Competing designs for drug combination in phase I dose-finding clinical trials

A new function for drug combination dose finding trials

Combination drugs play an essential role in treating cancers. The challenging part of the combination drugs are to specify the dose-toxicity ordering, which means the sequences of dose escalation and de-escalation in process of dose findings should be pre-determined. In the paper, we extend a novel function of the continual reassessment method based on the combination of the normal distribution for drug-combination dose-finding trials and systematically evaluate its performance using a template of four performance measures EARS (Efficiency, Accuracy, Reliability, Selection). Dose escalation and deescalation rules are based on the nearest neighborhood continual reassessment method for a combination drug, and we specify all possible dose-toxicity orderings in the trial. Simulation demonstrates that the new design is efficient, accurate and reasonably reliable.

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.

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.

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

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

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

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

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.

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.

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.

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.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

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.

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

BACKGROUND

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

METHODS

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

RESULTS AND CONCLUSION

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

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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

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

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

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

Practical designs for Phase I combination studies in oncology

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

Bayesian optimal interval design for dose finding in drug-combination trials

Interval designs have recently attracted enormous attention due to their simplicity and desirable properties. We develop a Bayesian optimal interval design for dose finding in drug-combination trials. To determine the next dose combination based on the cumulative data, we propose an allocation rule by maximizing the posterior probability that the toxicity rate of the next dose falls inside a prespecified probability interval. The entire dose-finding procedure is nonparametric (model-free), which is thus robust and also does not require the typical "nonparametric" prephase used in model-based designs for drug-combination trials. The proposed two-dimensional interval design enjoys convergence properties for large samples. We conduct simulation studies to demonstrate the finite-sample performance of the proposed method under various scenarios and further make a modication to estimate toxicity contours by parallel dose-finding paths. Simulation results show that on average the performance of the proposed design is comparable with model-based designs, but it is much easier to implement.

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.