Bayesian sample size determination in basket trials borrowing information between subsets.

Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomized basket trial design where patients are randomly assigned to the new treatment or control within each trial subset ("subtrial" for short). Closed-form sample size formulae are derived to ensure that each subtrial has a specified chance of correctly deciding whether the new treatment is superior to or not better than the control by some clinically relevant difference. Given prespecified levels of pairwise (in)commensurability, the subtrial sample sizes are solved simultaneously. The proposed Bayesian approach resembles the frequentist formulation of the problem in yielding comparable sample sizes for circumstances of no borrowing. When borrowing is enabled between commensurate subtrials, a considerably smaller trial sample size is required compared to the widely implemented approach of no borrowing. We illustrate the use of our sample size formulae with two examples based on real basket trials. A comprehensive simulation study further shows that the proposed methodology can maintain the true positive and false positive rates at desired levels.

A group-sequential randomized trial design utilizing supplemental trial data.

Definitive clinical trials are resource intensive, often requiring a large number of participants over several years. One approach to improve the efficiency of clinical trials is to incorporate historical information into the primary trial analysis. This approach has tremendous potential in the areas of pediatric or rare disease trials, where achieving reasonable power is difficult. In this article, we introduce a novel Bayesian group-sequential trial design based on Multisource Exchangeability Models, which allows for dynamic borrowing of historical information at the interim analyses. Our approach achieves synergy between group sequential and adaptive borrowing methodology to attain improved power and reduced sample size. We explore the frequentist operating characteristics of our design through simulation and compare our method to a traditional group-sequential design. Our method achieves earlier stopping of the primary study while increasing power under the alternative hypothesis but has a potential for type I error inflation under some null scenarios. We discuss the issues of decision boundary determination, power and sample size calculations, and the issue of information accrual. We present our method for a continuous and binary outcome, as well as in a linear regression setting.

On the feasibility of pediatric dose-finding trials in small samples with information from a preceding trial in adults.

We consider the case of pediatric dose-finding trials with extremely limited sample size. The operating characteristics of the standard design, the Continual Reassessment Method (CRM), are only well described for sample sizes of about 20 patients or more. In this simulation study, we assume the situation of a pediatric trial with only 10 patients and a preceding dose-finding trial in adults. Based on the adult data, we reduce the set of pediatric doses and formulate (partially) informative prior distributions for the pediatric trial. Our simulations show that such small pediatric dose-finding trials with robustified priors may provide sufficient operating characteristics.

Combined assessment of early and late-phase outcomes in orphan drug development.

In drug development programs, proof-of-concept Phase II clinical trials typically have a biomarker as a primary outcome, or an outcome that can be observed with relatively short follow-up. Subsequently, the Phase III clinical trials aim to demonstrate the treatment effect based on a clinical outcome that often needs a longer follow-up to be assessed. Early-phase outcomes or biomarkers are typically associated with late-phase outcomes and they are often included in Phase III trials. The decision to proceed to Phase III development is based on analysis of the early-Phase II outcome data. In rare diseases, it is likely that only one Phase II trial and one Phase III trial are available. In such cases and before drug marketing authorization requests, positive results of the early-phase outcome of Phase II trials are then likely seen as supporting (or even replicating) positive Phase III results on the late-phase outcome, without a formal retrospective combined assessment and without accounting for between-study differences. We used double-regression modeling applied to the Phase II and Phase III results to numerically mimic this informal retrospective assessment. We provide an analytical solution for the bias and mean square error of the overall effect that leads to a corrected double-regression. We further propose a flexible Bayesian double-regression approach that minimizes the bias by accounting for between-study differences via discounting the Phase II early-phase outcome when they are not in line with the Phase III biomarker outcome results. We illustrate all methods with an orphan drug example for Fabry disease.

Classifying information-sharing methods.

BACKGROUND: Sparse relative effectiveness evidence is a frequent problem in Health Technology Assessment (HTA). Where evidence directly pertaining to the decision problem is sparse, it may be feasible to expand the evidence-base to include studies that relate to the decision problem only indirectly: for instance, when there is no evidence on a comparator, evidence on other treatments of the same molecular class could be used; similarly, a decision on children may borrow-strength from evidence on adults. Usually, in HTA, such indirect evidence is either included by ignoring any differences ('lumping') or not included at all ('splitting'). However, a range of more sophisticated methods exists, primarily in the biostatistics literature. The objective of this study is to identify and classify the breadth of the available information-sharing methods. METHODS: Forwards and backwards citation-mining techniques were used on a set of seminal papers on the topic of information-sharing. Papers were included if they specified (network) meta-analytic methods for combining information from distinct populations, interventions, outcomes or study-designs. RESULTS: Overall, 89 papers were included. A plethora of evidence synthesis methods have been used for information-sharing. Most papers (n=79) described methods that shared information on relative treatment effects. Amongst these, there was a strong emphasis on methods for information-sharing across multiple outcomes (n=42) and treatments (n=25), with fewer papers focusing on study-designs (n=23) or populations (n=8). We categorise and discuss the methods under four 'core' relationships of information-sharing: functional, exchangeability-based, prior-based and multivariate relationships, and explain the assumptions made within each of these core approaches. CONCLUSIONS: This study highlights the range of information-sharing methods available. These methods often impose more moderate assumptions than lumping or splitting. Hence, the degree of information-sharing that they impose could potentially be considered more appropriate. Our identification of four 'core' methods of information-sharing allows for an improved understanding of the assumptions underpinning the different methods. Further research is required to understand how the methods differ in terms of the strength of sharing they impose and the implications of this for health care decisions.

Bayesian data integration and variable selection for pan-cancer survival prediction using protein expression data.

Accurate prognostic prediction using molecular information is a challenging area of research, which is essential to develop precision medicine. In this paper, we develop translational models to identify major actionable proteins that are associated with clinical outcomes, like the survival time of patients. There are considerable statistical and computational challenges due to the large dimension of the problems. Furthermore, data are available for different tumor types; hence data integration for various tumors is desirable. Having censored survival outcomes escalates one more level of complexity in the inferential procedure. We develop Bayesian hierarchical survival models, which accommodate all the challenges mentioned here. We use the hierarchical Bayesian accelerated failure time model for survival regression. Furthermore, we assume sparse horseshoe prior distribution for the regression coefficients to identify the major proteomic drivers. We borrow strength across tumor groups by introducing a correlation structure among the prior distributions. The proposed methods have been used to analyze data from the recently curated "The Cancer Proteome Atlas" (TCPA), which contains reverse-phase protein arrays-based high-quality protein expression data as well as detailed clinical annotation, including survival times. Our simulation and the TCPA data analysis illustrate the efficacy of the proposed integrative model, which links different tumors with the correlated prior structures.

Borrowing Strength and Borrowing Index for Bayesian Hierarchical Models.

A novel borrowing strength measure and an overall borrowing index to characterize the strength of borrowing behaviors among subgroups are proposed for a given Bayesian hierarchical model. The constructions of the proposed indexes are based on the Mallow's distance and can be easily computed using MCMC samples for univariate or multivariate posterior distributions. Consequently, the proposed indexes can serve as meaningful and useful exploratory tools to better understand the roles played by the priors in a hierarchical model, including their influences on the posteriors that are used to make statistical inferences. These relationships are otherwise ambiguous. The proposed methods can be applied to both the continuous and binary outcome variables. Furthermore, the proposed approach can be easily adapted to various settings of clinical trials, where Bayesian hierarchical models are deem appropriate. The effectiveness of the proposed method is illustrated using extensive simulation studies and a real data example.

Bayesian dose-finding phase I trial design incorporating historical data from a preceding trial.

We consider the problem of incorporating historical data from a preceding trial to design and conduct a subsequent dose-finding trial in a possibly different population of patients. In oncology, for example, after a phase I dose-finding trial is completed in Caucasian patients, investigators often conduct a further phase I trial to determine the maximum tolerated dose in Asian patients. This may be due to concerns about possible differences in treatment tolerability between populations. In this study, we propose to adaptively incorporate historical data into prior distributions assumed in a new dose-finding trial. Our proposed approach aims to appropriately borrow strength from a previous trial to improve the maximum tolerated dose determination in another patient population. We define a "historical-to-current (H-C)" parameter representing the degree of borrowing based on a retrospective analysis of previous trial data. In simulation studies, we examine the operating characteristics of the proposed method in comparison with 3 alternative approaches and assess how the H-C parameter functions across a variety of realistic settings.