Use of Bayesian Approach in Basket Trial Design

Advancements in biomarkers and momentum in precision medicine has paved the foundation for complex studies like basket trials. Basket trials are a type of master protocol, in which a targeted therapy is evaluated for multiple diseases that share common molecular alterations or risk factors that may help predict whether the patients will respond to the given therapy. Bayesian methods are particularly useful for these complex trial designs, as they enable greater flexibility and better ability to respond to the needs of the master protocol designs. Phase 2 Bayesian designs using hierarchical models, allow basket trials to efficiently assess the efficacy of a treatment in multiple disease indications.¹

General design concept for a Basket Trial

A Basket trial is essentially a multi-arm Phase 2 or Phase 3 study investigating a treatment for multiple diseases or sub-diseases. They are usually conducted without randomized control. Normally, each arm in a basket trial is compared with a historical control. Patients enrolled in a basket trial are often composed of a heterogeneous group across multiple indications, such as different cancer types. Therefore, it is difficult to evaluate time-to-event endpoints such as, progression-free survival (PFS) or overall survival (OS)). In basket trials, primary endpoints are often response rate (e.g., objective response rate (ORR) or pathological complete response (pCR)), which are less sensitive to the effects of population heterogeneity.

Basket trials often intend to use pooled population for primary analysis to gain broader indications across tumor types. However, clinical data to support pooling may be limited, and treatment effect may differ between tumor types. For example, Vemurafenib works in melanoma with BRAF V600E mutation but not in colorectal cancer with the same mutation.

When the homogeneity assumption is not valid, a separate stand-alone analysis for each arm is a simple alternative. However, conducting an independent evaluation in each arm is time- and resource-consuming. Also, the clinical trial sample size may be inflated under independent arms when compared to designs that borrow information.

Use of Bayesian approach

Recent publications have proposed adaptive designs that borrow information via model-based inference. Using the observed data, these methods borrow information by prior distributions that shrink the arm-specific estimates to a centered value . This is typically achieved through hierarchical models, where the shrinkage parameter, controlling the strength of information borrowing across different subgroups, is treated as an unknown parameter using a noninformative prior distribution.

In East Bayes, we implement a module of Basket Trial Designs and use simulation-based power calculation to evaluate four Bayesian approaches, including the Bayesian hierarchical model (BBHM) proposed by Berry et al. (2013), the calibrated Bayesian hierarchical model (CBHM) by Chu and Yuan (2018a), the exchangeabilitynonexchangeability (EXNEX) method in Neuenschwander et al. (2016) and a novel multiple cohort expansion (MUCE) method in Lyu et al. (2020). Users may choose desirable designs based on the software provided in this module. Below are some benefits of each of these approaches:

1. Bayesian Hierarchical Model (BBHM): The Bayesian hierarchical design is more likely to correctly conclude efficacy or futility when compared to Simon's Optimal Two-Stage design, in many scenarios. It is a strong design for addressing possibly differential effects in different patient groups. As stated above, the shrinkage parameter, which controls the strength of information borrowing, is treated as an unknown parameter following a noninformative prior. The data is allowed to determine how much information should be borrowed across tumor subgroups.
   
   
2. Calibrated Bayesian Hierarchical Model (CBHM): Chu and Yuan (2018a) proposed a calibrated Bayesian hierarchical model as an extension of BBHM. CBHM provides a practical approach to design basket trials with more flexibility and better controlled type I error rates than the Bayesian hierarchical model. By linking the shrinkage parameter with a measure of homogeneity among subgroups through an appropriately calibrated link function, the CBHM allows information borrowing when the treatment effect is homogeneous across subgroups and yields a much better controlled type I error rate than the BHM when the treatment effect is heterogeneous across subgroups.²
   
   
3. ExchangeabilityNonexchangeability (EXNEX) Method: EXNEX approach allows each arm-specific parameter to be exchangeable with other similar arm parameters or nonexchangeable with any of them. This is achieved through a mixture model with three components: first corresponding to exchangeable, efficacious groups, second corresponding to non-efficacious exchangeable groups and third corresponding to non-exchangeable groups.
   
   
4. Multiple Cohort Expansion (MUCE) Method: MUCE design was originally proposed for trials with multiple arms, including basket trials. Built on Bayesian hierarchical models with multiplicity control, MUCE adaptively borrows information across patient groups from different indications treated with different doses. A hierarchical model accounts for the fact that when aggregating data across patient groups, some treatment arms might have more significant differences than others, and this might require statisticians to make adjustments by weighting to achieve unbiased measurement. This enables MUCE to Control Type 1 Error while increasing power and reducing sample size. These efficient designs can be applied in any clinical trials with two or more arms. For an expansion cohort trial in the US, the MUCE design showed saving in sample size of up to 16.67% compared to Simon’s 2-stage design.

References:

1. Berry S, Broglio K, Groshen S, Berry D. Bayesian hierarchical modeling of patient subpopulations: Efficient designs of Phase II oncology clinical trials. Clinical Trials: Journal of the Society for Clinical Trials. 2013;10(5):720-734. doi:10.1177/1740774513497539
   
   
2. Chu, Y. and Yuan, Y. (2018a). A Bayesian basket trial design using a calibrated Bayesian hierarchical model. Clinical Trials, 15(2):149–158.
   
   

About Pantelis Vlachos

Pantelis is Principal/Strategic Consultant for Cytel, Inc. based in Geneva. He joined the company in January 2013. Before that, he was a Principal Biostatistician at Merck Serono as well as a Professor of Statistics at Carnegie Mellon University for 12 years. His research interests lie in the area of adaptive designs, mainly from a Bayesian perspective, as well as hierarchical model testing and checking although his secret passion is Text Mining. He has served as Managing Editor of the journal “Bayesian Analysis” as well as editorial boards of several other journals and online statistical data and software archives.