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Abstract

The scientific advances in medical research in the last two decades have shifted the focus to a personalized treatment approach. An immanent consequence is the need for clinical trials which cover these new treatment approaches. A group of clinical trial designs which account for this are gathered under the generic term master protocols. The basket trial design has evolved as the most prominent master protocol design and investigates one treatment in several different diseases. The joint investigation is justified by a common characteristic, such as a genetic aberration, which is prevalent in all of the diseases and which is used as an effect pathway by the investigated treatment. Basket trial designs have been a virulent field of research with respect to the statistical tools and characteristics of such trials. This has led to an unclear situation in literature and an increasing level of complexity in the statistical tools which are proposed for the use throughout a basket trial. However, a practical application as well as an increased interest in basket trials is rather hampered if the complexity is increased and if no access point to the topic is available. Hence, the aim of this thesis was to introduce a systematic approach to basket trial designs and to investigate the statistical tools in order to facilitate, connect, and improve statistical tools, all with the intention to make the complete basket trial setting more accessible, understandable, and applicable from a statistical perspective. The here elaborated systematic approach towards basket trial designs consists of two aspects, first a categorization of the trial designs and second a modular construction kit for basket trials. The categorization of basket trials is based on the purpose of the trial and on the statistical techniques that are applied. The modular construction separates a basket trial into four different components and presents available statistical tools for the components in a common notation. It moreover elaborates the methodological connections among the sharing tools and shows that they use different techniques. However, even though their complexity varies strongly, the tools are connected with each other or can be the same, even if they were proposed in different ways in different publications. The modular construction kit additionally serves as a catalogue to look up the available statistical tools when a basket trial is planned. The decision tools in basket trials were investigated with a focus on the difference in the statistical methodologies, namely between the frequentist one-sided binomial test and the Bayesian decision based on the posterior distribution from a beta-binomial model. It was shown that the decision tools can be tuned such that the same decisions are made. The difference between the frequentist p-value and the Bayesian posterior probability under a uniform prior was quantified analytically and it was shown by how much the two decision measures deviate from each other. With the elaborated difference, the p-value and the posterior probability can be given as functions of each other and therefore can be used interchangeably. The practical feasibility of that relationship for basket trials was shown with the conversion of the decision tools in a frequentist design into Bayesian decisions. Additionally, the connections between the other decision tools from the construction kit were investigated. The construction kit showed that the hierarchical model with normally distributed, logit-transformed response rate is the base for the majority of the sharing tools. In this thesis, a detailed investigation of a hierarchical model directly relying on the beta distributed, non-transformed response rate was conducted with respect to its feasibility as a basic sharing tool in basket trials. It was shown that the non-transformed model shares information to a slightly stronger degree, that the different underlying distributional assumption for the response rate persists, and that, in general, it is a feasible sharing tool which does have advantages in the interpretation of the hyperparameters. Therefore, its use in basket trial designs should be further investigated in future research. To conclude, this thesis provides a thorough investigation of basket trial designs, it starts with the elaboration of a systematic approach to them and continues with the investigation of the particular components and their statistical tools.