Comparative review of novel model‐assisted designs for phase I clinical trials

A number of novel phase I trial designs have been proposed that aim to combine the simplicity of algorithm‐based designs with the superior performance of model‐based designs, including the modified toxicity probability interval, Bayesian optimal interval, and Keyboard designs. In this article, we review these “model‐assisted” designs, contrast their statistical foundations and pros and cons, and compare their operating characteristics with the continual reassessment method. To provide unbiased and reliable results, our comparison is based on 10 000 dose‐toxicity scenarios randomly generated using the pseudo‐uniform algorithm recently proposed in the literature. The results showed that the continual reassessment method, Bayesian optimal interval, and Keyboard designs provide comparable, superior operating characteristics, and each outperforms the modified toxicity probability interval design. These designs are more likely to correctly select the maximum tolerated dose and less likely to overdose patients.     

A comparison of model choices for the continual reassessment method in phase I cancer trials

Determination of the maximum tolerated dose (MTD) is the main objective of phase I trials. Trials are typically carried out with restricted sample sizes. Model‐based approaches proposed to identify the MTD (including the Continual Reassessment Method or CRM) suppose a simple model for the dose‐toxicity relation. At this early stage of clinical development, the true family of models is not known and several proposals have been done. Asymptotic convergence of the recommendation to the true MTD can be obtained with a one‐parameter model even in case of model misspecification. Nevertheless, operating characteristics with finite sample sizes can be largely affected by the choice of the model. In this paper, we evaluate and compare several models in a simulation framework. This framework includes a large class of dose‐toxicity relations against which to test the competing models, an ‘optimal’ method that provides efficient non‐parametric estimates of the probability of dose limiting toxicity to serve as a benchmark and as a graphic representation. In particular we explore the use of a one‐parameter versus a two‐parameter model, we compare the power and the logistic models and finally we investigate the impact of dose recoding on the operating characteristics. Comparisons are carried out with both a likelihood approach and a Bayesian approach for model estimations. We show that average performances of a one‐parameter model are superior and that the power model has good operating characteristics. Some models can speed up dose escalation and lead to more aggressive designs. We derive some behavior related to the choice of model and insist on the use of simulations under several scenarios before the initiation of each new trial in order to determine the best model to be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive prior variance calibration in the Bayesian continual reassessment method

The use of the continual reassessment method (CRM) and other model‐based approaches to design Phase I clinical trials has increased owing to the ability of the CRM to identify the maximum tolerated dose better than the 3 + 3 method. However, the CRM can be sensitive to the variance selected for the prior distribution of the model parameter, especially when a small number of patients are enrolled. Although methods have emerged to adaptively select skeletons and to calibrate the prior variance only at the beginning of a trial, there has not been any approach developed to adaptively calibrate the prior variance throughout a trial. We propose three systematic approaches to adaptively calibrate the prior variance during a trial and compare them via simulation with methods proposed to calibrate the variance at the beginning of a trial. Copyright © 2012 John Wiley & Sons, Ltd.     

Practical modifications to the time-to-event continual reassessment method for phase I cancer trials with fast patient accrual and late-onset toxicities

The goal of phase I cancer trials is to determine the highest dose of a treatment regimen with an acceptable toxicity rate. Traditional designs for phase I trials, such as the Continual Reassessment Method (CRM) and the 3 + 3 design, require each patient or a cohort of patients to be fully evaluated for the dose-limiting toxicity (DLT) before new patients can be enrolled. As such, the trial duration may be prohibitively long. The Time-to-Event Continual Reassessment Method (TITE-CRM, Cheung and Chappell, 2000) circumvents this limitation by allowing staggered patient accrual without the need for complete DLT follow-up of previously treated patients. However, in the setting of fast patient accrual and late-onset toxicities, the TITE-CRM results in overly aggressive dose escalation and exposes a considerable number of patients to toxic doses. We examine a modification to the TITE-CRM proposed by the original TITE-CRM creator and propose an alternative approach useful in this setting by incorporating an accrual suspension rule. A simulation study designed based on a neuro-oncology trial indicates that the modified methods provide a much improved degree of safety than the TITE-CRM while maintaining desirable design accuracy. The practical aspects of the proposed designs are discussed. The modifications presented are useful when planning phase I trials involving chemoradiation therapy.     

A trivariate continual reassessment method for phase I/II trials of toxicity,efficacy, and surrogate efficacy

Recently, many Bayesian methods have been developed for dose finding when simultaneously modeling both toxicity and efficacy outcomes in a blended phase I/II fashion. A further challenge arises when all the true efficacy data cannot be obtained quickly after the treatment so that surrogate markers are instead used (e.g., in cancer trials). We propose a framework to jointly model the probabilities of toxicity, efficacy, and surrogate efficacy given a particular dose. Our trivariate binary model is specified as a composition of two bivariate binary submodels. In particular, we extend the bivariate continual reassessment method (CRM), as well as utilize a particular Gumbel copula. The resulting trivariate algorithm utilizes all the available data at any given time point and can flexibly stop the trial early for either toxicity or efficacy. Our simulation studies demonstrate that our proposed method can successfully improve dosage targeting efficiency and guard against excess toxicity over a variety of true model settings and degrees of surrogacy. Copyright © 2012 John Wiley & Sons, Ltd.     

An extension of the continual reassessment method using decision theory.

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q(*), of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q(*), a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q(*), that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q(*), among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.     

Escalation with overdose control for phase I drug‐combination trials

Dose finding for combined drugs has grown rapidly in oncology drug development. The escalation with overdose control (EWOC) method is a popular model‐based dose‐finding approach to single‐agent phase I clinical trials. When two drugs are combined as a treatment, we propose a two‐dimensional EWOC design for dose finding on the basis of a four‐parameter logistic regression model. During trial conduct, we continuously update the posterior distribution of the maximum tolerated dose (MTD) combination to find the most appropriate dose combination for each cohort of patients. The probability that the next assigned dose combination exceeds the MTD combination can be controlled by a feasibility bound, which is based on a prespecified quantile level of the MTD distribution such as to reduce the possibility of overdosing. We determine dose escalation, de‐escalation, or staying at the same doses by searching the MTD combination along the rows and columns in a two‐drug combination matrix, respectively. We conduct simulation studies to examine the performance of the two‐dimensional EWOC design under various practical scenarios, and illustrate it with a trial example. Copyright © 2013 John Wiley & Sons, Ltd.     

Toxicity‐dependent feasibility bounds for the escalation with overdose control approach in phase I cancer trials

Phase I trials of anti‐cancer therapies aim to identify a maximum tolerated dose (MTD), defined as the dose that causes unacceptable toxicity in a target proportion of patients. Both rule‐based and model‐based methods have been proposed for MTD recommendation. The escalation with overdose control (EWOC) approach is a model‐based design where the dose assigned to the next patient is one that, given all available data, has a posterior probability of exceeding the MTD equal to a pre‐specified value known as the feasibility bound. The aim is to conservatively dose‐escalate and approach the MTD, avoiding severe overdosing early on in a trial. The EWOC approach has been applied in practice with the feasibility bound either fixed or varying throughout a trial, yet some of the methods may recommend incoherent dose‐escalation, that is, an increase in dose after observing severe toxicity at the current dose. We present examples where varying feasibility bounds have been used in practice, and propose a toxicity‐dependent feasibility bound approach that guarantees coherent dose‐escalation and incorporates the desirable features of other EWOC approaches. We show via detailed simulation studies that the toxicity‐dependent feasibility bound approach provides improved MTD recommendation properties to the original EWOC approach for both discrete and continuous doses across most dose‐toxicity scenarios, with comparable performance to other approaches without recommending incoherent dose escalation. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

A robust two‐stage design identifying the optimal biological dose for phase I/II clinical trials

We propose a robust two‐stage design to identify the optimal biological dose for phase I/II clinical trials evaluating both toxicity and efficacy outcomes. In the first stage of dose finding, we use the Bayesian model averaging continual reassessment method to monitor the toxicity outcomes and adopt an isotonic regression method based on the efficacy outcomes to guide dose escalation. When the first stage ends, we use the Dirichlet‐multinomial distribution to jointly model the toxicity and efficacy outcomes and pick the candidate doses based on a three‐dimensional volume ratio. The selected candidate doses are then seamlessly advanced to the second stage for dose validation. Both toxicity and efficacy outcomes are continuously monitored so that any overly toxic and/or less efficacious dose can be dropped from the study as the trial continues. When the phase I/II trial ends, we select the optimal biological dose as the dose obtaining the minimal value of the volume ratio within the candidate set. An advantage of the proposed design is that it does not impose a monotonically increasing assumption on the shape of the dose–efficacy curve. We conduct extensive simulation studies to examine the operating characteristics of the proposed design. The simulation results show that the proposed design has desirable operating characteristics across different shapes of the underlying true dose–toxicity and dose–efficacy curves. The software to implement the proposed design is available upon request. Copyright © 2016 John Wiley & Sons, Ltd.     

Critical aspects of the Bayesian approach to phase I cancer trials

The Bayesian approach to finding the maximum-tolerated dose in phase I cancer trials is discussed. The suggested approach relies on a realistic dose-toxicity model, allows one to include prior information, and supports clinical decision making by presenting within-trial information in a transparent way. The modeling and decision-making components are flexible enough to be extendable to more complex settings. Critical aspects are emphasized and a comparison with the continual reassessment method (CRM) is performed with data from an actual trial and a simulation study. The comparison revealed similar operating characteristics while avoiding some of the difficulties encountered in the actual trial when applying the CRM.     

An adaptive dose‐finding method using a change‐point model for molecularly targeted agents in phase I trials

The paradigm of oncology drug development is expanding from developing cytotoxic agents to developing biological or molecularly targeted agents (MTAs). Although it is common for the efficacy and toxicity of cytotoxic agents to increase monotonically with dose escalation, the efficacy of some MTAs may exhibit non‐monotonic patterns in their dose–efficacy relationships. Many adaptive dose‐finding approaches in the available literature account for the non‐monotonic dose–efficacy behavior by including additional model parameters. In this study, we propose a novel adaptive dose‐finding approach based on binary efficacy and toxicity outcomes in phase I trials for monotherapy using an MTA. We develop a dose–efficacy model, the parameters of which are allowed to change in the vicinity of the change point of the dose level, in order to consider the non‐monotonic pattern of the dose–efficacy relationship. The change point is obtained as the dose that maximizes the log‐likelihood of the assumed dose–efficacy and dose‐toxicity models. The dose‐finding algorithm is based on the weighted Mahalanobis distance, calculated using the posterior probabilities of efficacy and toxicity outcomes. We compare the operating characteristics between the proposed and existing methods and examine the sensitivity of the proposed method by simulation studies under various scenarios. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of the continual reassessment method to a phase I dose-finding trial in Japanese patients: East meets West

After cancer-related phase I dose-finding trials are completed in Western countries, further phase I trials are often conducted to determine recommended doses (RDS) for Japanese patients. This may be due to concerns about possible differences in treatment tolerability between Caucasians and Japanese. In most of these, a conventional '3 +3' cohort study design is used in making dose escalation decisions, possibly due to its relatively easy implementation. Since its proposal by O'Quigleybiet al. (1990; Biometrics, 46:33-48), the continual reassessment method (CRM) has been used increasingly in cancer-related phase I dose-finding studies as an alternative to '3 +3' designs. One of the principal advantages of applying a Bayesian CRM may be the utilization of all available prior information to estimate RDS through prior distributions that are assumed for model parameters representing the dose-toxicity relationship. In this paper, we present an application of the Bayesian CRM to a phase I dose-finding study in Japanese patients with advanced breast cancer using an informative prior elicited from clinical investigators. In some settings, it may be appropriate to use an informative prior that reflects the accurate and comprehensive previous knowledge of clinical investigators. On the other hand, for a model-based Bayesian outcome-adaptive clinical trial, it is necessary to establish sufficiently vague priors so that accumulating data dominate decisions as the amount of observed data increases. Thus, we retrospectively investigated the relative strength of the prior using a recently proposed method to compute a prior effective sample size.     

Commentary on ‘Designs for dose–escalation trials with quantitative responses’

Bailey (Statist. Medi 2009; this issue) puts the focus on efficiency in dose‐finding studies and shows that some quite simple modifications to much current experimentation can lead to significant efficiency gains. Efficiency has not been the main focus of interest in this field, in particular when dealing with situations requiring other than healthy volunteers. Dr Bailey's results are important, both in theory and in practice and also raise the question as to what ought to be the guiding principle to statistical workers in this field. Safety, although escaping any simple definition, has mostly guided experimentation in dose‐finding studies; one reason being that the concept is one on which clinicians and statisticians can come to some broad agreement. Finding such agreement may still be the single major difficulty in these studies, alongside the establishment of criteria that all of the scientists involved believe are the most appropriate and useful ones. Copyright © 2009 John Wiley & Sons, Ltd.     

Flexible Bayesian methods for cancer phase I clinical trials. Dose escalation with overdose control

We examine a large class of prior distributions to model the dose-response relationship in cancer phase I clinical trials. We parameterize the dose-toxicity model in terms of the maximum tolerated dose (MTD) gamma and the probability of dose limiting toxicity (DLT) at the initial dose rho(0). The MTD is estimated using the EWOC (escalation with overdose control) method of Babb et al. We show through simulations that a candidate joint prior for (rho0,gamma) with negative a priori correlation structure results in a safer trial than the one that assumes independent priors for these two parameters while keeping the efficiency of the estimate of the MTD essentially unchanged.     

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

The aim of phase I combination dose‐finding studies in oncology is to estimate one or several maximum tolerated doses (MTDs) from a set of available dose levels of two or more agents. Combining several agents can indeed increase the overall anti‐tumor action but at the same time also increase the toxicity. It is, however, unreasonable to assume the same dose–toxicity relationship for the combination as for the simple addition of each single agent because of a potential antagonist or synergistic effect. Therefore, using single‐agent dose‐finding methods for combination therapies is not appropriate. In recent years, several authors have proposed novel dose‐finding designs for combination studies, which use either algorithm‐based or model‐based methods. The aim of our work was to compare, via a simulation study, six dose‐finding methods for combinations proposed in recent years. We chose eight scenarios that differ in terms of the number and location of the true MTD(s) in the combination space. We then compared the performance of each design in terms of correct combination selection, patient allocation, and mean number of observed toxicities during the trials. Our results showed that the model‐based methods performed better than the algorithm‐based ones. However, none of the compared model‐based designs gave consistently better results than the others. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved up-and-down designs for phase I trials

We consider several designs from the family of up-and-down rules for the sequential allocation of dose levels to subjects in a dose-response study. We show that an up-and-down design can be improved by using more information than the most recent response. For example, the k-in-a-row rule uses up to the k most recent responses. We introduce a new design, the Narayana rule, which uses a local estimate of the probability of toxicity calculated from all previous responses. For the Narayana rule, as the sample size gets large, the probability of assignment goes to zero for dose levels not among the two (or three) closest to the target. Different estimators of the target dose are compared. We find that the isotonic regression estimator is superior to other estimators for small to moderate sample sizes.     

Adaptive dose modification for phase I clinical trials

Most phase I dose‐finding methods in oncology aim to find the maximum‐tolerated dose from a set of prespecified doses. However, in practice, because of a lack of understanding of the true dose–toxicity relationship, it is likely that none of these prespecified doses are equal or reasonably close to the true maximum‐tolerated dose. To handle this issue, we propose an adaptive dose modification (ADM) method that can be coupled with any existing dose‐finding method to adaptively modify the dose, when it is needed, during the course of dose finding. To reflect clinical practice, we divide the toxicity probability into three regions: underdosing, acceptable, and overdosing regions. We adaptively add a new dose whenever the observed data suggest that none of the investigational doses are likely to be located in the acceptable region. The new dose is estimated via a nonparametric dose–toxicity model based on local polynomial regression. The simulation study shows that ADM substantially outperforms the similar existing method. We applied ADM to a phase I cancer trial. Copyright © 2016 John Wiley & Sons, Ltd.     

A model-based approach in the estimation of the maximum tolerated dose in phase I cancer clinical trials

The primary aim of a phase I cancer clinical trial is to determine the maximum tolerated dose (MTD) of a new agent. The MTD is determined as the highest dose level of a potential therapeutic agent at which the patients have experienced an acceptable level of dose limiting toxicity. Although many other types of designs have been proposed in recent years, the traditional algorithm-based designs, especially the 3+3 designs, are still widely used due to their practical simplicity. Simulation studies have shown that the traditional algorithm-based designs cannot provide reasonable estimates of the MTD due to their intrinsic design limitations. In this paper, we propose a model-based approach in the estimation of the MTD following a traditional 3+3 design. Simulation results indicate that our model-based approach produces much less biased estimates of the MTD compared to the estimates obtained from the traditional 3+3 designs. Furthermore, our model-based approach can be easily extended to any traditional A+B design.     

Competing designs for phase I clinical trials: a review

Phase I clinical trials are typically small, uncontrolled studies designed to determine a maximum tolerated dose of a drug which will be used in further testing. Two divergent schools have developed in designing phase I clinical trials. The first defines the maximum tolerated dose as a statistic computed from data, and hence it is identified, rather than estimated. The second defines the maximum tolerated dose as a parameter of a monotonic dose-response curve, and hence is estimated. We review techniques from both philosophies. The goal is to present these methods in a single package, to compare them from philosophical and statistical grounds, to hopefully clear up some common misconceptions, and to make a few recommendations. This paper is not a review of simulation studies of these designs, nor does it present any new simulations comparing these designs.     

STEIN: A simple toxicity and efficacy interval design for seamless phase I/II clinical trials

Seamless phase I/II dose‐finding trials are attracting increasing attention nowadays in early‐phase drug development for oncology. Most existing phase I/II dose‐finding methods use sophisticated yet untestable models to quantify dose‐toxicity and dose‐efficacy relationships, which always renders them difficult to implement in practice. To simplify the practical implementation, we extend the Bayesian optimal interval design from maximum tolerated dose finding to optimal biological dose finding in phase I/II trials. In particular, optimized intervals for toxicity and efficacy are respectively derived by minimizing probabilities of incorrect classifications. If the pair of observed toxicity and efficacy probabilities at the current dose is located inside the promising region, we retain the current dose; if the observed probabilities are outside of the promising region, we propose an allocation rule by maximizing the posterior probability that the response rate of the next dose falls inside a prespecified efficacy probability interval while still controlling the level of toxicity. The proposed interval design is model‐free, thus is suitable for various dose‐response relationships. We conduct extensive simulation studies to demonstrate the small‐ and large‐sample performance of the proposed method under various scenarios. Compared to existing phase I/II dose‐finding designs, not only is our interval design easy to implement in practice, but it also possesses desirable and robust operating characteristics.