Continual reassessment method for partial ordering

Dual-agent dose-finding in Phase I clinical trial-An extension of rapid enrollment design

Dual-agent treatment has become more and more popular in clinical trials. We have developed an approach called rapid enrollment dual-agent design (REDD) for dose-finding in Phase I clinical trials. This approach aims to administer treatment to patients using a dose combination that is highly probable to be the target dose combination. Unlike other non-model-based designs, rapid enrollment designs (RED and REDD) do not require waiting for all patients to complete an assessment before the assignment of the next participant. Simulations showed that across several scenarios, the average performance of REDD is comparable to that of the Bayesian optimal interval (BOIN) design and the partial order continual reassessment method (POCRM). The simulation results of REDD for late-onset toxicity assessments demonstrated that assigning patients to a dose combination as they are being enrolled, without waiting for the most recent cohort of patients to complete their follow-up, does not significantly compromise the quality of the maximum tolerated dose (MTD) estimation. Instead, it saves a considerable amount of time in clinical trial enrollment. User-friendly online applications have also been created to further facilitate the adoption of rapid enrollment designs in Phase I trials. In summary, being similar to BOIN and POCRM in performance, REDD is an approach that is easily comprehensible, straightforward to implement and offers an advantage of enrolling patients without having to wait for all current patients to complete their follow-ups for toxicity.

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.

The 3 + 3 design in dose-finding studies with small sample sizes: Pitfalls and possible remedies

In the last few years, numerous novel designs have been proposed to improve the efficiency and accuracy of phase I trials to identify the maximum-tolerated dose (MTD) or the optimal biological dose (OBD) for noncytotoxic agents. However, the conventional 3+3 approach, known for its and poor performance, continues to be an attractive choice for many trials despite these alternative suggestions. The article seeks to underscore the importance of moving beyond the 3+3 design by highlighting a different key element in trial design: the estimation of sample size and its crucial role in predicting toxicity and determining the MTD. We use simulation studies to compare the performance of the most used phase I approaches: 3+3, Continual Reassessment Method (CRM), Keyboard and Bayesian Optimal Interval (BOIN) designs regarding three key operating characteristics: the percentage of correct selection of the true MTD, the average number of patients allocated per dose level, and the average total sample size. The simulation results consistently show that the 3+3 algorithm underperforms in comparison to model-based and model-assisted designs across all scenarios and metrics. The 3+3 method yields significantly lower (up to three times) probabilities in identifying the correct MTD, often selecting doses one or even two levels below the actual MTD. The 3+3 design allocates significantly fewer patients at the true MTD, assigns higher numbers to lower dose levels, and rarely explores doses above the target dose-limiting toxicity (DLT) rate. The overall performance of the 3+3 method is suboptimal, with a high level of unexplained uncertainty and significant implications for accurately determining the MTD. While the primary focus of the article is to demonstrate the limitations of the 3+3 algorithm, the question remains about the preferred alternative approach. The intention is not to definitively recommend one model-based or model-assisted method over others, as their performance can vary based on parameters and model specifications. However, the presented results indicate that the CRM, Keyboard, and BOIN designs consistently outperform the 3+3 and offer improved efficiency and precision in determining the MTD, which is crucial in early-phase clinical trials.

A Pilot Study of the Combination of Entinostat with Capecitabine in Advanced Breast Cancer

Background

Breast cancer has an unacceptably high recurrence rate when any residual disease is found following neoadjuvant treatment of high-risk disease. Based on clinical data suggesting an adjuvant role for epigenetic modifying agents in breast cancer and preclinical data suggesting synergistic activity of entinostat combined with capecitabine, we conducted a phase I, open-label study of these agents in metastatic breast cancer (MBC). Both agents have published doses for use in combination therapy, but the agents had not previously been combined with each other in a human trial.

Methods

A multisite phase I dose escalation study was performed at two academic centers. Patients with pretreated, HER2-negative MBC, and measurable disease were enrolled. Dual dose escalation was performed via a Bayesian partial order continual assessment method. Dose levels ranged from entinostat 3 mg to 5 mg and capecitabine 800 mg/m2 to 1000 mg/m2.

Results

Thirteen patients with MBC and a median of 4 lines of prior therapy were enrolled across four dose level combinations. The most common toxicities were neutropenia, thrombocytopenia, and palmar-plantar dysesthesia, which were expected toxicities. No new safety signals were observed. One dose-limiting toxicity was observed, which did not exceed a prespecified toxicity rate of 25%. The median treatment duration was 2.37 months. No partial nor complete responses were observed. The study was halted early prior to entering an expansion phase, due to drug supply limitations.

Conclusion

The tested dosing combinations of entinostat and capecitabine are likely safe in heavily pretreated metastatic breast cancer. This study's clinical investigation of entinostat in breast cancer was halted, but drug development of this agent continues outside the US. There remains a need for postoperative adjuvant drug therapy for the subpopulation of breast cancer patients with high-risk residual cancer after curative therapy. This trial is registered with NCT03473639.

A comparison of model-free phase I dose escalation designs for dual-agent combination therapies

It is increasingly common for therapies in oncology to be given in combination. In some cases, patients can benefit from the interaction between two drugs, although often at the risk of higher toxicity. A large number of designs to conduct phase I trials in this setting are available, where the objective is to select the maximum tolerated dose combination. Recently, a number of model-free (also called model-assisted) designs have provoked interest, providing several practical advantages over the more conventional approaches of rule-based or model-based designs. In this paper, we demonstrate a novel calibration procedure for model-free designs to determine their most desirable parameters. Under the calibration procedure, we compare the behaviour of model-free designs to model-based designs in a comprehensive simulation study, covering a number of clinically plausible scenarios. It is found that model-free designs are competitive with the model-based designs in terms of the proportion of correct selections of the maximum tolerated dose combination. However, there are a number of scenarios in which model-free designs offer a safer alternative. This is also illustrated in the application of the designs to a case study using data from a phase I oncology trial.

Implementing the time-to-event continual reassessment method in the presence of partial orders in a phase I head and neck cancer trial

BACKGROUND

In this article we describe the methodology of the time-to-event continual reassessment method in the presence of partial orders (PO-TITE-CRM) and the process of implementing this trial design into a phase I trial in head and neck cancer called ADePT-DDR. The ADePT-DDR trial aims to find the maximum tolerated dose of an ATR inhibitor given in conjunction with radiotherapy in patients with head and neck squamous cell carcinoma.

METHODS

The PO-TITE-CRM is a phase I trial design that builds upon the time-to-event continual reassessment method (TITE-CRM) to allow for the presence of partial ordering of doses. Partial orders occur in the case where the monotonicity assumption does not hold and the ordering of doses in terms of toxicity is not fully known.

RESULTS

We arrived at a parameterisation of the design which performed well over a range of scenarios. Results from simulations were used iteratively to determine the best parameterisation of the design and we present the final set of simulations. We provide details on the methodology as well as insight into how it is applied to the trial.

CONCLUSIONS

Whilst being a very efficient design we highlight some of the difficulties and challenges that come with implementing such a design. As the issue of partial ordering may become more frequent due to the increasing investigations of combination therapies we believe this account will be beneficial to those wishing to implement a design with partial orders.

TRIAL REGISTRATION

ADePT-DDR was added to the European Clinical Trials Database (EudraCT number: 2020-001034-35) on 2020-08-07.

The quasi-CRM shift method for partially ordered groups

This paper proposes a phase-I clinical trial design that uses ordinal toxicity to locate group-specific doses when groups are partially or completely ordered prior to the start of the trial. There has been previous work on dose-finding for groups and on dose-finding with ordinal toxicity but a solution to the problem of dose-finding for groups with ordinal toxicity has not been proposed. Simulations compared the proposed method against two methods; one that uses ordinal toxicity but does not use group information and one that uses group information but does not use ordinal toxicity. One issue with the first method is the potential for reversals, when the recommended dose for a more sensitive group is higher than the recommended dose for a less sensitive group. The proposed method avoids reversals, allocates patients to optimal doses more frequently during the trial, and selects optimal doses more frequently at the end of the trial.

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.

Time-to-event calibration-free odds design: A robust efficient design for phase I trials with late-onset outcomes

Compared with most of the existing phase I designs, the recently proposed calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and easy to use in practice. However, the original CFO design cannot handle late-onset toxicities, which have been commonly encountered in phase I oncology dose-finding trials with targeted agents or immunotherapies. To account for late-onset outcomes, we extend the CFO design to its time-to-event (TITE) version, which inherits the calibration-free and model-free properties. One salient feature of CFO-type designs is to adopt game theory by competing three doses at a time, including the current dose and the two neighboring doses, while interval-based designs only use the data at the current dose and is thus less efficient. We conduct comprehensive numerical studies for the TITE-CFO design under both fixed and randomly generated scenarios. TITE-CFO shows robust and efficient performances compared with interval-based and model-based counterparts. As a conclusion, the TITE-CFO design provides robust, efficient, and easy-to-use alternatives for phase I trials when the toxicity outcome is late-onset.

Application of the patient-reported outcomes continual reassessment method to a phase I study of radiotherapy in endometrial cancer

This article considers the concept of designing Phase I clinical trials using both clinician- and patient-reported outcomes to adaptively allocate study participants to tolerable doses and determine the maximum tolerated dose (MTD) at the study conclusion. We describe an application of a Bayesian form of the patient-reported outcomes continual reassessment method (PRO-CRMB) in an ongoing Phase I study of adjuvant hypofractionated whole pelvis radiation therapy (WPRT) in endometrial cancer (NCT04458402). The study's primary objective is to determine the MTD per fraction of WPRT, defined by acceptable clinician- and patient-reported DLT rates. We conduct simulation studies of the operating characteristics of the design and compared them to a rule-based approach. We illustrate that the PRO-CRMB makes appropriate dose assignments during the study to give investigators and reviewers an idea of how the method behaves. In simulation studies, the PRO-CRMB demonstrates superior performance to a 5 + 2 stepwise design in terms of recommending target treatment courses and allocating patients to these courses. The design is accompanied by an easy-to-use R shiny web application to simulate operating characteristics at the design stage and sequentially update dose assignments throughout the trial's conduct.

Quasi-partial order continual reassessment method: Applying toxicity scores to cancer dose-finding drug combination trials

The primary endpoint of most dose-finding cancer trials is patient toxicity, and the primary goal is to identify the maximum tolerated dose (MTD), that is, the highest dose that falls below or within a pre-specified toxicity tolerability threshold. Conventionally, dose-finding methods have utilized a binary toxicity endpoint based on whether or not a patient experiences a dose limiting-toxicity (DLT). Improving upon this, in recent years several methods have been developed for modeling toxicity scores, a novel continuous endpoint designed to more precisely estimate patient toxicity burden. Separately, drug-combination trials have become increasingly prevalent, and due to added complexities regarding estimating 'true' dose ordering and potential for more complex patient toxicity profiles, provide an ideal setting which may benefit from the improved precision of toxicity scores. In this paper, we merge two frameworks based on the Continual Reassessment Method (CRM) - the Quasi-CRM and the Partial Order CRM (POCRM) - to propose a novel approach for modeling toxicity scores in a combination-trial setting. We demonstrate that utilizing toxicity scores has the potential to greatly improve correct dose-selection over a variety of trial scenarios. We further present a simple adaptation to the toxicity-score model to control for potential over-dosing issues such that it adheres to the conventional DLT definition and will, at worst, perform equivalently to that of the traditional binary DLT framework. We demonstrate that extending toxicity scores to the combination-trial setting offers potential for improvement over the conventional binary endpoint models.

Practical implementation of the partial ordering continual reassessment method in a Phase I combination-schedule dose-finding trial

There is a growing medical interest in combining several agents and optimizing their dosing schedules in a single trial in order to optimize the treatment for patients. Evaluating at doses of several drugs and their scheduling in a single Phase I trial simultaneously possess a number of statistical challenges, and specialized methods to tackle these have been proposed in the literature. However, the uptake of these methods is slow and implementation examples of such advanced methods are still sparse to date. In this work, we share our experience of proposing a model-based partial ordering continual reassessment method (POCRM) design for three-dimensional dose-finding in an oncology trial. In the trial, doses of two agents and the dosing schedule of one of them can be escalated/de-escalated. We provide a step-by-step summary on how the POCRM design was implemented and communicated to the trial team. We proposed an approach to specify toxicity orderings and their a-priori probabilities, and developed a number of visualization tools to communicate the statistical properties of the design. The design evaluation included both a comprehensive simulation study and considerations of the individual trial behavior. The study is now enrolling patients. We hope that sharing our experience of the successful implementation of an advanced design in practice that went through evaluations of several health authorities will facilitate a better uptake of more efficient methods in practice.

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.

Flexible use of copula-type model for dose-finding in drug combination clinical trials

Identification of the maximum tolerated dose combination (MTDC) of cancer drugs is an important objective in phase I oncology trials. Numerous dose-finding designs for drug combination have been proposed over the years. Copula-type models exhibit distinctive advantages in this task over other models used in existing competitive designs. For example, their application enables the consideration of dose-limiting toxicities attributable to one of two agents. However, if a particular combination therapy demonstrates extremely synergistic toxicity, copula-type models are liable to induce biases in toxicity probability estimators due to the associated Fréchet-Hoeffding bounds. Consequently, the dose-finding performance may be worse than those of other competitive designs. The objective of this study is to improve the performance of dose-finding designs based on copula-type models while maintaining their advantageous properties. We propose an extension of the parameter space of the interaction term in copula-type models. This releases the Fréchet-Hoeffding bounds, making the estimation of toxicity probabilities more flexible. Numerical examples in various scenarios demonstrate that the performance (e.g., the percentage of correct MTDC selection) of the proposed method is better than those exhibited by existing copula-type models and comparable with those of other competitive designs, irrespective of the existence of extreme synergistic toxicity. The results obtained in this study could motivate the real-world application of the proposed method in cases requiring the utilization of the properties of copula-type models.

Approximate Bayesian computation design for phase I clinical trials

In the development of new cancer treatment, an essential step is to determine the maximum tolerated dose in a phase I clinical trial. In general, phase I trial designs can be classified as either model-based or algorithm-based approaches. Model-based phase I designs are typically more efficient by using all observed data, while there is a potential risk of model misspecification that may lead to unreliable dose assignment and incorrect maximum tolerated dose identification. In contrast, most of the algorithm-based designs are less efficient in using cumulative information, because they tend to focus on the observed data in the neighborhood of the current dose level for dose movement. To use the data more efficiently yet without any model assumption, we propose a novel approximate Bayesian computation approach to phase I trial design. Not only is the approximate Bayesian computation design free of any dose-toxicity curve assumption, but it can also aggregate all the available information accrued in the trial for dose assignment. Extensive simulation studies demonstrate its robustness and efficiency compared with other phase I trial designs. We apply the approximate Bayesian computation design to the MEK inhibitor selumetinib trial to demonstrate its satisfactory performance. The proposed design can be a useful addition to the family of phase I clinical trial designs due to its simplicity, efficiency and robustness.

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.

Early-Phase Oncology Trials: Why So Many Designs?

The past 30 years have seen a considerable effort on the part of statisticians to improve the design and accuracy of early-phase oncology trials. Some of this effort has been rewarded via successful implementation in actual trials, yet it would be fair to say that among clinicians, there remains some reluctance to fully embrace more efficient model-based approaches. One reason for such reticence is the difficulty in understanding exactly what is being offered by more modern designs. Although it is generally accepted that these designs offer improvements over the old standard 3 + 3 design, a new question has then to be addressed: How should we decide among the new proposals which one is the best for our purpose? In this study, we recall 15 designs that are currently proposed and in use. We show that among these 15 designs, many are operationally identical. These 15 designs reduce to three broad classes of designs. This review helps summarize their properties and differences and highlights that certain designs require ad hoc modifications to ensure satisfactory performance.

A nonparametric Bayesian method for dose finding in drug combinations cancer trials

We propose an adaptive design for early-phase drug-combination cancer trials with the goal of estimating the maximum tolerated dose (MTD). A nonparametric Bayesian model, using beta priors truncated to the set of partially ordered dose combinations, is used to describe the probability of dose limiting toxicity (DLT). Dose allocation between successive cohorts of patients is estimated using a modified continual reassessment scheme. The updated probabilities of DLT are calculated with a Gibbs sampler that employs a weighting mechanism to calibrate the influence of data vs the prior. At the end of the trial, we recommend one or more dose combinations as the MTD based on our proposed algorithm. We apply our method to a Phase I clinical trial of CB-839 and Gemcitabine that motivated this nonparametric design. The design operating characteristics indicate that our method is comparable with existing methods.

An Open Label, Adaptive, Phase 1 Trial of High-Dose Oral Nitazoxanide in Healthy Volunteers: An Antiviral Candidate for SARS-CoV-2

Repurposing approved drugs may rapidly establish effective interventions during a public health crisis. This has yielded immunomodulatory treatments for severe coronavirus disease 2019 (COVID-19), but repurposed antivirals have not been successful to date because of redundancy of the target in vivo or suboptimal exposures at studied doses. Nitazoxanide is a US Food and Drug Administration (FDA) approved antiparasitic medicine, that physiologically-based pharmacokinetic (PBPK) modeling has indicated may provide antiviral concentrations across the dosing interval, when repurposed at higher than approved doses. Within the AGILE trial platform (NCT04746183) an open label, adaptive, phase I trial in healthy adult participants was undertaken with high-dose nitazoxanide. Participants received 1,500 mg nitazoxanide orally twice-daily with food for 7 days. Primary outcomes were safety, tolerability, optimum dose, and schedule. Intensive pharmacokinetic (PK) sampling was undertaken day 1 and 5 with minimum concentration (Cmin ) sampling on days 3 and 7. Fourteen healthy participants were enrolled between February 18 and May 11, 2021. All 14 doses were completed by 10 of 14 participants. Nitazoxanide was safe and with no significant adverse events. Moderate gastrointestinal disturbance (loose stools or diarrhea) occurred in 8 participants (57.1%), with urine and sclera discoloration in 12 (85.7%) and 9 (64.3%) participants, respectively, without clinically significant bilirubin elevation. This was self-limiting and resolved upon drug discontinuation. PBPK predictions were confirmed on day 1 but with underprediction at day 5. Median Cmin was above the in vitro target concentration on the first dose and maintained throughout. Nitazoxanide administered at 1,500 mg b.i.d. with food was safe with acceptable tolerability a phase Ib/IIa study is now being initiated in patients with COVID-19.

Stopping rules for phase I clinical trials with dose expansion cohorts

Many clinical trials incorporate stopping rules to terminate early if the clinical question under study can be answered with a high degree of confidence. While common in later-stage trials, these rules are rarely implemented in dose escalation studies, due in part to the relatively smaller sample size of these designs. However, even with a small sample size, this paper shows that easily implementable stopping rules can terminate dose-escalation early with minimal loss to the accuracy of maximum tolerated dose estimation. These stopping rules are developed when the goal is to identify one or two dose levels, as the maximum tolerated dose and co-maximum tolerated dose. In oncology, this latter goal is frequently considered when the study includes dose-expansion cohorts, which are used to further estimate and compare the safety and efficacy of one or two dose levels. As study protocols do not typically halt accrual between escalation and expansion, early termination is of clinical importance as it either allows for additional patients to be treated as part of the dose expansion cohort to obtain more precise estimates of the study endpoints or allows for an overall reduction in the total sample size.

CUSUMIN: A cumulative sum interval design for cancer phase I dose finding studies

Recently, model-assisted designs, including the Bayesian optimal interval (BOIN) design with optimal thresholds to determine the dose for the next cohort, have been proposed for cancer phase I studies. Model-assisted designs are useful because of their good performance as model-based designs in addition to their algorithm-based simplicity. In BOIN, escalation and de-escalation based on boundaries can be understood as a type of change point detection based on a sequential test procedure. Notably, the sequential test procedure is used in a wide range of fields and is known for its application to control charts, statistical monitoring methods used for detecting abnormalities in manufacturing processes. In control charts, abnormalities are detected if the control chart statistics are observed to be outside of the optimal boundaries. The cumulative sum (CUSUM) statistic, which is developed for control chart applications, derives higher power under the same erroneous judgment rate. Hence, it is expected that a more efficient model-assisted design can be achieved by the application of CUSUM statistics. In this study, a model-assisted design based on the CUSUM statistic is proposed. In the proposed design, the dose for the next cohort is decided by CUSUM statistics calculated from the counts of the dose-limiting toxicity and pre-defined boundaries, based on the CUSUM control chart scheme. Intensive simulation shows that our proposed method performs better than BOIN, and other representative model-assisted designs, including modified toxicity probability interval (mTPI) and Keyboard, in terms of controlling over-dosing rates while maintaining similar performance in the determination of maximum tolerated dose.

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.

A dose-finding design for dual-agent trials with patient-specific doses for one agent with application to an opiate detoxification trial

There is a growing interest in early phase dose-finding clinical trials studying combinations of several treatments. While the majority of dose finding designs for such setting were proposed for oncology trials, the corresponding designs are also essential in other therapeutic areas. Furthermore, there is increased recognition of recommending the patient-specific doses/combinations, rather than a single target one that would be recommended to all patients in later phases regardless of their characteristics. In this paper, we propose a dose-finding design for a dual-agent combination trial motivated by an opiate detoxification trial. The distinguishing feature of the trial is that the (continuous) dose of one compound is defined externally by the clinicians and is individual for every patient. The objective of the trial is to define the dosing function that for each patient would recommend the optimal dosage of the second compound. Via a simulation study, we have found that the proposed design results in high accuracy of individual dose recommendation and is robust to the model misspecification and assumptions on the distribution of externally defined doses.

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.

The Ci3+3 design for dual-agent combination dose-finding clinical trials

We propose a rule-based statistical design for combination dose-finding trials with two agents. The Ci3 + 3 design is an extension of the i3 + 3 design with simple up-and-down decision rules comparing the observed toxicity rates and equivalence intervals that define the maximum tolerated dose combination. Ci3 + 3 consists of two stages to allow fast and efficient exploration of the dose-combination space. Statistical inference is restricted to a beta-binomial model for dose evaluation, and the entire design is built upon a set of fixed rules. We show via simulation studies that the Ci3 + 3 design exhibits similar and comparable operating characteristics to more complex designs utilizing model-based inferences. Implementation of Ci3 + 3 for practical trials is simple for the first stage, where the up-and-down decisions may be carried out using a decision table based on the preselected escalation path and i3 + 3. The second stage is not simpler than model-based designs, however, since it also requires computation of posterior probabilities based on a Bayesian model. We believe that the Ci3 + 3 design may provide an alternative choice to help simplify the design and conduct of combination dose-finding trials in practice.

Bayesian Design for Identifying Cohort-Specific Optimal Dose Combinations Based on Multiple Endpoints: Application to a Phase I Trial in Non-Small Cell Lung Cancer

Immunotherapy and chemotherapy combinations have proven to be a safe and efficacious treatment approach in multiple settings. However, it is not clear whether approved doses of chemotherapy developed to achieve a maximum tolerated dose are the ideal dose when combining cytotoxic chemotherapy with immunotherapy to induce immune responses. This trial of a modulated dose chemotherapy and Pembrolizumab, with or without a second immunomodulatory agent, uses a Bayesian design to select the optimal treatment combination by balancing both safety and efficacy of the chemotherapy and immunotherapy agents within each of two cohorts. The simulation study provides evidence that the proposed Bayesian design successfully addresses the primary study aim to identify the optimal dose combination for each of the two independent patient cohorts. This conclusion is supported by the high percentage of simulated trials which select a treatment combination that is both safe and highly efficacious. The proposed trial was funded and was being finalized when the sponsoring company decided not to proceed due to negative findings in another patient population. The proposed trial design will continue to be relevant as multiple chemotherapy and immunotherapy combinations become the standard of care and future research will require evaluating the appropriate doses of various components of multiple drug regimens.

Adaptive Bayesian phase I clinical trial designs for estimating the maximum tolerated doses for two drugs while fully utilizing all toxicity information

The combined treatments with multiple drugs are very common in the contemporary medicine, especially for medical oncology. Therefore, we developed a Bayesian adaptive Phase I clinical trial design entitled escalation with overdoing control using normalized equivalent toxicity score for estimating maximum tolerated dose (MTD) contour of two drug combination (EWOC-NETS-COM) used for oncology trials. The normalized equivalent toxicity score (NETS) as the primary endpoint of clinical trial is assumed to follow quasi-Bernoulli distribution and treated as quasi-continuous random variable in the logistic linear regression model which is used to describe the relationship between the doses of the two agents and the toxicity response. Four parameters in the dose-toxicity model were re-parameterized to parameters with explicit clinical meanings to describe the association between NETS and doses of two agents. Noninformative priors were used and Markov chain Monte Carlo was employed to update the posteriors of the four parameters in dose-toxicity model. Extensive simulations were conducted to evaluate the safety, trial efficiency, and MTD estimation accuracy of EWOC-NETS-COM under different scenarios, using the EWOC as reference. The results demonstrated that EWOC-NETS-COM not only efficiently estimates MTD contour of multiple drugs but also provides better trial efficiency by fully utilizing all toxicity information.

Randomised Phase 1 clinical trials in oncology

The aims of Phase 1 trials in oncology have broadened considerably from simply demonstrating that the agent/regimen of interest is well tolerated in a relatively heterogeneous patient population to addressing multiple objectives under the heading of early-phase trials and, if possible, obtaining reliable evidence regarding clinical activity to lead to drug approvals via the Accelerated Approval approach or Breakthrough Therapy designation in cases where the tumours are rare, prognosis is poor or where there might be an unmet therapeutic need. Constructing a Phase 1 design that can address multiple objectives within the context of a single trial is not simple. Randomisation can play an important role, but carrying out such randomisation according to the principles of equipoise is a significant challenge in the Phase 1 setting. If the emerging data are not sufficient to definitively address the aims early on, then a proper design can reduce biases, enhance interpretability, and maximise information so that the Phase 1 data can be more compelling. This article outlines objectives and design considerations that need to be adhered to in order to respect ethical and scientific principles required for research in human subjects in early phase clinical trials.

A Bayesian dose-finding design for outcomes evaluated with uncertainty

INTRODUCTION

In some phase I trial settings, there is uncertainty in assessing whether a given patient meets the criteria for dose-limiting toxicity.

METHODS

We present a design which accommodates dose-limiting toxicity outcomes that are assessed with uncertainty for some patients. Our approach could be utilized in many available phase I trial designs, but we focus on the continual reassessment method due to its popularity. We assume that for some patients, instead of the usual binary dose-limiting toxicity outcome, we observe a physician-assessed probability of dose-limiting toxicity specific to a given patient. Data augmentation is used to estimate the posterior probabilities of dose-limiting toxicity at each dose level based on both the fully observed and partially observed patient outcomes. A simulation study is used to assess the performance of the design relative to using the continual reassessment method on the true dose-limiting toxicity outcomes (available in simulation setting only) and relative to simple thresholding approaches.

RESULTS

Among the designs utilizing the partially observed outcomes, our proposed design has the best overall performance in terms of probability of selecting correct maximum tolerated dose and number of patients treated at the maximum tolerated dose.

CONCLUSION

Incorporating uncertainty in dose-limiting toxicity assessment can improve the performance of the continual reassessment method design.

Early completion of phase I cancer clinical trials with Bayesian optimal interval design

Phase I cancer clinical trials have been proposed novel designs such as algorithm-based, model-based, and model-assisted designs. Model-based and model-assisted designs have a higher identification rate of maximum tolerated dose (MTD) than algorithm-based designs, but are limited by the fact that the sample size is fixed. Hence, it would be very attractive to estimate the MTD with sufficient accuracy and complete the trial early. O'Quigley proposed the early completion of a trial with the continual reassessment method among model-based designs when the MTD is estimated with sufficient accuracy. However, the proposed early completion method based on the binary outcome trees has a problem that the calculation cost is high when the number of remaining patients is large. Among model-assisted designs, the Bayesian optimal interval (BOIN) design provides the simplest approach for dose adjustment. We propose the novel early completion method for the clinical trials with the BOIN design when the MTD is estimated with sufficient accuracy. This completion method can be easily calculated. In addition, the method does not require many more patients treated for the determination of early completion. We confirm that the BOIN design applying the early completion method has almost the same MTD identification rate compared to the BOIN design through simulations conducted based on over 30 000 scenarios.

Bayesian optimization design for finding a maximum tolerated dose combination in phase I clinical trials

The development of combination therapies has become commonplace because potential synergistic benefits are expected for resistant patients of single-agent treatment. In phase I clinical trials, the underlying premise is toxicity increases monotonically with increasing dose levels. This assumption cannot be applied in drug combination trials, however, as there are complex drug-drug interactions. Although many parametric model-based designs have been developed, strong assumptions may be inappropriate owing to little information available about dose-toxicity relationships. No standard solution for finding a maximum tolerated dose combination has been established. With these considerations, we propose a Bayesian optimization design for identifying a single maximum tolerated dose combination. Our proposed design utilizing Bayesian optimization guides the next dose by a balance of information between exploration and exploitation on the nonparametrically estimated dose-toxicity function, thereby allowing us to reach a global optimum with fewer evaluations. We evaluate the proposed design by comparing it with a Bayesian optimal interval design and with the partial-ordering continual reassessment method. The simulation results suggest that the proposed design works well in terms of correct selection probabilities and dose allocations. The proposed design has high potential as a powerful tool for use in finding a maximum tolerated dose combination.

Consistency of the CRM when the dose-toxicity curve is not monotone and its application to the POCRM

The continual reassessment method (CRM) is a well-known design for dose-finding trials with the goal of estimating the maximum tolerated dose (MTD), the dose with a given probability of toxicity. The standard assumption is that the probability of toxicity monotonically increases with dose. We show that the CRM can still be consistent and correctly identify the MTD even when the dose-toxicity curve is not monotone as long as there is monotonicity of the true toxicity probabilities right below and right above the true MTD. In the case of multiple therapies, where it is unclear how to order combinations of dose levels of multiple therapies, our findings provide insight into the performance of the partial order CRM (POCRM). To select the correct dose combination at the end of a trial, the POCRM does not have to select a monotone ordering of drug combinations. We illustrate the connection between our results for the CRM with a nonmonotone dose-toxicity curve and the POCRM via simulations.

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.

Using an Interaction Parameter in Model-Based Phase I Trials for Combination Treatments? A Simulation Study

There is growing interest in Phase I dose-finding studies studying several doses of more than one agent simultaneously. A number of combination dose-finding designs were recently proposed to guide escalation/de-escalation decisions during the trials. The majority of these proposals are model-based: a parametric combination-toxicity relationship is fitted as data accumulates. Various parameter shapes were considered but the unifying theme for many of these is that typically between 4 and 6 parameters are to be estimated. While more parameters allow for more flexible modelling of the combination-toxicity relationship, this is a challenging estimation problem given the typically small sample size in Phase I trials of between 20 and 60 patients. These concerns gave raise to an ongoing debate whether including more parameters into combination-toxicity model leads to more accurate combination selection. In this work, we extensively study two variants of a 4-parameter logistic model with reduced number of parameters to investigate the effect of modelling assumptions. A framework to calibrate the prior distributions for a given parametric model is proposed to allow for fair comparisons. Via a comprehensive simulation study, we have found that the inclusion of the interaction parameter between two compounds does not provide any benefit in terms of the accuracy of selection, on average, but is found to result in fewer patients allocated to the target combination during the trial.

A benchmark for dose-finding studies with unknown ordering

An important tool to evaluate the performance of a dose-finding design is the nonparametric optimal benchmark that provides an upper bound on the performance of a design under a given scenario. A fundamental assumption of the benchmark is that the investigator can arrange doses in a monotonically increasing toxicity order. While the benchmark can be still applied to combination studies in which not all dose combinations can be ordered, it does not account for the uncertainty in the ordering. In this article, we propose a generalization of the benchmark that accounts for this uncertainty and, as a result, provides a sharper upper bound on the performance. The benchmark assesses how probable the occurrence of each ordering is, given the complete information about each patient. The proposed approach can be applied to trials with an arbitrary number of endpoints with discrete or continuous distributions. We illustrate the utility of the benchmark using recently proposed dose-finding designs for Phase I combination trials with a binary toxicity endpoint and Phase I/II combination trials with binary toxicity and continuous efficacy.

A simulation-free approach to assessing the performance of the continual reassessment method

The continual reassessment method (CRM) is an adaptive design for Phase I trials whose operating characteristics, including appropriate sample size, probability of correctly identifying the maximum tolerated dose, and the expected proportion of participants assigned to each dose, can only be determined via simulation. The actual time to determine a final "best" design can take several hours or days, depending on the number of scenarios that are examined. The computational cost increases as the kernel of the one-parameter CRM design is expanded to other settings, including additional parameters, monitoring of both toxicity and efficacy, and studies of combinations of two agents. For a given vector of true DLT probabilities, we have developed an approach that replaces a simulation study of thousands of hypothetical trials with a single simulation. Our approach, which is founded on the consistency of the CRM, very accurately reflects the results produced by the simulation study, but does so in a fraction of time required by the simulation study. Relative to traditional simulations, we extensively examine how our method is able to assess the operating characteristics of a CRM design for a hypothetical trial whose characteristics are based upon a previously published Phase I trial. We also provide a metric of nonconsistency and demonstrate that although nonconsistency can impact the operating characteristics of our method, the degree of over- or under-estimation is unpredictable. As a solution, we provide an algorithm for maintaining the consistency of a chosen CRM design so that our method is applicable for any trial.

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.

On the coherence of model-based dose-finding designs for drug combination trials

The concept of coherence was proposed for single-agent phase I clinical trials to describe the property that a design never escalates the dose when the most recently treated patient has toxicity and never de-escalates the dose when the most recently treated patient has no toxicity. It provides a useful theoretical tool for investigating the properties of phase I trial designs. In this paper, we generalize the concept of coherence to drug combination trials, which are substantially different and more challenging than single-agent trials. For example, in the dose-combination matrix, each dose has up to 8 neighboring doses as candidates for dose escalation and de-escalation, and the toxicity orders of these doses are only partially known. We derive sufficient conditions for a model-based drug combination trial design to be coherent. Our results are more general and relaxed than the existing results and are applicable to both single-agent and drug combination trials. We illustrate the application of our theoretical results with a number of drug combination dose-finding designs in the literature.

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 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.

A surface-free design for phase I dual-agent combination trials

In oncology, there is a growing number of therapies given in combination. Recently, several dose-finding designs for Phase I dose-escalation trials for combinations were proposed. The majority of novel designs use a pre-specified parametric model restricting the search of the target combination to a surface of a particular form. In this work, we propose a novel model-free design for combination studies, which is based on the assumption of monotonicity within each agent only. Specifically, we parametrise the ratios between each neighbouring combination by independent Beta distributions. As a result, the design does not require the specification of any particular parametric model or knowledge about increasing orderings of toxicity. We compare the performance of the proposed design to the model-based continual reassessment method for partial ordering and to another model-free alternative, the product of independent beta design. In an extensive simulation study, we show that the proposed design leads to comparable or better proportions of correct selections of the target combination while leading to the same or fewer average number of toxic responses in a trial.

A comparative study of Bayesian optimal interval (BOIN) design with interval 3+3 (i3+3) design for phase I oncology dose-finding trials

Bayesian optimal interval (BOIN) design is a model-assisted phase I dose-finding design to find the maximum tolerated dose (MTD). The hallmark of the BOIN design is its concise decision rule - making the decision of dose escalation and de-escalation by simply comparing the observed dose-limiting toxicity (DLT) rate at the current dose with a pair of optimal dose escalation and de-escalation boundaries. The interval 3+3 (i3+3) design is a recently proposed algorithm-based dose-finding design based on a similar decision rule with some modifications. The similarity in the appearance of the two designs has caused confusions among practitioners. In this article, we demystify the i3+3 design by elucidating its links with the BOIN design and compare their similarities and differences, as well as pros and cons. We perform comprehensive simulation studies to compare the operating characteristics of the two designs. Our results show that, compared to the algorithm-based i3+3 design, which are characterized by ad hoc and often scientifically and logically incoherent decision rules, the mode-assisted BOIN design is not only simpler, but also statistically more rigorous with better operating characteristics, thus providing a better design choice for phase I oncology trials.

A comparison of phase I dose-finding designs in clinical trials with monotonicity assumption violation

BACKGROUND/AIMS

In oncology, new combined treatments make it difficult to order dose levels according to monotonically increasing toxicity. New flexible dose-finding designs that take into account uncertainty in dose levels ordering were compared with classical designs through simulations in the setting of the monotonicity assumption violation. We give recommendations for the choice of dose-finding design.

METHODS

Motivated by a clinical trial for patients with high-risk neuroblastoma, we considered designs that require a monotonicity assumption, the Bayesian Continual Reassessment Method, the modified Toxicity Probability Interval, the Bayesian Optimal Interval design, and designs that relax monotonicity assumption, the Bayesian Partial Ordering Continual Reassessment Method and the No Monotonicity Assumption design. We considered 15 scenarios including monotonic and non-monotonic dose-toxicity relationships among six dose levels.

RESULTS

The No Monotonicity Assumption and Partial Ordering Continual Reassessment Method designs were robust to the violation of the monotonicity assumption. Under non-monotonic scenarios, the No Monotonicity Assumption design selected the correct dose level more often than alternative methods on average. Under the majority of monotonic scenarios, the Partial Ordering Continual Reassessment Method selected the correct dose level more often than the No Monotonicity Assumption design. Other designs were impacted by the violation of the monotonicity assumption with a proportion of correct selections below 20% in most scenarios. Under monotonic scenarios, the highest proportions of correct selections were achieved using the Continual Reassessment Method and the Bayesian Optimal Interval design (between 52.8% and 73.1%). The costs of relaxing the monotonicity assumption by the No Monotonicity Assumption design and Partial Ordering Continual Reassessment Method were decreases in the proportions of correct selections under monotonic scenarios ranging from 5.3% to 20.7% and from 1.4% to 16.1%, respectively, compared with the best performing design and were higher proportions of patients allocated to toxic dose levels during the trial.

CONCLUSIONS

Innovative oncology treatments may no longer follow monotonic dose levels ordering which makes standard phase I methods fail. In such a setting, appropriate designs, as the No Monotonicity Assumption or Partial Ordering Continual Reassessment Method designs, should be used to safely determine recommended for phase II dose.