Success Probability Estimation with Applications to Clinical Trials

CHAPTER 1

BASIC STATISTICAL TOOLS

This Chapter provides some basic statistical concepts and tools. Pointwise estimation and confidence interval estimation are introduced; conservative estimation follows. Then, an explanation is given on what statistical tests are. The power function of the tests together with the errors of first and second type are defined. The p-value is presented, as an index for evaluating the outcome of the test. Some applications in the context of clinical trials are shown and numerical examples and figures are also provided. The probability of success in a trial (i.e. success probability) is illustrated, including how to estimate it. Superiority tests are adopted first to illustrate the above topics. Then, inequality tests are considered. Finally, there is a brief Section regarding how success probability estimation can be derived for tests of clinical superiority, of non-inferiority and for equality tests.

1.1 Pointwise estimation

Two populations are in the study, representing tho one treated with a new drag and that treated with a control drug. In order to estimate the unknown parameters of interest of these populations, for example their averages (i.e. means), experimental samples are drawn from the populations. Then, experimental data are used to provide an estimated value, which is often the most likely one, of these parameters: this is pointwise estimation.

Often, the effect size of the new drug is the quantity of clinical interest and is expressed ...