total Sharp Score (TSS) under different treatments for rheumatoid arthritis. In this article, we propose a more powerful test that detects treatment effects through the expected shortfalls. We show how the expected shortfall can be adjusted for covariates, and demonstrate that the proposed test can achieve a substantial sample size reduction over the conventional tests on the mean effects.
"Detection of treatment effects by covariate-adjusted expected shortfall." Ann. Appl. Stat. 4 (4) 2114 - 2125, December 2010. https://doi.org/10.1214/10-AOAS347