Application of Bayesian hierarchical models for phase I/II clinical trials in oncology

Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade‐offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving‐reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.     

Dynamic ordering design for dose finding in drug-combination trials

Drug-combination studies have become increasingly popular in oncology. One of the critical concerns in phase I drug-combination trials is the uncertainty in toxicity evaluation. Most of the existing phase I designs aim to identify the maximum tolerated dose (MTD) by reducing the two-dimensional searching space to one dimension via a prespecified model or splitting the two-dimensional space into multiple one-dimensional subspaces based on the partially known toxicity order. Nevertheless, both strategies often lead to complicated trials which may either be sensitive to model assumptions or induce longer trial durations due to subtrial split. We develop two versions of dynamic ordering design (DOD) for dose finding in drug-combination trials, where the dose-finding problem is cast in the Bayesian model selection framework. The toxicity order of dose combinations is continuously updated via a two-dimensional pool-adjacent-violators algorithm, and then the dose assignment for each incoming cohort is selected based on the optimal model under the dynamic toxicity order. We conduct extensive simulation studies to evaluate the performance of DOD in comparison with four other commonly used designs under various scenarios. Simulation results show that the two versions of DOD possess competitive performances in terms of correct MTD selection as well as safety, and we apply both versions of DOD to two real oncology trials for illustration.     

A Bayesian dose‐finding design for drug combination clinical trials based on the logistic model

In early phase dose‐finding cancer studies, the objective is to determine the maximum tolerated dose, defined as the highest dose with an acceptable dose‐limiting toxicity rate. Finding this dose for drug‐combination trials is complicated because of drug–drug interactions, and many trial designs have been proposed to address this issue. These designs rely on complicated statistical models that typically are not familiar to clinicians, and are rarely used in practice. The aim of this paper is to propose a Bayesian dose‐finding design for drug combination trials based on standard logistic regression. Under the proposed design, we continuously update the posterior estimates of the model parameters to make the decisions of dose assignment and early stopping. Simulation studies show that the proposed design is competitive and outperforms some existing designs. We also extend our design to handle delayed toxicities. Copyright © 2014 John Wiley & Sons, Ltd.     

Escalation strategies for combination therapy Phase I trials

Phase I clinical trials aim to identify a maximum tolerated dose (MTD), the highest possible dose that does not cause an unacceptable amount of toxicity in the patients. In trials of combination therapies, however, many different dose combinations may have a similar probability of causing a dose‐limiting toxicity, and hence, a number of MTDs may exist. Furthermore, escalation strategies in combination trials are more complex, with possible escalation/de‐escalation of either or both drugs. This paper investigates the properties of two existing proposed Bayesian adaptive models for combination therapy dose‐escalation when a number of different escalation strategies are applied. We assess operating characteristics through a series of simulation studies and show that strategies that only allow ‘non‐diagonal’ moves in the escalation process (that is, both drugs cannot increase simultaneously) are inefficient and identify fewer MTDs for Phase II comparisons. Such strategies tend to escalate a single agent first while keeping the other agent fixed, which can be a severe restriction when exploring dose surfaces using a limited sample size. Meanwhile, escalation designs based on Bayesian D‐optimality allow more varied experimentation around the dose space and, consequently, are better at identifying more MTDs. We argue that for Phase I combination trials it is sensible to take forward a number of identified MTDs for Phase II experimentation so that their efficacy can be directly compared. Researchers, therefore, need to carefully consider the escalation strategy and model that best allows the identification of these MTDs. Copyright © 2012 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.     

Specifications of a continual reassessment method design for phase I trials of combined drugs

In studies of combinations of agents in phase I oncology trials, the dose–toxicity relationship may not be monotone for all combinations, in which case the toxicity probabilities follow a partial order. The continual reassessment method for partial orders (PO‐CRM) is a design for phase I trials of combinations that leans upon identifying possible complete orders associated with the partial order. This article addresses some practical design considerations not previously undertaken when describing the PO‐CRM. We describe an approach in choosing a proper subset of possible orderings, formulated according to the known toxicity relationships within a matrix of combination therapies. Other design issues, such as working model selection and stopping rules, are also discussed. We demonstrate the practical ability of PO‐CRM as a phase I design for combinations through its use in a recent trial designed at the University of Virginia Cancer Center. Copyright © 2013 John Wiley & Sons, Ltd.     

Phase I trial design for drug combinations with Bayesian model averaging

Various statistical models have been proposed for two‐dimensional dose finding in drug‐combination trials. However, it is often a dilemma to decide which model to use when conducting a particular drug‐combination trial. We make a comprehensive comparison of four dose‐finding methods, and for fairness, we apply the same dose‐finding algorithm under the four model structures. Through extensive simulation studies, we compare the operating characteristics of these methods in various practical scenarios. The results show that different models may lead to different design properties and that no single model performs uniformly better in all scenarios. As a result, we propose using Bayesian model averaging to overcome the arbitrariness of the model specification and enhance the robustness of the design. We assign a discrete probability mass to each model as the prior model probability and then estimate the toxicity probabilities of combined doses in the Bayesian model averaging framework. During the trial, we adaptively allocated each new cohort of patients to the most appropriate dose combination by comparing the posterior estimates of the toxicity probabilities with the prespecified toxicity target. The simulation results demonstrate that the Bayesian model averaging approach is robust under various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian adaptive dose‐escalation designs for simultaneously estimating the optimal and maximum safe dose based on safety and efficacy

The main purpose of dose‐escalation trials is to identify the dose(s) that is/are safe and efficacious for further investigations in later studies. In this paper, we introduce dose‐escalation designs that incorporate both the dose‐limiting events and dose‐limiting toxicities (DLTs) and indicative responses of efficacy into the procedure. A flexible nonparametric model is used for modelling the continuous efficacy responses while a logistic model is used for the binary DLTs. Escalation decisions are based on the combination of the probabilities of DLTs and expected efficacy through a gain function. On the basis of this setup, we then introduce 2 types of Bayesian adaptive dose‐escalation strategies. The first type of procedures, called “single objective,” aims to identify and recommend a single dose, either the maximum tolerated dose, the highest dose that is considered as safe, or the optimal dose, a safe dose that gives optimum benefit risk. The second type, called “dual objective,” aims to jointly estimate both the maximum tolerated dose and the optimal dose accurately. The recommended doses obtained under these dose‐escalation procedures provide information about the safety and efficacy profile of the novel drug to facilitate later studies. We evaluate different strategies via simulations based on an example constructed from a real trial on patients with type 2 diabetes, and the use of stopping rules is assessed. We find that the nonparametric model estimates the efficacy responses well for different underlying true shapes. The dual‐objective designs give better results in terms of identifying the 2 real target doses compared to the single‐objective designs.     

Generalized phase I-II designs to increase long term therapeutic success rate

Designs for early phase dose finding clinical trials typically are either phase I based on toxicity, or phase I-II based on toxicity and efficacy. These designs rely on the implicit assumption that the dose of an experimental agent chosen using these short-term outcomes will maximize the agent's long-term therapeutic success rate. In many clinical settings, this assumption is not true. A dose selected in an early phase oncology trial may give suboptimal progression-free survival or overall survival time, often due to a high rate of relapse following response. To address this problem, a new family of Bayesian generalized phase I-II designs is proposed. First, a conventional phase I-II design based on short-term outcomes is used to identify a set of candidate doses, rather than selecting one dose. Additional patients then are randomized among the candidates, patients are followed for a predefined longer time period, and a final dose is selected to maximize the long-term therapeutic success rate, defined in terms of duration of response. Dose-specific sample sizes in the randomization are determined adaptively to obtain a desired level of selection reliability. The design was motivated by a phase I-II trial to find an optimal dose of natural killer cells as targeted immunotherapy for recurrent or treatment-resistant B-cell hematologic malignancies. A simulation study shows that, under a range of scenarios in the context of this trial, the proposed design has much better performance than two conventional phase I-II designs.     

TSNP: A two-stage nonparametric phase I/II clinical trial design for immunotherapy

We develop a transparent and efficient two-stage nonparametric (TSNP) phase I/II clinical trial design to identify the optimal biological dose (OBD) of immunotherapy. We propose a nonparametric approach to derive the closed-form estimates of the joint toxicity–efficacy response probabilities under the monotonic increasing constraint for the toxicity outcomes. These estimates are then used to measure the immunotherapy's toxicity–efficacy profiles at each dose and guide the dose finding. The first stage of the design aims to explore the toxicity profile. The second stage aims to find the OBD, which can achieve the optimal therapeutic effect by considering both the toxicity and efficacy outcomes through a utility function. The closed-form estimates and concise dose-finding algorithm make the TSNP design appealing in practice. The simulation results show that the TSNP design yields superior operating characteristics than the existing Bayesian parametric designs. User-friendly computational software is freely available to facilitate the application of the proposed design to real trials. We provide comprehensive illustrations and examples about implementing the proposed design with associated software.     

A randomized phase I Bayesian dose escalation design for the combination of anti‐cancer drugs

Nowadays, treatment regimens for cancer often involve a combination of drugs. The determination of the doses of each of the combined drugs in phase I dose escalation studies poses methodological challenges. The most common phase I design, the classic ‘3+3' design, has been criticized for poorly estimating the maximum tolerated dose (MTD) and for treating too many subjects at doses below the MTD. In addition, the classic ‘3+3' is not able to address the challenges posed by combinations of drugs. Here, we assume that a control drug (commonly used and well‐studied) is administered at a fixed dose in combination with a new agent (the experimental drug) of which the appropriate dose has to be determined. We propose a randomized design in which subjects are assigned to the control or to the combination of the control and experimental. The MTD is determined using a model‐based Bayesian technique based on the difference of probability of dose limiting toxicities (DLT) between the control and the combination arm. We show, through a simulation study, that this approach provides better and more accurate estimates of the MTD. We argue that this approach may differentiate between an extreme high probability of DLT observed from the control and a high probability of DLT of the combination. We also report on a fictive (simulation) analysis based on published data of a phase I trial of ifosfamide combined with sunitinib.Copyright © 2014 John Wiley & Sons, Ltd.     

TITE‐BOIN‐ET: Time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on both efficacy and toxicity outcomes

One of the primary purposes of an oncology dose‐finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de‐escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late‐onset outcomes. To solve these issues, we propose the time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on cumulative and pending data of both efficacy and toxicity. The new design, named “TITE‐BOIN‐ET” design, is nonparametric and a model‐assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose‐finding trials compared with the model‐based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE‐BOIN‐ET design has advantages compared with the model‐based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE‐BOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose‐finding trials.     

Dose finding with continuous outcome in phase I oncology trials

The goal of a phase I clinical trial in oncology is to find a dose with acceptable dose‐limiting toxicity rate. Often, when a cytostatic drug is investigated or when the maximum tolerated dose is defined using a toxicity score, the main endpoint in a phase I trial is continuous. We propose a new method to use in a dose‐finding trial with continuous endpoints. The new method selects the right dose on par with other methods and provides more flexibility in assigning patients to doses in the course of the trial when the rate of accrual is fast relative to the follow‐up time. Copyright © 2014 John Wiley & Sons, Ltd.     

Incorporating historical information to improve phase I clinical trials

Incorporating historical data has a great potential to improve the efficiency of phase I clinical trials and to accelerate drug development. For model-based designs, such as the continuous reassessment method (CRM), this can be conveniently carried out by specifying a “skeleton,” that is, the prior estimate of dose limiting toxicity (DLT) probability at each dose. In contrast, little work has been done to incorporate historical data into model-assisted designs, such as the Bayesian optimal interval (BOIN), Keyboard, and modified toxicity probability interval (mTPI) designs. This has led to the misconception that model-assisted designs cannot incorporate prior information. In this paper, we propose a unified framework that allows for incorporating historical data into model-assisted designs. The proposed approach uses the well-established “skeleton” approach, combined with the concept of prior effective sample size, thus it is easy to understand and use. More importantly, our approach maintains the hallmark of model-assisted designs: simplicity—the dose escalation/de-escalation rule can be tabulated prior to the trial conduct. Extensive simulation studies show that the proposed method can effectively incorporate prior information to improve the operating characteristics of model-assisted designs, similarly to model-based designs.     

Bayesian optimization design for dose-finding based on toxicity and efficacy outcomes in phase I/II clinical trials

In phase I trials, the main goal is to identify a maximum tolerated dose under an assumption of monotonicity in dose–response relationships. On the other hand, such monotonicity is no longer applied to biologic agents because a different mode of action from that of cytotoxic agents potentially draws unimodal or flat dose–efficacy curves. Therefore, biologic agents require an optimal dose that provides a sufficient efficacy rate under an acceptable toxicity rate instead of a maximum tolerated dose. Many trials incorporate both toxicity and efficacy data, and drugs with a variety of modes of actions are increasingly being developed; thus, optimal dose estimation designs have been receiving increased attention. Although numerous authors have introduced parametric model-based designs, it is not always appropriate to apply strong assumptions in dose–response relationships. We propose a new design based on a Bayesian optimization framework for identifying optimal doses for biologic agents in phase I/II trials. Our proposed design models dose–response relationships via nonparametric models utilizing a Gaussian process prior, and the uncertainty of estimates is considered in the dose selection process. We compared the operating characteristics of our proposed design against those of three other designs through simulation studies. These include an expansion of Bayesian optimal interval design, the parametric model-based EffTox design, and the isotonic design. In simulations, our proposed design performed well and provided results that were more stable than those from the other designs, in terms of the accuracy of optimal dose estimations and the percentage of correct recommendations.     

Dose finding when the target dose is on a plateau of a dose–response curve: comparison of fully sequential designs

Consider the problem of estimating a dose with a certain response rate. Many multistage dose‐finding designs for this problem were originally developed for oncology studies where the mean dose–response is strictly increasing in dose. In non‐oncology phase II dose‐finding studies, the dose–response curve often plateaus in the range of interest, and there are several doses with the mean response equal to the target. In this case, it is usually of interest to find the lowest of these doses because higher doses might have higher adverse event rates. It is often desirable to compare the response rate at the estimated target dose with a placebo and/or active control. We investigate which of the several known dose‐finding methods developed for oncology phase I trials is the most suitable when the dose–response curve plateaus. Some of the designs tend to spread the allocation among the doses on the plateau. Others, such as the continual reassessment method and the t‐statistic design, concentrate allocation at one of the doses with the t‐statistic design selecting the lowest dose on the plateau more frequently. Copyright © 2013 John Wiley & Sons, Ltd.     

Improving early phase oncology clinical trial design: The case for finding the optimal biological dose

Historically early phase oncology drug development programmes have been based on the belief that “more is better”. Furthermore, rule-based study designs such as the “3 + 3” design are still often used to identify the MTD. Phillips and Clark argue that newer Bayesian model-assisted designs such as the BOIN design should become the go to designs for statisticians for MTD finding. This short communication goes one stage further and argues that Bayesian model-assisted designs such as the BOIN12 which balances risk-benefit should be included as one of the go to designs for early phase oncology trials, depending on the study objectives. Identifying the optimal biological dose for future research for many modern targeted drugs, immunotherapies, cell therapies and vaccine therapies can save significant time and resources.     

A simulation study of methods for selecting subgroup‐specific doses in phase 1 trials

Patient heterogeneity may complicate dose‐finding in phase 1 clinical trials if the dose‐toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively,it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem,we consider a generalization of the continual reassessment method on the basis of a hierarchical Bayesian dose‐toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup‐specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to 3 alternative approaches,on the basis of nonhierarchical models,that make different types of assumptions about within‐subgroup dose‐toxicity curves. The simulations show that the hierarchical model‐based method is recommended in settings where the dose‐toxicity curves are exchangeable between subgroups. We present practical guidelines for application and provide computer programs for trial simulation and conduct.     

Modelling PK/QT relationships from Phase I dose‐escalation trials for drug combinations and developing quantitative risk assessments of clinically relevant QT prolongations

In current industry practice, it is difficult to assess QT effects at potential therapeutic doses based on Phase I dose‐escalation trials in oncology due to data scarcity, particularly in combinations trials. In this paper, we propose to use dose‐concentration and concentration‐QT models jointly to model the exposures and effects of multiple drugs in combination. The fitted models then can be used to make early predictions for QT prolongation to aid choosing recommended dose combinations for further investigation. The models consider potential correlation between concentrations of test drugs and potential drug–drug interactions at PK and QT levels. In addition, this approach allows for the assessment of the probability of QT prolongation exceeding given thresholds of clinical significance. The performance of this approach was examined via simulation under practical scenarios for dose‐escalation trials for a combination of two drugs. The simulation results show that invaluable information of QT effects at therapeutic dose combinations can be gained by the proposed approaches. Early detection of dose combinations with substantial QT prolongation is evaluated effectively through the CIs of the predicted peak QT prolongation at each dose combination. Furthermore, the probability of QT prolongation exceeding a certain threshold is also computed to support early detection of safety signals while accounting for uncertainty associated with data from Phase I studies. While the prediction of QT effects is sensitive to the dose escalation process, the sensitivity and limited sample size should be considered when providing support to the decision‐making process for further developing certain dose combinations. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental designs for detecting synergy and antagonism between two drugs in a pre‐clinical study

The identification of synergistic interactions between combinations of drugs is an important area within drug discovery and development. Pre‐clinically, large numbers of screening studies to identify synergistic pairs of compounds can often be ran, necessitating efficient and robust experimental designs. We consider experimental designs for detecting interaction between two drugs in a pre‐clinical in vitro assay in the presence of uncertainty of the monotherapy response. The monotherapies are assumed to follow the Hill equation with common lower and upper asymptotes, and a common variance. The optimality criterion used is the variance of the interaction parameter. We focus on ray designs and investigate two algorithms for selecting the optimum set of dose combinations. The first is a forward algorithm in which design points are added sequentially. This is found to give useful solutions in simple cases but can lack robustness when knowledge about the monotherapy parameters is insufficient. The second algorithm is a more pragmatic approach where the design points are constrained to be distributed log‐normally along the rays and monotherapy doses. We find that the pragmatic algorithm is more stable than the forward algorithm, and even when the forward algorithm has converged, the pragmatic algorithm can still out‐perform it. Practically, we find that good designs for detecting an interaction have equal numbers of points on monotherapies and combination therapies, with those points typically placed in positions where a 50% response is expected. More uncertainty in monotherapy parameters leads to an optimal design with design points that are more spread out. Copyright © 2015 John Wiley & Sons, Ltd.