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Abstract

Basket trials are a new type of clinical trial in which a treatment is investigated in several subgroups. They are often used in uncontrolled oncology trials with a binary endpoint such as tumour response. The subgroups, for example, comprise patients with different tumour locations but all patients in the trial share a common genetic feature. Several designs for the analysis of such trials were proposed in the literature. The main element of basket trial designs is information sharing between subgroups depending on the observed similarity. Mostly Bayesian methods have been proposed for that. For example, in Fujikawa's design information is shared based on the pairwise similarity between the individual posterior distributions of the subgroups. The main objective of this thesis is to extend and improve Fujikawa's design and to compare the performance of the original and the modified design to that of other Bayesian basket trial designs.

It is shown that the sharing mechanism in Fujikawa's design is closely related to power priors, which were originally proposed to borrow strength from historical data. Using this connection, different methods for computing the sharing weights from the power prior literature are adapted to basket trials. While in Fujikawa's design the amount of information that is shared between subgroups only depends on their pairwise similarity, approaches that additionally consider the overall heterogeneity were also explored.

In a comparison study, it is demonstrated that the design based on power priors performs similarly to Fujikawa's design and other Bayesian basket trial designs in terms of the expected number of correct decisions and rejection probabilities across a range of different scenarios. The power prior design leads to minimal improvements compared to Fujikawa's design. Considering the overall heterogeneity had, however, no additional benefits. However, with the different power prior variants better fine tuning of the information sharing is possible.

It is also shown that information sharing in basket trials can lead to a number of rejected null hypotheses that is not monotonically increasing in the number of observed events. Two types of nonmonotonicity are identified and monotonicity conditions are proposed. Results that violate these conditions can occur in Fujikawa's design and the power prior design. A pruning strategy is suggested that helps to prevent nonmonotonicty in many cases but also has relevant influence on the operating characteristics.

Two R packages, baskexact and basksim, in which the power prior design is implemented, were developed. A benefit of the power prior design is that it is computationally very cheap such that posterior probabilities can be calculated analytically and even analytical computation of operating characteristics is feasible in some cases.

The finding that, regardless of their complexity, different basket trial designs perform similarly, is in line with the existing literature. While further research is necessary to investigate the power prior design in settings with different sample sizes per basket and with interim assessments, the design is attractive as the sharing can be flexibly tuned and as it is computationally cheaper than other Bayesian basket trial designs.