[Paper Review] Analyzing Basket Trials under Multisource Exchangeability Assumptions

Michael J. Kane, Nan Chen+4 more|arXiv (Cornell University)|Aug 1, 2019

Statistical Methods in Clinical Trials4 references4 citations

TL;DR

This paper proposes a Bayesian multisource exchangeability model (MEM) for basket trials that enables hierarchical shrinkage across multiple subpopulations, allowing for data-driven identification of exchangeable clusters. By evaluating pairwise exchangeability, the method improves response rate estimation in sparse subpopulations, as demonstrated in an oncology trial where cluster 2 (NSCLC, ED/LH, ATC) showed a posterior mean response rate of 0.383 with 94.5% posterior probability of exceeding the null rate of 0.25.

ABSTRACT

Basket designs are prospective clinical trials that are devised with the hypothesis that the presence of selected molecular features determine a patient's subsequent response to a particular "targeted" treatment strategy. Basket trials are designed to enroll multiple clinical subpopulations to which it is assumed that the therapy in question offers beneficial efficacy in the presence of the targeted molecular profile. The treatment, however, may not offer acceptable efficacy to all subpopulations enrolled. Moreover, for rare disease settings, such as oncology wherein these trials have become popular, marginal measures of statistical evidence are difficult to interpret for sparsely enrolled subpopulations. Consequently, basket trials pose challenges to the traditional paradigm for trial design, which assumes inter-patient exchangeability. The R-package \pkg{basket} facilitates the analysis of basket trials by implementing multi-source exchangeability models. By evaluating all possible pairwise exchangeability relationships, this hierarchical modeling framework facilitates Bayesian posterior shrinkage among a collection of discrete and pre-specified subpopulations. Analysis functions are provided to implement posterior inference of the response rates and all possible exchangeability relationships between subpopulations. In addition, the package can identify "poolable" subsets of and report their response characteristics. The functionality of the package is demonstrated using data from an oncology study with subpopulations defined by tumor histology.

Motivation & Objective

• Address the challenge of limited statistical power in basket trials with sparse subpopulations, especially in rare diseases like oncology.
• Overcome the limitations of traditional single-source hierarchical models that fail to detect non-exchangeability among subpopulations.
• Develop a method to identify 'poolable' subpopulations based on data-driven exchangeability relationships.
• Provide a robust Bayesian framework that enables posterior inference on response rates and cluster membership.
• Facilitate evidence-based decision-making in precision medicine by quantifying heterogeneity across molecularly defined subpopulations.

Proposed method

• Implement a Bayesian multisource exchangeability model (MEM) that allows for source-specific smoothing parameters, enabling multi-resolution shrinkage.
• Use Markov Chain Monte Carlo (MCMC) sampling to estimate posterior distributions of response rates and exchangeability relationships.
• Evaluate all possible pairwise exchangeability relationships among discrete subpopulations to identify closed subgraphs (meta-baskets).
• Apply a reference prior distribution to model exchangeability and compute posterior probabilities for each potential cluster configuration.
• Utilize posterior effective sample size to quantify the strength of evidence for each subpopulation’s response rate.
• Generate posterior density plots for individual baskets and clusters to visualize response rate distributions and uncertainty.

Experimental results

Research questions

• RQ1 Which subpopulations in a basket trial exhibit statistically exchangeable response patterns, and how can these be identified from data?
• RQ2 How does the MEM framework improve response rate estimation in subpopulations with sparse enrollment compared to traditional methods?
• RQ3 What is the posterior probability that a given subpopulation’s response rate exceeds a predefined null rate (e.g., 0.25) under the MEM framework?
• RQ4 Can the model detect and quantify heterogeneity in treatment response across different histological subtypes in oncology basket trials?
• RQ5 How does the inclusion of multiple sources of shrinkage in MEM enhance inference compared to single-source hierarchical models?

Key findings

• Cluster 1 (CRC.v, CRC.vc, Bile Duct) had a posterior mean response rate of 0.085, with only 7.7% posterior probability of exceeding the null rate of 0.25.
• Cluster 2 (NSCLC, ED/LH, ATC) had a posterior mean response rate of 0.383, with 94.5% posterior probability of exceeding the null rate of 0.25.
• The posterior effective sample size was 9.528 for Cluster 1 and 30.779 for Cluster 2, indicating stronger evidence for the latter.
• The most likely MEM configuration consisted of two closed subgraphs (meta-baskets), with Cluster 1 including CRC.v, CRC.vc, and Bile Duct, and Cluster 2 including NSCLC, ED/LH, and ATC.
• Posterior density plots confirmed that Cluster 2 subpopulations demonstrated more promising activity, with higher and less dispersed response rate estimates.
• The model successfully identified non-exchangeable subpopulations, avoiding over-shrinkage in heterogeneous settings where single-source models would fail.