Inference for Comparing Two Treatments Using Kernel Density Estimation

In randomized clinical trials, nonparametric approaches are considered when assumptions of a parametric approach are not reasonable. Nonparametric approaches have typically concentrated on hypothesis testing and, unlike parametric approaches, have not been amenable to providing measures of treatment efficacy. If X and Y denote the random variables representing the responses on two treatments A and B, respectively, P(Y>X) is an intuitive measure of efficacy. We consider point and interval estimation of P(Y>X) using kernel density estimation and bootstrapping. We illustrate this methodology on a data set, where comparison is made with point and interval estimates obtained by inverting the nonparametric Wilcoxon-Mann-Whitney test.