Success Probability Estimation with Applications to Clinical Trials

CHAPTER 9

GENERAL NONPARAMETRIC SP ESTIMATION - WITH APPLICATIONS TO THE WILCOXON TEST

In this Chapter the techniques for estimating the SP through the adoption of a completely nonparametric approach are first developed. They are based on the plug-in of the empirical distribution functions, which are nonparametric estimators of the unknown distributions of the variables of interest. Then, lower bounds for the SP can be obtained thanks to bootstrap techniques.

Applications of SP estimation are provided for one of the most widely used two-sample nonparametric tests, viz. the two-sample Wilcoxon rank-sum test. Moreover, also semi-parametric SP estimation techniques, based on the asymptotic normality of the test statistic, are shown for this test. Applications to RP estimation and testing and to conservative sample size estimation are given, together with numerical examples. It is worth noting that the nonparametric plug-in and bootstrap approach for estimating the SP can be easily applied to other nonparametric tests.

9.1 The nonparametric model

The general model of the nonparametric framework is, regarding the first part of its definition, analogous to that of the parametric one introduced in Chapter 5. F₁ and F₂ represent the generic distributions of the variables of interest in the new treatment and in the control populations. The couple (F₁, F₂) belongs to , a family of couples ...