Search arXivSearch

arXiv · 1908.00618

Analyzing Basket Trials under Multisource Exchangeability Assumptions

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.

Explore related subjects

Keep this discovery

BibTeXRIS

Michael J. Kane, Nan Chen, Alexander M. Kaizer, Xun Jiang, H. Amy Xia, Brian P. Hobbs. 2019-08-01. Analyzing Basket Trials under Multisource Exchangeability Assumptions. https://arxiv.org/abs/1908.00618

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Estimating Hierarchically Rank Structured Covariance Matrices

We consider the problem of estimating a high-dimensional covariance matrix from a very limited number of samples. This problem is ubiquitous in computational fluid dynamics, where a small number of fluid snapshots must be used to construct a Gramian matrix determining a reduced-order model, as well as in computational geoscience, where a small ensemble of Earth system forecasts must be used to estimate the covariance matrix associated with the forecast uncertainty. It is common practice to regularize the small-sample covariance by imposing a "localization" structure that enforces a physically realistic correlation length scale, imposing a sparsity constraint, "shrinking" towards a prescribed target, or attenuating small correlations. We propose an alternate technique that regularizes the small-sample covariance by imposing hierarchical rank structure. Compared to regularization methods that assume sparsity such as spatial localization, hierarchical rank structure accommodates a wider range of covariance matrices, roughly corresponding to situations where long-range correlations vary more smoothly than short-range ones. It also results in a data-sparse matrix format that permits highly efficient matrix-vector products. We present theory and algorithms which show how to efficiently estimate a high-dimensional, hierarchically rank structured covariance matrix from limited samples. Through an error analysis and numerical experiments with a variety of model problems, we demonstrate that these techniques are effective at reducing sampling errors, and that in many cases they achieve smaller estimation error than conventional techniques.

stat.CO

Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length $w>0$, with a computational cost that depends on $w$. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of $w$, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of $w$.

stat.CO