In clinical research it is very common to compare two treatments on the basis of an efficacy variable. More specifically, if X and Y denote the responses of patients on the two treatments A and B, respectively, the quantity P(Y>X) (which can be called the probabilistic index for the Effect Size), is of interest in clinical statistics. The objective of this study is to derive an efficacy measure that would compare two treatments more informatively and objectively compared to the earlier approaches. Kernel density estimation is a useful non-parametric method that has not been well utilized as an applied statistical tool, mainly due to its computational complexity. The current study shows that this method is robust even under correlation structures that arise during the computation of all possible differences. The kernel methods can be applied to the estimation of the ROC (Receiver Operating Characteristic) curve as well as to the implementation of nonparametric regression of ROC. The area under the ROC curve (AUC), which is exactly equal to the quantity P(Y>X), is also explored in this dissertation. The methodology used for this study is easy to generalize to other areas of application.