Monotonicity conditions for avoiding counterintuitive decisions in basket trials.

In a basket trial, a new treatment is tested in different subgroups, called the baskets. In oncology, the baskets usually comprise patients with different primary tumor sites but a common biomarker. Most basket trials are uncontrolled phase II trials and investigate a binary endpoint such as tumor response. To combine the data of baskets that show a similar response to the treatment, many basket trial designs use Bayesian borrowing methods. This increases the power compared to a basketwise analysis. However, it can lead to posterior probabilities that are not monotonically increasing in the number of responses. We show that, as a consequence, two types of counterintuitive decisions can arise-one that occurs within a single trial and one that occurs when the results are compared between different trials. We propose two monotonicity conditions for the inference in basket trials. Using a design recently proposed by Fujikawa and colleagues, we investigate the case of a single-stage basket trial with equal sample sizes in all baskets and show that, as the number of baskets increases, these conditions are violated for a wide range of different borrowing strengths. We show that in the investigated scenarios pruning baskets can help to ensure that the monotonicity conditions hold and investigate how this affects type I error rate and power.