Dynamic borrowing methods for basket trials with order restrictions

The purpose of a basket trial is to evaluate a new therapy in multiple populations under the same protocol. Each population, referred to as a "basket", can be defined by disease type, biomarkers, or other patient characteristics. In some basket trials we may have information about the order of the response between baskets. For example, consider a basket trial of a cancer drug where the baskets are defined by tumor type and levels of a biomarker. We may know based on the mechanism of action of the drug that the response rate among those who are biomarker positive will be greater than or equal to the response rate among those who are biomarker negative. In this paper we present modifications to two previously published dynamic borrowing methods for single-arm basket trials with a binary endpoint that incorporate information about known orders between baskets. We show that when the order assumptions hold and the study is powered to identify all promising baskets, the order-restricted methods require marginally smaller sample sizes than methods without order restrictions. Under the considered settings, the sample size for a two-stage basket trial with five baskets was reduced by approximately 10%. However, when the assumed orders do not hold, the order-restricted methods have inflated type 1 error rate and reduced power compared to methods without order restrictions.