Flexible Designs für klinische Studien in Verteilungssituationen mit Störparametern

Controlled clinical trials are an experimental method of clinical research. They are used to demonstrate the efficacy of a therapy and hence to ensure therapeutic improvement. During such trials there are often reasons to change the design of the trial when the assumptions made at the planning stage turn out to be wrong. For example, the expected effect size or the estimated variance might be smaller or greater than assumed at the beginning. Conventional statistical methods do not allow for data dependent changes to the design during the course of the trial while still controlling the error rates. For this reason many clinical trials fail to show efficacy, or the strict control of the error rates, especially the type I error rate, is abandoned. In the last years, new methods have been developed which allow for design modification during the course of a trial without violating the integrity of the trial. Among these methods are the so-called adaptive designs, first proposed by Bauer (1989), which make it possible to change the design at preplanned interim analyses without inflating the type I error rate. Adaptive designs are later renamed flexible designs because the name adaptive designs was already in use. More recently, Müller and Schäfer (2004) proposed the so-called CRP-principle. Unlike the flexible designs, here the design can be changed at any time during the course of the trial, which means that the possibility of design modifications and the suitable time points do not have to be specified at the planning stage. Nevertheless, the type I error rate is still controlled. This approach thus allows for corrections of the study design at the moment when misspecfications become apparent. Although the CRP-principle is a general principle, its exact application was restricted to problems where only one parameter of the underlying distribution is unknown. For example, this is the case, when the data are normally distributed with unknown expectation but known variance. Until now, if the variance is also unknown (t-test), the CRP-principle could only be applied approximately. Particularly for small sample sizes, this does not control the type I error rate adequately. The aim of this thesis is the development of a method on the basis of the CRP-principle, which is applicable for exact design modifications in situations with more than one unknown parameter such as the t-test. In chapter 2 an introduction to the special problems of clinical trials is given. Chapter 3 gives an overview of the literature of group-sequential and flexible designs. In chapter 4 a general mathematical theory is developed, which includes the flexible designs and the CRP-principle. This theory is an extension of the well-known concept of decision functions. The main findings will be represented in chapter 5, and it is then possible to make exact design modifications in problems where the underlying distribution forms a k-parametric exponential family. At the end of this chapter the application to a normal distribution with unknown variance (t-test) and to the comparison of two binomial probabilities (Fishers exact test) is shown.