Summation of absolute value test for multiple outcome comparison with moderate effect

In biomedical research, in order to evaluate the effect of a drug, investigators often need to compare the differences between one treatment group and another one by using multiple outcomes. The rank-sum tests can handle the case where the outcome differences between two groups are in the same direction. If they are not, MAX can handle it and is very useful when one/some of the differences is/are relatively larger than the others. When the individual outcome difference between two groups is moderate, a new method, summation of the absolute value of rank-based test for each outcome, is proposed in this work. Power comparison with the existing methods based on simulation studies and a real example show that the proposed test is a robust test, and works well when the difference for each outcome is moderate. The authors also derive some theoretical results for comparing the power between MAX and the the proposed method.