A Bayesian basket trial design using a calibrated Bayesian hierarchical model

Abstract

Background: The basket trial evaluates the treatment effect of a targeted therapy in patients with the same genetic or molecular aberration, regardless of their cancer types. Bayesian hierarchical modeling has been proposed to adaptively borrow information across cancer types to improve the statistical power of basket trials. Although conceptually attractive, research has shown that Bayesian hierarchical models cannot appropriately determine the degree of information borrowing and may lead to substantially inflated type I error rates.

Methods: We propose a novel calibrated Bayesian hierarchical model approach to evaluate the treatment effect in basket trials. In our approach, the shrinkage parameter that controls information borrowing is not regarded as an unknown parameter. Instead, it is defined as a function of a similarity measure of the treatment effect across tumor subgroups. The key is that the function is calibrated using simulation such that information is strongly borrowed across subgroups if their treatment effects are similar and barely borrowed if the treatment effects are heterogeneous.

Results: The simulation study shows that our method has substantially better controlled type I error rates than the Bayesian hierarchical model. In some scenarios, for example, when the true response rate is between the null and alternative, the type I error rate of the proposed method can be inflated from 10% up to 20%, but is still better than that of the Bayesian hierarchical model.

Limitation: The proposed design assumes a binary endpoint. Extension of the proposed design to ordinal and time-to-event endpoints is worthy of further investigation.

Conclusion: The calibrated Bayesian hierarchical model provides a practical approach to design basket trials with more flexibility and better controlled type I error rates than the Bayesian hierarchical model. The software for implementing the proposed design is available at http://odin.mdacc.tmc.edu/~yyuan/index_code.html.

Keywords: Basket trials; Bayesian adaptive trial design; Bayesian hierarchical model; adaptive borrowing; borrow information.

Figure 1

An illustration of basket trials.

Figure 2

The posterior distributions of σ² under the BHM approach in scenario 2, in which strong shrinkage or information borrowing is appropriate, and scenario 3, in which little shrinkage or information borrowing is appropriate.