Success Probability Estimation with Applications to Clinical Trials

CHAPTER 5

GENERAL PARAMETRIC SP ESTIMATION

In this Chapter, SP estimation is extended to a general parametric model. Firstly, this model is presented, which considers families of distributions based on a single noncentrality parameter. Then, it is shown that the power function of the test depends on the noncentrality parameter, whose estimation is the basis for performing SP estimation. Consequently, RP estimation and RP-testing are presented in the general context of the model, as well as conservative sample size estimation. Finally, some examples of applications are given, introducing those more related to clinical trials that will be extensively illustrated in the following Chapters.

5.1 The parametric model

The parametric model for comparing some features of two distributions, i.e. for testing differences among the latter, is introduced here and a general theoretical framework is adopted.

Let us define F₁ as the generic distribution of the variable of interest of the population under the new treatment and F₂ as that of the control population. The couple (F₁, F₂) belongs to a family of couples of distributions over a space S ⊂ R × R. The latter family is divided into two parts: ₀, containing the couples representing an ineffective new treatment, and its complement \₀.

Being _t