Success Probability Estimation with Applications to Clinical Trials

PART II

SUCCESS PROBABILITY ESTIMATION FOR SOME WIDELY USED STATISTICAL TESTS

In the second part of the book the techniques for SP estimation are studied in depth. Applications to both RP estimation, as in Chapter 2, and to CSSE, as in Chapters 3 and 4 are provided. The language adopted is more formal (in the mathematical-statistical sense) than that of Part I.

In Chapter 5 a general parametric setting for the distribution of the test statistic, which is based on two independent samples from different distributions, is considered. A general technique for SP estimation is provided. Then, RP estimation, together with RP-testing, and CSSE are derived for a wide class of parametric tests.

In the remaining Chapters 6-9 some statistical tests for comparing the outcomes of two groups, as if the two-arm parallel design were adopted, are taken into account. For these tests RP estimation and CSSE are studied in depth, illustrated and exemplified.

Following the SP estimation technique revealed in Chapter 5, some parametric situations are studied in Chapters 6-8. In Chapter 6 the tests to compare two means with unknown variances (both with equal or unequal variances) are considered, which refer to the Student’s t distribution. Then, the test to compare two proportions and the one to compare two survival rates over time (i.e. two survival curves) are discussed together in Chapter 7, since they both refer to the Gaussian distribution. Finally, the test to compare two C-categorical variables ...