RoBoT: a robust Bayesian hypothesis testing method for basket trials

Using Subject Level Covariate Information in Bayesian Mixture Models for Basket Trials

Basket trials are gaining importance with advancements in precision medicine. A basket trial evaluates one or more treatments for efficacy among more than one cancer type (histology) in a single clinical trial. Compared to traditional designs, basket trials can reduce the time required for testing and, by pooling across cancer types, they also allow the drugs to be tested for rare cancers. However, the potential for heterogeneity in treatment efficacy in different cancer types poses modeling challenges. Our model aims to assist the cancer type level go/no-go decisions in the initial phases of the trial through a latent cluster structure that incorporates subject-level covariate information. We model subjects' responses using a Bayesian mixture model where the mixture weights depend on a measure of similarly among subjects' covariate values. A simulation study demonstrates that our proposed Bayesian Partition Model with Covariates (BPMx) robustly estimates basket-level mean response and can provide insight about the latent cluster structure. We further illustrate the model using response data from a published basket trial.

A basket trial design based on constrained hierarchical Bayesian model for latent subgroups

It is well known a basket trial consisting of multiple cancer types has the potential of borrowing strength across the baskets defined by the cancer types, leading to an efficient design in terms of sample size and trial duration. The treatment effects in those baskets are often heterogeneous and categorized by the cancer types being sensitive or insensitive to the treatment. Hence, the assumption of exchangeability in many existing basket trials may be violated, and there is a need to design trials without this assumption. In this paper, we simplify the constrained hierarchical Bayesian model for latent subgroups (CHBM-LS) for two classifiers to deal with the potential heterogeneity of treatment effects due to the single classifier of the cancer type. Different baskets are aggregated into subgroups using a latent subgroup modeling approach. The treatment effects are similar and exchangeable to facilitate information borrowing within each latent subgroup. Applying the simplified CHBM-LS approach to the real basket trials where baskets defined by only cancer types shows better performance than other available approaches. Further simulation study also demonstrates this CHBM-LS approach outperforms other approaches with higher statistical power and better-controlled type I error rates under various scenarios.

Biomarker-driven basket trial designs: origins and new methodological developments

Due to increased use of gene sequencing techniques, understanding of cancer on a molecular level has evolved, in terms of both diagnosis and evaluation in response to initial therapies. In parallel, clinical trials meant to evaluate molecularly-driven interventions through assessment of both treatment effects and putative predictive biomarker effects are being employed to advance the goals of precision medicine. Basket trials investigate one or more biomarker-targeted therapies across multiple cancer types in a tumor location agnostic fashion. The review article offers an overview of the traditional forms of such designs, the practical challenges facing each type of design, and then review novel adaptations proposed in the last few years, categorized into Bayesian and Classical Frequentist perspectives. The review article concludes by summarizing potential advantages and limitations of the new trial design solutions.

rBMA: A robust Bayesian Model Averaging Method for phase II basket trials based on informative mixture priors

Oncology drug research in the last few decades has been driven by the development of targeted agents. In the era of targeted therapies, basket trials are often used to test the antitumor activity of a novel treatment in multiple indications sharing the same genomic alteration. As patient population are further fragmented into biomarker-defined subgroups in basket trials, novel statistical methods are needed to facilitate cross-indication learning to improve the statistical power in basket trial design. Here we propose a robust Bayesian model averaging (rBMA) technique for the design and analysis of phase II basket trials. We consider the posterior distribution of each indication (basket) as the weighted average of three different models which only differ in their priors (enthusiastic, pessimistic and non-informative). The posterior weights of these models are determined based on the effect of the experimental treatment in all the indications tested. In early phase oncology trials, different binary endpoints might be chosen for different indications (objective response, disease control or PFS at landmark times), which makes it even more challenging to borrow information across indications. Compared to previous approaches, the proposed method has the flexibility to support cross-indication learning in the presence of mixed endpoints. We evaluate and compare the performance of the proposed rBMA approach to competing approaches in simulation studies. R scripts to implement the proposed method are available at https://github.com/xwang317/rBMA.

A generalized calibrated Bayesian hierarchical modeling approach to basket trials with multiple endpoints

A basket trial simultaneously evaluates a treatment in multiple cancer subtypes, offering an effective way to accelerate drug development in multiple indications. Many basket trials are designed and monitored based on a single efficacy endpoint, primarily the tumor response. For molecular targeted or immunotherapy agents, however, a single efficacy endpoint cannot adequately characterize the treatment effect. It is increasingly important to use more complex endpoints to comprehensively assess the risk-benefit profile of such targeted therapies. We extend the calibrated Bayesian hierarchical modeling approach to monitor phase II basket trials with multiple endpoints. We propose two generalizations, one based on the latent variable approach and the other based on the multinomial-normal hierarchical model, to accommodate different types of endpoints and dependence assumptions regarding information sharing. We introduce shrinkage parameters as functions of statistics measuring homogeneity among subgroups and propose a general calibration approach to determine the functional forms. Theoretical properties of the generalized hierarchical models are investigated. Simulation studies demonstrate that the monitoring procedure based on the generalized approach yields desirable operating characteristics.

Tumor-Agnostic Approvals: Insights and Practical Considerations

Since the first approval of a tumor-agnostic indication in 2017, a total of seven tumor-agnostic indications involving six drugs have received approval from the FDA. In this paper, the master protocol subteam of the Statistical Methods in Oncology Scientific Working Group, Biopharmaceutical Session, American Statistical Association, provides a comprehensive summary of these seven tumor-agnostic approvals, describing their mechanisms of action; biomarker prevalence; study design; companion diagnostics; regulatory aspects, including comparisons of global regulatory requirements; and health technology assessment approval. Also discussed are practical considerations relating to the regulatory approval of tumor-agnostic indications, specifically (i) recommendations for the design stage to mitigate the risk that exceptions may occur if a treatment is initially hypothesized to be effective for all tumor types and (ii) because drug development continues after approval of a tumor-agnostic indication, recommendations for further development of tumor-specific indications in first-line patients in the setting of a randomized confirmatory basket trial, acknowledging the challenges in this area. These recommendations and practical considerations may provide insights for the future development of drugs for tumor-agnostic indications.

A frequentist design for basket trials using adaptive lasso

A basket trial aims to expedite the drug development process by evaluating a new therapy in multiple populations within the same clinical trial. Each population, referred to as a "basket", can be defined by disease type, biomarkers, or other patient characteristics. The objective of a basket trial is to identify the subset of baskets for which the new therapy shows promise. The conventional approach would be to analyze each of the baskets independently. Alternatively, several Bayesian dynamic borrowing methods have been proposed that share data across baskets when responses appear similar. These methods can achieve higher power than independent testing in exchange for a risk of some inflation in the type 1 error rate. In this paper we propose a frequentist approach to dynamic borrowing for basket trials using adaptive lasso. Through simulation studies we demonstrate adaptive lasso can achieve similar power and type 1 error to the existing Bayesian methods. The proposed approach has the benefit of being easier to implement and faster than existing methods. In addition, the adaptive lasso approach is very flexible: it can be extended to basket trials with any number of treatment arms and any type of endpoint.

Bayesian Methods for Information Borrowing in Basket Trials: An Overview

Basket trials allow simultaneous evaluation of a single therapy across multiple cancer types or subtypes of the same cancer. Since the same treatment is tested across all baskets, it may be desirable to borrow information across them to improve the statistical precision and power in estimating and detecting the treatment effects in different baskets. We review recent developments in Bayesian methods for the design and analysis of basket trials, focusing on the mechanism of information borrowing. We explain the common components of these methods, such as a prior model for the treatment effects that embodies an assumption of exchangeability. We also discuss the distinct features of these methods that lead to different degrees of borrowing. Through simulation studies, we demonstrate the impact of information borrowing on the operating characteristics of these methods and discuss its broader implications for drug development. Examples of basket trials are presented in both phase I and phase II settings.

Bayesian design of multi-regional clinical trials with time-to-event endpoints

Sponsors often rely on multi-regional clinical trials (MRCTs) to introduce new treatments more rapidly into the global market. Many commonly used statistical methods do not account for regional differences, and small regional sample sizes frequently result in lower estimation quality of region-specific treatment effects. The International Council for Harmonization E17 guidelines suggest consideration of methods that allow for information borrowing across regions to improve estimation. In response to these guidelines, we develop a novel methodology to estimate global and region-specific treatment effects from MRCTs with time-to-event endpoints using Bayesian model averaging (BMA). This approach accounts for the possibility of heterogeneous treatment effects between regions, and we discuss how to assess the consistency of these effects using posterior model probabilities. We obtain posterior samples of the treatment effects using a Laplace approximation, and we show through simulation studies that the proposed modeling approach estimates region-specific treatment effects with lower mean squared error than a Cox proportional hazards model while resulting in a similar rejection rate of the global treatment effect. We then apply the BMA approach to data from the LEADER trial, an MRCT designed to evaluate the cardiovascular safety of an anti-diabetic treatment.

Frequentist analysis of basket trials with one-sample Mantel-Haenszel procedures

Recent substantial advances of molecular targeted oncology drug development is requiring new paradigms for early-phase clinical trial methodologies to enable us to evaluate efficacy of several subtypes simultaneously and efficiently. The concept of the basket trial is getting of much attention to realize this requirement borrowing information across subtypes, which are called baskets. Bayesian approach is a natural approach to this end and indeed the majority of the existing proposals relies on it. On the other hand, it required complicated modeling and may not necessarily control the type 1 error probabilities at the nominal level. In this article, we develop a purely frequentist approach for basket trials based on one-sample Mantel-Haenszel procedure relying on a very simple idea for borrowing information under the common treatment effect assumption over baskets. We show that the proposed Mantel-Haenszel estimator for the treatment effect is consistent under two limiting models of the large strata and sparse data limiting models (dually consistent) and propose dually consistent variance estimators. The proposed estimators are interpretable even if the common treatment effect assumptions are violated. Then, we can design basket trials in a confirmatory matter. We also propose an information criterion approach to identify effective subclasses of baskets.

Basket trials in oncology: a systematic review of practices and methods, comparative analysis of innovative methods, and an appraisal of a missed opportunity

Background

Basket trials are increasingly used in oncology drug development for early signal detection, accelerated tumor-agnostic approvals, and prioritization of promising tumor types in selected patients with the same mutation or biomarker. Participants are grouped into so-called baskets according to tumor type, allowing investigators to identify tumors with promising responses to treatment for further study. However, it remains a question as to whether and how much the adoption of basket trial designs in oncology have translated into patient benefits, increased pace and scale of clinical development, and de-risking of downstream confirmatory trials.

Methods

Innovation in basket trial design and analysis includes methods that borrow information across tumor types to increase the quality of statistical inference within each tumor type. We build on the existing systematic reviews of basket trials in oncology to discuss the current practices and landscape. We conceptually illustrate recent innovative methods for basket trials, with application to actual data from recently completed basket trials. We explore and discuss the extent to which innovative basket trials can be used to de-risk future trials through their ability to aid prioritization of promising tumor types for subsequent clinical development.

Results

We found increasing adoption of basket trial design in oncology, but largely in the design of single-arm phase II trials with a very low adoption of innovative statistical methods. Furthermore, the current practice of basket trial design, which does not consider its impact on the clinical development plan, may lead to a missed opportunity in improving the probability of success of a future trial. Gating phase II with a phase Ib basket trial reduced the size of phase II trials, and losses in the probability of success as a result of not using innovative methods may not be recoverable by running a larger phase II trial.

Conclusion

Innovative basket trial methods can reduce the size of early phase clinical trials, with sustained improvement in the probability of success of the clinical development plan. We need to do more as a community to improve the adoption of these methods.

A comparison of Bayesian information borrowing methods in basket trials and a novel proposal of modified exchangeability-nonexchangeability method

Recent innovation in trial design to improve study efficiency has led to the development of basket trials in which a single therapeutic treatment is tested on several patient populations, each of which forms a basket. In a common setting, patients across all baskets share a genetic marker and as such, an assumption can be made that all patients may have a homogeneous response to treatments. Bayesian information borrowing procedures utilize this assumption to draw on information regarding the response in one basket when estimating the response rate in others. This can improve power and precision of estimates particularly in the presence of small sample sizes, however, can come at a cost of biased estimates and an inflation of error rates, bringing into question validity of trial conclusions. We review and compare the performance of several Bayesian borrowing methods, namely: the Bayesian hierarchical model (BHM), calibrated Bayesian hierarchical model (CBHM), exchangeability-nonexchangeability (EXNEX) model and a Bayesian model averaging procedure. A generalization of the CBHM is made to account for unequal sample sizes across baskets. We also propose a modification of the EXNEX model that allows for better control of a type I error. The proposed method uses a data-driven approach to account for the homogeneity of the response data, measured through Hellinger distances. Through an extensive simulation study motivated by a real basket trial, for both equal and unequal sample sizes across baskets, we show that in the presence of a basket with a heterogeneous response, unlike the other methods discussed, this model can control type I error rates to a nominal level whilst yielding improved power.

An adaptive biomarker basket design in phase II oncology trials

The phase II basket trial in oncology is a novel design that enables the simultaneous assessment of treatment effects of one anti-cancer targeted agent in multiple cancer types. Biomarkers could potentially associate with the clinical outcomes and re-define clinically meaningful treatment effects. It is therefore natural to develop a biomarker-based basket design to allow the prospective enrichment of the trials with the adaptive selection of the biomarker-positive (BM+) subjects who are most sensitive to the experimental treatment. We propose a two-stage phase II adaptive biomarker basket (ABB) design based on a potential predictive biomarker measured on a continuous scale. At Stage 1, the design incorporates a biomarker cutoff estimation procedure via a hierarchical Bayesian model with biomarker as a covariate (HBMbc). At Stage 2, the design enrolls only BM+ subjects, defined as those with the biomarker values exceeding the biomarker cutoff within each cancer type, and subsequently assesses the early efficacy and/or futility stopping through the pre-defined interim analyses. At the end of the trial, the response rate of all BM+ subjects for each cancer type can guide drug development, while the data from all subjects can be used to further model the relationship between the biomarker value and the clinical outcome for potential future research. The extensive simulation studies show that the ABB design could produce a good estimate of the biomarker cutoff to select BM+ subjects with high accuracy and could outperform the existing phase II basket biomarker cutoff design under various scenarios.

Bayesian local exchangeability design for phase II basket trials

We propose an information borrowing strategy for the design and monitoring of phase II basket trials based on the local multisource exchangeability assumption between baskets (disease types). In our proposed local-MEM framework, information borrowing is only allowed to occur locally, that is, among baskets with similar response rate and the amount of information borrowing is determined by the level of similarity in response rate, whereas baskets not considered similar are not allowed to share information. We construct a two-stage design for phase II basket trials using the proposed strategy. The proposed method is compared to competing Bayesian methods and Simon's two-stage design in a variety of simulation scenarios. We demonstrate the proposed method is able to maintain the family-wise type I error rate at a reasonable level and has desirable basket-wise power compared to Simon's two-stage design. In addition, our method is computationally efficient compared to existing Bayesian methods in that the posterior profiles of interest can be derived explicitly without the need for sampling algorithms. R scripts to implement the proposed method are available at https://github.com/yilinyl/Bayesian-localMEM.

Bayesian and frequentist approaches to sequential monitoring for futility in oncology basket trials: A comparison of Simon's two-stage design and Bayesian predictive probability monitoring with information sharing across baskets

This article discusses and compares statistical designs of basket trial, from both frequentist and Bayesian perspectives. Baskets trials are used in oncology to study interventions that are developed to target a specific feature (often genetic alteration or immune phenotype) that is observed across multiple tissue types and/or tumor histologies. Patient heterogeneity has become pivotal to the development of non-cytotoxic treatment strategies. Treatment targets are often rare and exist among several histologies, making prospective clinical inquiry challenging for individual tumor types. More generally, basket trials are a type of master protocol often used for label expansion. Master protocol is used to refer to designs that accommodates multiple targets, multiple treatments, or both within one overarching protocol. For the purpose of making sequential decisions about treatment futility, Simon's two-stage design is often embedded within master protocols. In basket trials, this frequentist design is often applied to independent evaluations of tumor histologies and/or indications. In the tumor agnostic setting, rarer indications may fail to reach the sample size needed for even the first evaluation for futility. With recent innovations in Bayesian methods, it is possible to evaluate for futility with smaller sample sizes, even for rarer indications. Novel Bayesian methodology for a sequential basket trial design based on predictive probability is introduced. The Bayesian predictive probability designs allow interim analyses with any desired frequency, including continual assessments after each patient observed. The sequential design is compared with and without Bayesian methods for sharing information among a collection of discrete, and potentially non-exchangeable tumor types. Bayesian designs are compared with Simon's two-stage minimax design.

PMED: Optimal Bayesian Platform Trial Design with Multiple Endpoints

In oncology drug development, indication selection and optimal dose identification are the primary objectives for the early phase of clinical trials and could significantly impact the probability of success. Master protocols, e.g., basket trial, umbrella trial, and platform trial, have become popular in practice considering the connection of trial designs with multiple indications and treatment candidates. They also enable the optimization of operational resources and maximize the capability of data-driven decision-making. However, most of the available designs are developed with the efficacy endpoint only for treatment effect estimation and testing, without consideration of the safety end point. Thus, it often lacks a comprehensive quantitative framework to allow optimal treatment selection, which could put future development at risk. We propose an optimal Bayesian platform trial design with multiple end points (PMED) to characterize the overall benefit-risk profile. The design is further extended to allow treatment and indication selection within and across arms, with continuous monitoring on multiple interim analyses for futility. In addition, we propose dynamic borrowing across arms to increase the efficiency and accuracy of estimation given the level of similarity across arms. A hierarchical hypothesis structure is utilized to achieve optimal indication and treatment combination selection by controlling family-wise error. Through simulation studies, we show that PMED is a robust design under the studied scenarios with superb power and controlled family-wise error rate.

Regulatory issues and the potential use of Bayesian approaches for early drug approval systems in Japan

Bayesian methods quantify and interpret the therapeutic effects of investigational drugs based on probability statements of the posterior distribution. However, the basic principle underlying the use of Bayesian methods in registration trials for new drug applications in Japan has not been adequately discussed. Motivated by the two drug approval systems for early approval recently enacted in Japan, we present our perspectives on the application of the Bayesian approach in registration trials in Japan. These are based on discussions among academic, industry, and regulatory experts at invited workshops. Based on the aforementioned early approval systems, we discuss putative common regulatory issues related to the use of the Bayesian approach and introduce instances of clinical trials in which the Bayesian approach is expected to be used. This article provides a well-defined premise for the discussion between industry and regulatory agencies on the use of Bayesian approaches for early drug approval in Japan.

Constrained hierarchical Bayesian model for latent subgroups in basket trials with two classifiers

The basket trial in oncology is a novel clinical trial design that enables the simultaneous assessment of one treatment in multiple cancer types. In addition to the usual basket classifier of the cancer types, many recent basket trials further contain other classifiers like biomarkers that potentially affect the clinical outcomes. In other words, the treatment effects in those baskets are often categorized by not only the cancer types but also the levels of other classifiers. Therefore, the assumption of exchangeability is often violated when some baskets are more sensitive to the targeted treatment, whereas others are less. In this article, we propose a constrained hierarchical Bayesian model for latent subgroups (CHBM-LS) to deal with potential heterogeneity of treatment effects due to both the cancer type (first classifier) and another classifier (second classifier) in basket trials. Different baskets defined by multiple cancer types and multiple levels of the second classifier are aggregated into subgroups using a latent subgroup modeling approach. Within each latent subgroup, the treatment effects are similar and approximately exchangeable to borrow information. The CHBM-LS approach evaluates the treatment effect for each basket while allowing adaptive information borrowing across the baskets by identifying latent subgroups. The simulation study shows that the CHBM-LS approach outperforms other approaches with higher statistical power and better-controlled type I error rates under various scenarios with heterogeneous treatment effects across baskets.

Categories, components, and techniques in a modular construction of basket trials for application and further research

Basket trials have become a virulent topic in medical and statistical research during the last decade. The core idea of them is to treat patients, who express the same genetic predisposition-either personally or their disease-with the same treatment irrespective of the location of the disease. The location of the disease defines each basket and the pathway of the treatment uses the common genetic predisposition among the baskets. This opens the opportunity to share information among baskets, which can consequently increase the information of the basket-wise response with respect to the investigated treatment. This further allows dynamic decisions regarding futility and efficacy of individual baskets during the ongoing trial. Several statistical designs have been proposed on how a basket trial can be conducted and this has left an unclear situation with many options. The different designs propose different mathematical and statistical techniques, different decision rules, and also different trial purposes. This paper presents a broad overview of existing designs, categorizes them, and elaborates their similarities and differences. A uniform and consistent notation facilitates the first contact, introduction, and understanding of the statistical methodologies and techniques used in basket trials. Finally, this paper presents a modular approach for the construction of basket trials in applied medical science and forms a base for further research of basket trial designs and their techniques.