A hierarchical Bayesian design for phase I trials of novel combinations of cancer therapeutic agents

Applications of the partial-order continual reassessment method in the early development of treatment combinations

Combination therapy is increasingly being explored as a promising approach for improving cancer treatment outcomes. However, identifying effective dose combinations in early oncology drug development is challenging due to limited sample sizes in early-phase clinical trials. This task becomes even more complex when multiple agents are being escalated simultaneously, potentially leading to a loss of monotonic toxicity order with respect to the dose. Traditional single-agent trial designs are insufficient for this multi-dimensional problem, necessitating the development and implementation of dose-finding methods specifically designed for drug combinations. While, in practice, approaches to this problem have focused on preselecting combinations with a known toxicity order and applying single-agent designs, this limits the number of combinations considered and may miss promising dose combinations. In recent years, several novel designs have been proposed for exploring partially ordered drug combination spaces with the goal of identifying a maximum tolerated dose combination, based on safety, or an optimal dose combination, based on toxicity and efficacy. However, their implementation in clinical practice remains limited. In this article, we describe the application of the partial order continual reassessment method and its extensions for combination therapies in early-phase clinical trials. We present completed trials that use safety endpoints to identify maximum tolerated dose combinations and adaptively use both safety and efficacy endpoints to determine optimal treatment strategies. We discuss the effectiveness of the partial-order continual reassessment method and its extensions in identifying optimal treatment strategies and provide our experience with executing these novel adaptive designs in practice. By utilizing innovative dose-finding methods, researchers and clinicians can more effectively navigate the challenges of combination therapy development, ultimately improving patient outcomes in the treatment of cancer.

Local continual reassessment methods for dose finding and optimization in drug-combination trials

Due to the limited sample size and large dose exploration space, obtaining a desirable dose combination is a challenging task in the early development of combination treatments for cancer patients. Most existing designs for optimizing the dose combination are model-based, requiring significant efforts to elicit parameters or prior distributions. Model-based designs also rely on intensive model calibration and may yield unstable performance in the case of model misspecification or sparse data. We propose to employ local, underparameterized models for dose exploration to reduce the hurdle of model calibration and enhance the design robustness. Building upon the framework of the partial ordering continual reassessment method, we develop local data-based continual reassessment method designs for identifying the maximum tolerated dose combination, using toxicity only, and the optimal biological dose combination, using both toxicity and efficacy, respectively. The local data-based continual reassessment method designs only model the local data from neighboring dose combinations. Therefore, they are flexible in estimating the local space and circumventing unstable characterization of the entire dose-exploration surface. Our simulation studies show that our approach has competitive performance compared to widely used methods for finding maximum tolerated dose combination, and it has advantages over existing model-based methods for optimizing optimal biological dose combination.

A clinical phase I dose-finding design with adaptive shrinking boundaries for drug combination trials

BACKGROUND

Combinations of drugs are becoming increasingly common in oncology treatment. In some cases, patients can benefit from the interaction between two drugs, although there is usually a higher risk of developing toxicity. Due to drug-drug interactions, multidrug combinations often exhibit different toxicity profiles than those of single drugs, leading to a complex trial scenario. Numerous methods have been proposed for the design of phase I drug combination trials. For example, the two-dimensional Bayesian optimal interval design for combination drug (BOINcomb) is simple to implement and has desirable performance. However, in scenarios where the lowest and starting dose is close to being toxic, the BOINcomb design may tend to allocate more patients to overly toxic doses, and select an overly toxic dose combination as the maximum tolerated dose combination.

METHOD

To improve the performance of BOINcomb in the above extreme scenarios, we widen the range of variation of the boundaries by setting the self-shrinking dose escalation and de-escalation boundaries. We refer to the new design as adaptive shrinking Bayesian optimal interval design for combination drug (asBOINcomb). We conduct a simulation study to evaluate the performance of the proposed design using a real clinical trial example.

RESULTS

Our simulation results show that asBOINcomb is more accurate and stable than BOINcomb, especially in some extreme scenarios. Specifically, in all ten scenarios, the percentage of correct selection is higher than the BOINcomb design within 30 to 60 patients.

CONCLUSION

The proposed asBOINcomb design is transparent and simple to implement and can reduce the trial sample size while maintaining accuracy compared with the BOINcomb design.

Modeling synergism in early phase cancer trials with drug combination with continuous dose levels: is there an added value?

In parametric Bayesian designs of early phase cancer clinical trials with drug combinations exploring a discrete set of partially ordered doses, several authors claimed that there is no added value in including an interaction term to model synergism between the two drugs. In this paper, we investigate these claims in the setting of continuous dose levels of the two agents. Parametric models will be used to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity and efficacy. Trial design proceeds by treating cohorts of two patients simultaneously receiving different dose combinations and response adaptive randomization. We compare trial safety and efficiency of the estimated maximum tolerated dose (MTD) curve between models that include an interaction term with models without the synergism parameter with extensive simulations. Under a selected class of dose-toxicity models and dose escalation algorithm, we found that not including an interaction term in the model can compromise the safety of the trial and reduce the pointwise reliability of the estimated MTD curve.

A NOVEL FRAMEWORK TO ESTIMATE MULTIDIMENSIONAL MINIMUM EFFECTIVE DOSES USING ASYMMETRIC POSTERIOR GAIN AND ϵ-TAPERING

In this article we address the problem of estimating minimum effective doses in dose-finding clinical trials of multidimensional treatment. We are motivated by a behavioral intervention trial where we introduce sedentary breaks to subjects with a goal to reduce their glucose level monitored over 8 hours. Each sedentary break regimen is defined by two elements: break frequency and break duration. The trial aims to identify minimum combinations of frequency and duration that shift mean glucose, that is, the minimum effective dose (MED) combinations. The means of glucose reduction associated with the dose combinations are only partially ordered. To circumvent constrained estimation due to partial ordering, we propose estimating the MED by maximizing a weighted product of combinationwise posterior gains. The estimation adopts an asymmetric gain function, indexed by a decision parameter ϵ , which defines the relative gains of a true negative decision and a true positive decision. We also introduce an adaptive ϵ -tapering algorithm to be used in conjunction with the estimation method. Simulation studies show that using asymmetric gain with a carefully chosen ϵ is critical to keeping false discoveries low, while ϵ -tapering adds to the probability of identifying truly effective doses (i.e., true positives). Under an ensemble of scenarios for the sedentary break study, ϵ -tapering yields consistently high true positive rates across scenarios and achieves about 90% true positive rate, compared to 68% by a nonadaptive design with comparable false discovery rate.

Accuracy and Safety of Novel Designs for Phase I Drug-Combination Oncology Trials*

Despite numerous innovative designs having been published for phase I drug-combination dose finding trials, their use in real applications is rather limited. As a working group under the American Statistical Association Biopharmaceutical Section, our goal is to identify the unique challenges associated with drug combination, share industry's experiences with combination trials, and investigate the pros and cons of the existing designs. Toward this goal, we review seven existing designs and distinguish them based on the criterion of whether their primary objectives are to find a single maximum tolerated dose (MTD) or the MTD contour (i.e., multiple MTDs). Numerical studies, based on either industry-specified fixed scenarios or randomly generated scenarios, are performed to assess their relative accuracy, safety, and ease of implementation. We show that the algorithm-based 3+3 design has poor performance and often fails to find the MTD. The performance of model-based combination trial designs is mixed: some demonstrate high accuracy of finding the MTD but poor safety, while others are safe but with compromised identification accuracy. In comparison, the model-assisted designs, such as BOIN and waterfall designs, have competitive and balanced performance in the accuracy of MTD identification and patient safety, and are also simple to implement, thus offering an attractive approach to designing phase I drug-combination trials. By taking into consideration the design's operating characteristics, ease of implementation and regulation, the need for advanced infrastructures, as well as the risk of regulatory acceptance, our paper offers practical guidance on the selection of a suitable dose-finding approach for designing future combination trials.

SEMIPARAMETRIC DOSE FINDING METHODS FOR PARTIALLY ORDERED DRUG COMBINATIONS

We investigate a statistical framework for Phase I clinical trials that test the safety of two or more agents in combination. For such studies, the traditional assumption of a simple monotonic relation between dose and the probability of an adverse event no longer holds. Nonetheless, the dose toxicity (adverse event) relationship will obey an assumption of partial ordering in that there will be pairs of combinations for which the ordering of the toxicity probabilities is known. Some authors have considered how to best estimate the maximum tolerated dose (a dose providing a rate of toxicity as close as possible to some target rate) in this setting. A related, and equally interesting, problem is to partition the 2-dimensional dose space into two sub-regions: doses with probabilities of toxicity lower and greater than the target. We carry out a detailed investigation of this problem. The theoretical framework for this is the recently presented semiparametric dose finding method. This results in a number of proposals one of which can be viewed as an extension of the Product of Independent beta Priors Escalation method (PIPE). We derive useful asymptotic properties which also apply to the PIPE method when seen as a special case of the more general method given here. Simulation studies provide added confidence concerning the good behaviour of the operating characteristics.

BOIN: a novel Bayesian design platform to accelerate early phase brain tumor clinical trials

Despite decades of extensive research, the progress in developing effective treatments for primary brain tumors lags behind that of other cancers, largely due to the unique challenges of brain tumors (eg, the blood-brain barrier and high heterogeneity) that limit the delivery and efficacy of many therapeutic agents. One way to address this issue is to employ novel trial designs to better optimize the treatment regimen (eg, dose and schedule) in early phase trials to improve the success rate of subsequent phase III trials. The objective of this article is to introduce Bayesian optimal interval (BOIN) designs as a novel platform to design various types of early phase brain tumor trials, including single-agent and combination regimen trials, trials with late-onset toxicities, and trials aiming to find the optimal biological dose (OBD) based on both toxicity and efficacy. Unlike many novel Bayesian adaptive designs, which are difficult to understand and complicated to implement by clinical investigators, the BOIN designs are self-explanatory and user friendly, yet yield more robust and powerful operating characteristics than conventional designs. We illustrate the BOIN designs using a phase I clinical trial of brain tumor and provide software (freely available at www.trialdesign.org) to facilitate the application of the BOIN design.

Adapting isotonic dose-finding to a dynamic set of drug combinations with application to a phase I leukemia trial

BACKGROUND/AIMS

This article describes the proposed design of a phase I study evaluating the safety of ceramide nanoliposome and vinblastine among an initial set of 19 possible dose combinations in patients with relapsed/refractory acute myeloid leukemia and patients with untreated acute myeloid leukemia who are not candidates for intensive induction chemotherapy.

METHODS

Extensive collaboration between statisticians and clinical investigators revealed the need to incorporate several adaptive features into the design, including the flexibility of adding or eliminating certain dose combinations based on safety criteria applied to multiple dose pairs. During the design stage, additional dose levels of vinblastine were added, increasing the dimension of the drug combination space and thus the complexity of the problem. Increased complexity made application of existing drug combination dose-finding methods unsuitable in their current form.

RESULTS

Our solution to these challenges was to adapt a method based on isotonic regression to meet the research objectives of the study. Application of this adapted method is described herein, and a simulation study of the design's operating characteristics is conducted.

CONCLUSION

The aim of this article is to bring to light examples of novel design applications as a means of augmenting the implementation of innovative designs in the future and to demonstrate the flexibility of adaptive designs in satisfying changing design conditions.

CWL: A conditional weighted likelihood method to account for the delayed joint toxicity-efficacy outcomes for phase I/II clinical trials

The delayed outcome issue is common in early phase dose-finding clinical trials. This problem becomes more intractable in phase I/II clinical trials because both toxicity and efficacy responses are subject to the delayed outcome issue. The existing methods applying for the phase I trials cannot be used directly for the phase I/II trial due to a lack of capability to model the joint toxicity-efficacy distribution. In this paper, we propose a conditional weighted likelihood (CWL) method to circumvent this issue. The key idea of the CWL method is to decompose the joint probability into the product of marginal and conditional probabilities and then weight each probability based on each patient's actual follow-up time. The CWL method makes no parametric model assumption on either the dose-response curve or the toxicity-efficacy correlation and therefore can be applied to any existing phase I/II trial design. Numerical trial applications show that the proposed CWL method yields desirable operating characteristics.

A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades

We propose a Bayesian adaptive design for early phase drug combination cancer trials incorporating ordinal grade of toxicities. Parametric models are used to describe the relationship between the dose combinations and the probabilities of the ordinal toxicities under the proportional odds assumption. Trial design proceeds by treating cohorts of two patients simultaneously receiving different dose combinations. Specifically, at each stage of the trial, we seek the dose of one agent by minimizing the Bayes risk with respect to a loss function given the current dose of the other agent. We consider two types of loss functions corresponding to the Continual Reassessment Method (CRM) and Escalation with Overdose Control (EWOC). At the end of the trial, we estimate the MTD curve as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD by comparing this design to the one that uses a binary indicator of DLT. The methodology is further adapted to the case of a pre-specified discrete set of dose combinations.

Bayesian adaptive linearization method for phase I drug combination trials with dimension reduction

Many phase I drug combination designs have been proposed to find the maximum tolerated combination (MTC). Due to the two-dimension nature of drug combination trials, these designs typically require complicated statistical modeling and estimation, which limit their use in practice. In this article, we propose an easy-to-implement Bayesian phase I combination design, called Bayesian adaptive linearization method (BALM), to simplify the dose finding for drug combination trials. BALM takes the dimension reduction approach. It selects a subset of combinations, through a procedure called linearization, to convert the two-dimensional dose matrix into a string of combinations that are fully ordered in toxicity. As a result, existing single-agent dose-finding methods can be directly used to find the MTC. In case that the selected linear path does not contain the MTC, a dose-insertion procedure is performed to add new doses whose expected toxicity rate is equal to the target toxicity rate. Our simulation studies show that the proposed BALM design performs better than competing, more complicated combination designs.

How to design a dose-finding study on combined agents: Choice of design and development of R functions

BACKGROUND

In oncology, the aim of dose-finding phase I studies is to find the maximum tolerated dose for further studies. The use of combinations of two or more agents is increasing. Several dose-finding designs have been proposed for this situation. Numerous publications have however pointed out the complexity of evaluating therapies in combination due to difficulties in choosing between different designs for an actual trial, as well as complications related to their implementation and application in practice.

METHODS

In this work, we propose R functions for Wang and Ivanova's approach. These functions compute the dose for the next patients enrolled and provide a simulation study in order to calibrate the design before it is applied and to assess the performance of the design in different scenarios of dose-toxicity relationships. This choice of the method was supported by a simulation study which the aim was to compare two designs in the context of an actual phase I trial: i) in 2005, Wang and Ivanova developed an empirical three-parameter model-based method in Bayesian inference, ii) in 2008, Yuan and Yin proposed a simple, adaptive two-dimensional dose-finding design. In particular, they converted the two-dimensional dose-finding trial to a series of one-dimensional dose-finding sub-trials by setting the dose of one drug at a fixed level. The performance assessment of Wang's design was then compared with those of designs presented in the paper by Hirakawa et al. (2015) in their simulation context.

RESULTS AND CONCLUSION

It is recommended to assess the performances of the designs in the context of the clinical trial before beginning the trial. The two-dimensional dose-finding design proposed by Wang and Ivanova is a comprehensive approach that yields good performances. The two R functions that we propose can facilitate the use of this design in practice.

Model-Assisted Designs for Early-Phase Clinical Trials: Simplicity Meets Superiority

Drug development enterprise is struggling because of prohibitively high costs and slow progress. There is urgent need for adoption of novel adaptive designs to improve the efficiency and success of clinical trials. A major barrier is that many conventional designs are inadequate for modern drug development, yet most novel adaptive designs are difficult to understand, require complicated statistical modeling, demand complex computation, and need expensive infrastructure for implementation. The objective of this article is to introduce and review a class of novel adaptive designs, known as model-assisted designs, to remove this barrier and increase the use of novel adaptive designs. Model-assisted designs enjoy superior performance comparable to more complicated, model-based adaptive designs, but their decision rule can be pretabulated and included in the protocol-thus implemented as simply as the conventional designs. We review state-of-the-art model-assisted designs for phase I clinical trials for single-agent, drug-combination and late-onset toxicity scenarios. We also briefly introduce model-assisted designs for phase II trials to handle binary, coprimary endpoints and delayed response. Freely available user-friendly software and trial examples (trialdesign.org) facilitate the adoption of model-assisted designs.

CRM2DIM: A SAS macro for implementing the dual-agent Bayesian continual reassessment method

BACKGROUND AND OBJECTIVE

The continual reassessment method (CRM) is a model-based dose-finding design for single-agent phase I oncology trials. With the advance of targeted therapies in oncology, more and more phase I trials investigate drug combinations rather than a single agent in order to find one or more maximum tolerated dose combinations. Several designs have been proposed for such dose-finding trials but only a few software packages are available to implement them. One of the designs is the two-dimensional Bayesian CRM proposed by Wang and Ivanova. Our goal was to provide an easy-to-use program to implement this design.

METHODS

We developed a new SAS macro, CRM2DIM, for implementing this design. This macro can be used to run a phase I dose-finding trial for two-drug combination and to perform simulations.

RESULTS

We describe the program with its different features, including the possibility of running an initial design (start-up rule), the possibility of incorporating historical data, and the choice of using either a power or a logistic regression model with or without interaction term. We illustrate our program by presenting simulation results and by a hypothetical trial example.

CONCLUSIONS

The CRM2DIM macro provides a SAS implementation of the two-dimensional Bayesian CRM for dual-agent phase I oncology trials. It is an easy-to-use program that includes many useful features and provides statisticians involved in the early phases of development a new tool for designing dual-agent phase I oncology trials.

AAA: triple adaptive Bayesian designs for the identification of optimal dose combinations in dual-agent dose finding trials

We propose a flexible design for the identification of optimal dose combinations in dual-agent dose finding clinical trials. The design is called AAA, standing for three adaptations: adaptive model selection, adaptive dose insertion and adaptive cohort division. The adaptations highlight the need and opportunity for innovation for dual-agent dose finding and are supported by the numerical results presented in the proposed simulation studies. To our knowledge, this is the first design that allows for all three adaptations at the same time. We find that AAA enhances the chance of finding the optimal dose combinations and shortens the trial duration. A clinical trial is being planned to apply the AAA design and a Web tool is being developed for both statisticians and non-statisticians.

Two-stage design for phase I-II cancer clinical trials using continuous dose combinations of cytotoxic agents

We present a two-stage phase I/II design of a combination of two drugs in cancer clinical trials. The goal is to estimate safe dose combination regions with a desired level of efficacy. In stage I, conditional escalation with overdose control is used to allocate dose combinations to successive cohorts of patients and the maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. In stage II, we propose a Bayesian adaptive design for conducting the phase II trial to determine dose combination regions along the MTD curve with a desired level of efficacy. The methodology is evaluated by extensive simulations and application to a real trial.

Cancer phase I trial design using drug combinations when a fraction of dose limiting toxicities is attributable to one or more agents

Drug combination trials are increasingly common nowadays in clinical research. However, very few methods have been developed to consider toxicity attributions in the dose escalation process. We are motivated by a trial in which the clinician is able to identify certain toxicities that can be attributed to one of the agents. We present a Bayesian adaptive design in which toxicity attributions are modeled via copula regression and the maximum tolerated dose (MTD) curve is estimated as a function of model parameters. The dose escalation algorithm uses cohorts of two patients, following the continual reassessment method (CRM) scheme, where at each stage of the trial, we search for the dose of one agent given the current dose of the other agent. The performance of the design is studied by evaluating its operating characteristics when the underlying model is either correctly specified or misspecified. We show that this method can be extended to accommodate discrete dose combinations.

A Bayesian Adaptive Design in Cancer Phase I Trials using Dose Combinations in the Presence of a Baseline Covariate

A Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials that takes into account patients heterogeneity thought to be related to treatment susceptibility is described. The estimation of the maximum tolerated dose (MTD) curves is a function of a baseline covariate using two cytotoxic agents. A logistic model is used to describe the relationship between the doses, baseline covariate, and the probability of dose limiting toxicity (DLT). Trial design proceeds by treating cohorts of two patients simultaneously using escalation with overdose control (EWOC), where at each stage of the trial, the next dose combination corresponds to the α quantile of the current posterior distribution of the MTD of one of two agents at the current dose of the other agent and the next patient's baseline covariate value. The MTD curves are estimated as function of Bayes estimates of the model parameters at the end of trial. Average DLT, pointwise average bias, and percent of dose recommendation at dose combination neighborhoods around the true MTD are compared to the design that uses the covariate to the one that ignores the baseline characteristic. We also examine the performance of the approach under model misspecifications for the true dose-toxicity relationship. The methodology is further illustrated by the case of a pre-specified discrete set of dose combinations.

Predicting Successful Phase Advancement and Regulatory Approval in Multiple Myeloma From Phase I Overall Response Rates

PURPOSE

Drug development in oncology is resource intensive, time consuming, and frequently unsuccessful. Here, we hypothesized that therapeutic benefit of published phase I studies of antimyeloma investigational agents was associated with advancement to phase II and future regulatory approval.

PATIENTS AND METHODS

Seventy four phase I trials that treated patients with multiple myeloma (n = 2,408) conducted from 2004 to 2015 were analyzed to assess drug safety, efficacy, phase advancement, and regulatory approval.

RESULTS

The median overall response rate (ORR) for all single-agent trials evaluated was 13.2%. However, the ORR in trials that advanced to phase II was 19%, whereas it was only 4% in trials that failed to advance. The median ORR was 23% for trials testing agents that were ultimately approved by the US Food and Drug Administration compared with only 8% for trials testing agents that were not approved (hazard ratio, 2.21; 95% CI, 2.01 to 2.61; P = .012). Importantly, the absolute number of phase I trials in multiple myeloma, but not the success rate, significantly increased over the period studied. The proportion of industry-sponsored trials also steadily increased over that same period. The ratio of initial dose to maximum tolerated dose was 0.29, suggesting that many patients were undertreated.

CONCLUSION

Investigational agents with higher ORRs in phase I trials were more likely to advance to phase II trials and achieve US Food and Drug Administration approval. Our results suggest that designing phase I trials to maximize the antimyeloma efficacy of a given compound may lead to more successful and cost-effective drug development.

Hierarchical models for sharing information across populations in phase I dose-escalation studies

The primary goal of a phase I clinical trial in oncology is to evaluate the safety of a novel treatment and identify the maximum tolerated dose, defined as the maximum dose with a toxicity rate below some pre-specified threshold. Researchers are often interested in evaluating the performance of a novel treatment in multiple patient populations, which may require multiple phase I trials if the treatment is to be used with background standard-of-care that varies by population. An alternate approach is to run parallel trials but combine the data through a hierarchical model that allows for a different maximum tolerated dose in each population but shares information across populations to achieve a more accurate estimate of the maximum tolerated dose. In this manuscript, we discuss hierarchical extensions of three commonly used models for the dose–toxicity relationship in phase I oncology trials. We then propose three dose-finding guidelines for phase I oncology trials using hierarchical modeling. The proposed guidelines allow us to fully realize the benefits of hierarchical modeling while achieving a similar toxicity profile to standard phase I designs. Finally, we evaluate the operating characteristics of a phase I clinical trial using the proposed hierarchical models and dose-finding guidelines by simulation. Our simulation results suggest that incorporating hierarchical modeling in phase I dose-escalation studies will increase the probability of correctly identifying the maximum tolerated dose and the number of patients treated at the maximum tolerated dose, while decreasing the rate of dose-limiting toxicities and number of patients treated above the maximum tolerated dose, in most cases.

Dose Finding for Drug Combination in Early Cancer Phase I Trials using Conditional Continual Reassessment Method

We describe a dose escalation algorithm for drug combinations in cancer phase I clinical trials. Parametric models for describing the association between the doses and the probability of dose limiting toxicity are used assuming univariate monotonicity of the dose-toxicity relationship. Trial design proceeds using the continual reassessment method, where at each stage of the trial, we seek the dose of one agent with estimated probability of toxicity closest to a target probability of toxicity given the current dose of the other agent. A Bayes estimate of the maximum tolerated dose (MTD) curve is proposed at the conclusion of the trial for continuous doses or a set of MTDs is determined in the case of discrete dose levels. We evaluate design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD under various model generated scenarios and misspecification. The method is further assessed for varying algorithms enrolling cohorts of two and three patients receiving different doses and compared to previous approaches such as escalation with overdose control and two-dimensional design.

A practical Bayesian design to identify the maximum tolerated dose contour for drug combination trials

Drug combination therapy has become the mainstream approach to cancer treatment. One fundamental feature that makes combination trials different from single-agent trials is the existence of the maximum tolerated dose (MTD) contour, that is, multiple MTDs. As a result, unlike single-agent phase I trials, which aim to find a single MTD, it is often of interest to find the MTD contour for combination trials. We propose a new dose-finding design, the waterfall design, to find the MTD contour for drug combination trials. Taking the divide-and-conquer strategy, the waterfall design divides the task of finding the MTD contour into a sequence of one-dimensional dose-finding processes, known as subtrials. The subtrials are conducted sequentially in a certain order, such that the results of each subtrial will be used to inform the design of subsequent subtrials. Such information borrowing allows the waterfall design to explore the two-dimensional dose space efficiently using a limited sample size and decreases the chance of overdosing and underdosing patients. To accommodate the consideration that doses on the MTD contour may have very different efficacy or synergistic effects because of drug-drug interaction, we further extend our approach to a phase I/II design with the goal of finding the MTD with the highest efficacy. Simulation studies show that the waterfall design is safer and has higher probability of identifying the true MTD contour than some existing designs. The R package "BOIN" to implement the waterfall design is freely available from CRAN. Copyright © 2016 John Wiley & Sons, Ltd.

Effect of design specifications in dose-finding trials for combination therapies in oncology

Model-based dose-finding methods for a combination therapy involving two agents in phase I oncology trials typically include four design aspects namely, size of the patient cohort, three-parameter dose-toxicity model, choice of start-up rule, and whether or not to include a restriction on dose-level skipping. The effect of each design aspect on the operating characteristics of the dose-finding method has not been adequately studied. However, some studies compared the performance of rival dose-finding methods using design aspects outlined by the original studies. In this study, we featured the well-known four design aspects and evaluated the impact of each independent effect on the operating characteristics of the dose-finding method including these aspects. We performed simulation studies to examine the effect of these design aspects on the determination of the true maximum tolerated dose combinations as well as exposure to unacceptable toxic dose combinations. The results demonstrated that the selection rates of maximum tolerated dose combinations and UTDCs vary depending on the patient cohort size and restrictions on dose-level skipping However, the three-parameter dose-toxicity models and start-up rules did not affect these parameters. Copyright © 2016 John Wiley & Sons, Ltd.

A Bayesian adaptive design for estimating the maximum tolerated dose curve using drug combinations in cancer phase I clinical trials

We present a cancer phase I clinical trial design of a combination of two drugs with the goal of estimating the maximum tolerated dose curve in the two-dimensional Cartesian plane. A parametric model is used to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re-parameterized in terms of the probabilities of toxicities at dose combinations corresponding to the minimum and maximum doses available in the trial and the interaction parameter. Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC), where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. The maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. Performance of the trial is studied by evaluating its design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD curve and under model misspecifications for the true dose-toxicity relationship. The method is further extended to accommodate discrete dose combinations and compared with previous approaches under several scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

A Bayesian Adaptive Design for Combination of Three Drugs in Cancer Phase I Clinical Trials

We describe a Bayesian adaptive design for early phase cancer trials of a combination of three agents. This is an extension of an earlier work by the authors by allowing all three agents to vary during the trial and by assigning different drug combinations to cohorts of three patients. The primary objective is to estimate the Maximum Tolerated Dose (MTD) surface in the three-dimensional Cartesian space. A class of linear models on the logit of the probability of Dose Limiting Toxicity (DLT) are used to describe the relationship between doses of the three drugs and the probability of DLT. Trial design proceeds using conditional escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current doses of the other two agents. The MTD surface is estimated at the end of the trial as a function of Bayes estimates of the model parameters. Operating characteristics are evaluated with respect to trial safety and percent of dose recommendation at dose combination neighborhoods around the true MTD surface.

A comparative study of adaptive dose-finding designs for phase I oncology trials of combination therapies

Little is known about the relative performance of competing model-based dose-finding methods for combination phase I trials. In this study, we focused on five model-based dose-finding methods that have been recently developed. We compared the recommendation rates for true maximum-tolerated dose combinations (MTDCs) and over-dose combinations among these methods under 16 scenarios for 3 × 3, 4 × 4, 2 × 4, and 3 × 5 dose combination matrices. We found that performance of the model-based dose-finding methods varied depending on (1) whether the dose combination matrix is square or not; (2) whether the true MTDCs exist within the same group along the diagonals of the dose combination matrix; and (3) the number of true MTDCs. We discuss the details of the operating characteristics and the advantages and disadvantages of the five methods compared.

Practical designs for Phase I combination studies in oncology

Phase I trials evaluating the safety of multidrug combinations are becoming more common in oncology. Despite the emergence of novel methodology in the area, it is rare that innovative approaches are used in practice. In this article, we review three methods for Phase I combination studies that are easy to understand and straightforward to implement. We demonstrate the operating characteristics of the designs through illustration in a single trial, as well as through extensive simulation studies, with the aim of increasing the use of novel approaches in Phase I combination studies. Design specifications and software capabilities are also discussed.

A two-dimensional biased coin design for dual-agent dose-finding trials

Background:

Given the limited efficacy observed with single agents, there is growing interest in Phase I clinical trial designs that allow for identification of the maximum tolerated combination of two agents.

Purpose:

Existing parametric designs may suffer from over- or under-parameterization. Thus, we have designed a nonparametric approach that can be easily understood and implemented for combination trials.

Methods:

We propose a two-stage adaptive biased coin design that extends existing methods for single-agent trials to dual-agent dose-finding trials. The basic idea of our design is to divide the entire trial into two stages and apply the biased coin design, with modification, in each stage.

Results:

We compare the operating characteristics of our design to four competing parametric approaches via simulation in several numerical examples. Under all simulation scenarios we have examined, our method performs well in terms of identification of the maximum tolerated combination and allocation of patients relative to the performance of its competitors.

Limitations:

In our design, stopping rule criteria and the distribution of the total sample size among the two stages are context-dependent, and both need careful consideration before adopting our design in practice. Efficacy is not a part of the dose-assignment algorithm, nor used to define the maximum tolerated combination.

Conclusion:

Our design inherits the favorable statistical properties of the biased coin design, is competitive with existing designs, and promotes patient safety by limiting patient exposure to toxic combinations whenever possible.

A practical design for a dual-agent dose-escalation trial that incorporates pharmacokinetic data

Traditionally, model-based dose-escalation trial designs recommend a dose for escalation based on an assumed dose-toxicity relationship. Pharmacokinetic data are often available but are currently only utilised by clinical teams in a subjective manner to aid decision making if the dose-toxicity model recommendation is felt to be too high. Formal incorporation of pharmacokinetic data in dose-escalation could therefore make the decision process more efficient and lead to an increase in the precision of the resulting recommended dose, as well as decreasing the subjectivity of its use. Such an approach is investigated in the dual-agent setting using a Bayesian design, where historical single-agent data are available to advise the use of pharmacokinetic data in the dual-agent setting. The dose-toxicity and dose-exposure relationships are modelled independently and the outputs combined in the escalation rules. Implementation of stopping rules highlight the practicality of the design. This is demonstrated through an example which is evaluated using simulation.

A product of independent beta probabilities dose escalation design for dual-agent phase I trials

Dual-agent trials are now increasingly common in oncology research, and many proposed dose-escalation designs are available in the statistical literature. Despite this, the translation from statistical design to practical application is slow, as has been highlighted in single-agent phase I trials, where a 3 + 3 rule-based design is often still used. To expedite this process, new dose-escalation designs need to be not only scientifically beneficial but also easy to understand and implement by clinicians. In this paper, we propose a curve-free (nonparametric) design for a dual-agent trial in which the model parameters are the probabilities of toxicity at each of the dose combinations. We show that it is relatively trivial for a clinician's prior beliefs or historical information to be incorporated in the model and updating is fast and computationally simple through the use of conjugate Bayesian inference. Monotonicity is ensured by considering only a set of monotonic contours for the distribution of the maximum tolerated contour, which defines the dose-escalation decision process. Varied experimentation around the contour is achievable, and multiple dose combinations can be recommended to take forward to phase II. Code for R, Stata and Excel are available for implementation.

Advances in Statistical Approaches Oncology Drug Development

We describe some recent developments in statistical methodology and practice in oncology drug development from an academic and an industry perspective. Many adaptive designs were pioneered in oncology, and oncology is still at the forefront of novel methods to enable better and faster Go/No-Go decision making while controlling the cost.

Bayesian dose-finding designs for combination of molecularly targeted agents assuming partial stochastic ordering

Molecularly targeted agent (MTA) combination therapy is in the early stages of development. When using a fixed dose of one agent in combinations of MTAs, toxicity and efficacy do not necessarily increase with an increasing dose of the other agent. Thus, in dose-finding trials for combinations of MTAs, interest may lie in identifying the optimal biological dose combinations (OBDCs), defined as the lowest dose combinations (in a certain sense) that are safe and have the highest efficacy level meeting a prespecified target. The limited existing designs for these trials use parametric dose–efficacy and dose–toxicity models. Motivated by a phase I/II clinical trial of a combination of two MTAs in patients with pancreatic, endometrial, or colorectal cancer, we propose Bayesian dose-finding designs to identify the OBDCs without parametric model assumptions. The proposed approach is based only on partial stochastic ordering assumptions for the effects of the combined MTAs and uses isotonic regression to estimate partially stochastically ordered marginal posterior distributions of the efficacy and toxicity probabilities. We demonstrate that our proposed method appropriately accounts for the partial ordering constraints, including potential plateaus on the dose–response surfaces, and is computationally efficient. We develop a dose-combination-finding algorithm to identify the OBDCs. We use simulations to compare the proposed designs with an alternative design based on Bayesian isotonic regression transformation and a design based on parametric change-point dose–toxicity and dose–efficacy models and demonstrate desirable operating characteristics of the proposed designs. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

A Dose-Finding Method Based on Multiple Dosing in Two-Agent Combination Phase I Trials

Here, we developed a new dose-finding method that partitions a cohort of patients based on the number of dose combinations within a prespecified acceptable toxicity range in two-agent combination Phase I trials. In the proposed method, patients in the same cohort are partitioned according to several dose combinations, although most of the existing methods allocate patients in the same cohort according to a single-dose combination. We compared the operating characteristics of the proposed and existing methods through simulation studies.

Effective sample size for computing prior hyperparameters in Bayesian phase I-II dose-finding

BACKGROUND

The efficacy-toxicity trade-off based design is a practical Bayesian phase I-II dose-finding methodology. Because the design's performance is very sensitive to prior hyperparameters and the shape of the target trade-off contour, specifying these two design elements properly is essential.

PURPOSE

The goals are to provide a method that uses elicited mean outcome probabilities to derive a prior that is neither overly informative nor overly disperse, and practical guidelines for specifying the target trade-off contour.

METHODS

A general algorithm is presented that determines prior hyperparameters using least squares penalized by effective sample size. Guidelines for specifying the trade-off contour are provided. These methods are illustrated by a clinical trial in advanced prostate cancer. A new version of the efficacy-toxicity program is provided for implementation.

RESULTS

Together, the algorithm and guidelines provide substantive improvements in the design's operating characteristics.

LIMITATIONS

The method requires a substantial number of elicited values and design parameters, and computer simulations are required to obtain an acceptable design.

CONCLUSION

The two key improvements greatly enhance the efficacy-toxicity design's practical usefulness and are straightforward to implement using the updated computer program. The algorithm for determining prior hyperparameters to ensure a specified level of informativeness is general, and may be applied to models other than that underlying the efficacy-toxicity method.

Dose finding with drug combinations in cancer phase I clinical trials using conditional escalation with overdose control

We present a Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials. The goal is to estimate the maximum tolerated dose (MTD) as a curve in the two-dimensional Cartesian plane. We use a logistic model to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re-parameterized in terms of parameters clinicians can easily interpret. Trial design proceeds using univariate escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. At the end of the trial, an estimate of the MTD curve is proposed as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial design and percent of dose recommendation at dose combination neighborhoods around the true MTD curve. We also examine the performance of the approach under model misspecifications for the true dose-toxicity relationship.

Phase I/II adaptive design for drug combination oncology trials

Existing statistical methodology on dose finding for combination chemotherapies has focused on toxicity considerations alone in finding a maximum tolerated dose combination to recommend for further testing of efficacy in a phase II setting. Recently, there has been increasing interest in integrating phase I and phase II trials in order to facilitate drug development. In this article, we propose a new adaptive phase I/II method for dual-agent combinations that takes into account both toxicity and efficacy after each cohort inclusion. The primary objective, both within and at the conclusion of the trial, becomes finding a single dose combination with an acceptable level of toxicity that maximizes efficacious response. We assume that there exist monotone dose-toxicity and dose-efficacy relationships among doses of one agent when the dose of other agent is fixed. We perform extensive simulation studies that demonstrate the operating characteristics of our proposed approach, and we compare simulated results to existing methodology in phase I/II design for combinations of agents.

A Bayesian Dose-finding Design for Oncology Clinical Trials of Combinational Biological Agents

Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which efficacy and toxicity monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a dose-finding design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships.

A Bayesian Dose-finding Design for Drug Combination Trials with Delayed Toxicities

We propose a Bayesian adaptive dose-finding design for drug combination trials with delayed toxicity. We model the dose-toxicity relationship using the Finney model, a model widely used in drug-drug interaction studies. The intuitive interpretations of the Finney model facilitate incorporating the available prior dose-toxicity information from single-agent trials into combination trials through prior elicitation. We treat unobserved delayed toxicity outcomes as missing data and handle them using Bayesian data augmentation. We conduct extensive simulation studies to examine the operating characteristics of the proposed method under various practical scenarios. Results show that the proposed design is safe and able to select the target dose combinations with high probabilities.

Use of Bayesian statistics in drug development: Advantages and challenges

Mainly, two statistical methodologies are applicable to the design and analysis of clinical trials: frequentist and Bayesian. Most traditional clinical trial designs are based on frequentist statistics. In frequentist statistics prior information is utilized formally only in the design of a clinical trial but not in the analysis of the data. On the other hand, Bayesian statistics provide a formal mathematical method for combining prior information with current information at the design stage, during the conduct of the trial, and at the analysis stage. It is easier to implement adaptive trial designs using Bayesian methods than frequentist methods. The Bayesian approach can also be applied for post-marketing surveillance purposes and in meta-analysis. The basic tenets of good trial design are same for both Bayesian and frequentist trials. It has been recommended that the type of analysis to be used (Bayesian or frequentist) should be chosen beforehand. Switching to an analysis method that produces a more favorable outcome after observing the data is not recommended.

Adaptive designs for dual-agent phase I dose-escalation studies

Anticancer agents used in combination are fundamental to successful cancer treatment, particularly in a curative setting. For dual-agent phase I trials, the goal is to identify drug doses and schedules for further clinical testing. However, current methods for establishing the recommended phase II dose for agents in combination can fail to fully explore drug interactions. With increasing numbers of anticancer drugs requiring testing, new adaptive model-based trial designs that improve on current practice have been proposed, although uptake has been minimal. We describe the methods available and discuss some of the opportunities and challenges faced in dual-agent phase I trials, as well as giving examples of trials in which adaptive designs have been implemented successfully. Improving the design and execution of phase I trials of drug combinations critically relies on collaboration between the statistical and clinical communities to facilitate the implementation of adaptive, model-based designs.