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

Traditionally, model‐based dose‐escalation trial designs recommend a dose for escalation based on an assumed dose‐toxicity relationship. Pharmacokinetic data are often available but are currently only utilised by clinical teams in a subjective manner to aid decision making if the dose‐toxicity model recommendation is felt to be too high. Formal incorporation of pharmacokinetic data in dose‐escalation could therefore make the decision process more efficient and lead to an increase in the precision of the resulting recommended dose, as well as decreasing the subjectivity of its use. Such an approach is investigated in the dual‐agent setting using a Bayesian design, where historical single‐agent data are available to advise the use of pharmacokinetic data in the dual‐agent setting. The dose‐toxicity and dose‐exposure relationships are modelled independently and the outputs combined in the escalation rules. Implementation of stopping rules highlight the practicality of the design. This is demonstrated through an example which is evaluated using simulation. Copyright © 2015 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.     

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.     

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.     

A Bayesian dose‐finding design for phase I/II clinical trials with nonignorable dropouts

Phase I/II trials utilize both toxicity and efficacy data to achieve efficient dose finding. However, due to the requirement of assessing efficacy outcome, which often takes a long period of time to be evaluated, the duration of phase I/II trials is often longer than that of the conventional dose‐finding trials. As a result, phase I/II trials are susceptible to the missing data problem caused by patient dropout, and the missing efficacy outcomes are often nonignorable in the sense that patients who do not experience treatment efficacy are more likely to drop out of the trial. We propose a Bayesian phase I/II trial design to accommodate nonignorable dropouts. We treat toxicity as a binary outcome and efficacy as a time‐to‐event outcome. We model the marginal distribution of toxicity using a logistic regression and jointly model the times to efficacy and dropout using proportional hazard models to adjust for nonignorable dropouts. The correlation between times to efficacy and dropout is modeled using a shared frailty. We propose a two‐stage dose‐finding algorithm to adaptively assign patients to desirable doses. Simulation studies show that the proposed design has desirable operating characteristics. Our design selects the target dose with a high probability and assigns most patients to the target dose. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive dose finding for phase I clinical trials of drugs used for chemotherapy of cancer

Phase I clinical trials of cancer chemotherapy drugs are intended to determine the maximum tolerable dose (MTD). Thestandard method employed is a rule-based dose-escalation scheme in which escalation depends on the number of patients at a dose level that have dose-limiting toxicity (DLT). The MTD is thus defined in terms of the rules and a series of dose levels selected for sampling. For some trials it is desirable to have a more precise definition of the MTD, and to determine the MTD more accurately than possible with the rule-based schemes. Continuous reassessment methods (CRMs) define the MTD to be the dose at which a fixed fraction of patients experience DLT, and thus appear suited to these trials. It is shown, however, that these methods can have failure modes that in fact make them unattractive. An alternative data-driven dose-finding method is described that combines the robustness of the rule-based methods and with features of CRMs. The method has two stages. In the first stage, doses are escalated by a factor of 1.5. In the second stage, which begins at the first instance of DLT, a two-parameter logistic dose-response model estimates the MTD from the DLT experience of all patients. The model is initialized by setting the dose (d10) at which 10 per cent of patients would experience DLT to half the dose at which the first DLT was observed, and the dose (d90) at which 90 per cent would experience DLT to ten times d10. Weights are assigned such that the information at d10 and d90 is equivalent to that of one patient at each of the two doses. Cohorts of three patients are treated in both stages, and the dose for a new cohort in the second stage is the estimated MTD. The only prior information required to specify the design completely is the dose which will be given to the first cohort. Two stopping rules are investigated; among the requirements for these are that at least three (or four) DLTs be observed and at least nine patients be treated in the second stage. Simulations show that a coefficient of variation of approximately 0.4 on a target DLT probability of 0.3 is obtained over a wide variation in dose-response characteristics of the study drug. The performance of the new method is compared to that of rule-based methods.     

A Bayesian dose finding design for dual endpoint phase I trials

We propose a dose-finding weighted design for an early clinical trial which aims to determine the optimal dose, selected on the basis of both efficacy and toxicity, to be used in patients entering subsequent studies in a drug development process. The goal is to identify the optimal dose, while using a minimal number of subjects. For each dose under test, a decision table is defined with a utility value attached to each possible decision. The relationship between the utility and the target probability for each outcome is shown. A Dirichlet prior is used and we illustrate the process of maximizing the expected utility under the resulting posterior distribution to find the optimal decision at each stage of the trial. We show how this affects the eventual choice of optimal dose in various scenarios. Properties of our design are discussed and compared with a current standard design.     

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.     

Two‐stage dose finding for cytostatic agents in phase I oncology trials

Conventional dose‐finding methods in oncology are mainly developed for cytotoxic agents with the aim of finding the maximum tolerated dose. In phase I clinical trials with cytostatic agents, such as targeted therapies, designs with toxicity endpoints alone may not work well. For cytostatic agents, the goal is often to find the most efficacious dose that is still tolerable, although these agents are typically less toxic than cytotoxic agents and their efficacy may not monotonically increase with the dose. To effectively differentiate doses for cytostatic agents, we develop a two‐stage dose‐finding procedure by first identifying the toxicity upper bound of the searching range through dose escalation and then determining the most efficacious dose through dose de‐escalation while toxicity is continuously monitored. In oncology, treatment efficacy often takes a relatively long period to exhibit compared with toxicity. To accommodate such delayed response, we model the time to the efficacy event by redistributing the mass of the censored observation to the right and compute the fractional contribution of the censored data. We evaluate the operating characteristics of the new dose‐finding design for cytostatic agents and demonstrate its satisfactory performance through simulation studies. Copyright © 2012 John Wiley & Sons, Ltd.     

A Bayesian dose‐finding procedure for phase I clinical trials based only on the assumption of monotonicity

Despite an enormous and growing statistical literature, formal procedures for dose‐finding are only slowly being implemented in phase I clinical trials. Even in oncology and other life‐threatening conditions in which a balance between efficacy and toxicity has to be struck, model‐based approaches, such as the Continual Reassessment Method, have not been universally adopted. Two related concerns have limited the adoption of the new methods. One relates to doubts about the appropriateness of models assumed to link the risk of toxicity to dose, and the other is the difficulty of communicating the nature of the process to clinical investigators responsible for early phase studies. In this paper, we adopt a new Bayesian approach involving a simple model assuming only monotonicity in the dose‐toxicity relationship. The parameters that define the model have immediate and simple interpretation. The approach can be applied automatically, and we present a simulation investigation of its properties when it is. More importantly, it can be used in a transparent fashion as one element in the expert consideration of what dose to administer to the next patient or group of patients. The procedure serves to summarize the opinions and the data concerning risks of a binary characterization of toxicity which can then be considered, together with additional and less tidy trial information, by the clinicians responsible for making decisions on the allocation of doses. Graphical displays of these opinions can be used to ease communication with investigators. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

A three-outcome design for randomized comparative phase II clinical trials

Randomized designs have been increasingly called for use in phase II oncology clinical trials to protect against potential patient selection bias. However, formal statistical comparison is rarely conducted due to the sample size restriction, despite its appeal. In this paper, we offer an approach to sample size reduction by extending the three-outcome design of Sargent et al. (Control Clin. Trials 2001; 22:117-125) for single-arm trials to randomized comparative trials. In addition to the usual two outcomes of a hypothesis testing (rejecting the null hypothesis or rejecting the alternative hypothesis), the three-outcome comparative design allows a third outcome of rejecting neither hypotheses when the testing result is in some 'grey area' and leaves the decision to the clinical judgment based on the overall evaluation of trial outcomes and other relevant factors. By allowing a reasonable region of uncertainty, the three-outcome design enables formal statistical comparison with considerably smaller sample size, compared to the standard two-outcome comparative design. Statistical formulation of the three-outcome comparative design is discussed for both the single-stage and two-stage trials. Sample sizes are tabulated for some common clinical scenarios.     

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. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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

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

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

We present a Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials. The goal is to estimate the maximum tolerated dose (MTD) as a curve in the two‐dimensional Cartesian plane. We use a logistic model to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re‐parameterized in terms of parameters clinicians can easily interpret. Trial design proceeds using univariate escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. At the end of the trial, an estimate of the MTD curve is proposed as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial design and percent of dose recommendation at dose combination neighborhoods around the true MTD curve. We also examine the performance of the approach under model misspecifications for the true dose–toxicity relationship. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayesian adaptive phase I/II platform trial design for pediatric immunotherapy trials

Immunotherapy is the most promising new cancer treatment for various pediatric tumors and has resulted in an unprecedented surge in the number of novel immunotherapeutic treatments that need to be evaluated in clinical trials. Most phase I/II trial designs have been developed for evaluating only one candidate treatment at a time, and are thus not optimal for this task. To address these issues, we propose a Bayesian phase I/II platform trial design, which accounts for the unique features of immunotherapy, thereby allowing investigators to continuously screen a large number of immunotherapeutic treatments in an efficient and seamless manner. The elicited numerical utility is adopted to account for the risk‐benefit trade‐off and to quantify the desirability of the dose. During the trial, inefficacious or overly toxic treatments are adaptively dropped from the trial and the promising treatments are graduated from the trial to the next stage of development. Once an experimental treatment is dropped or graduated, the next available new treatment can be immediately added and tested. Extensive simulation studies have demonstrated the desirable operating characteristics of the proposed design.     

A varying‐stage adaptive phase II/III clinical trial design

Currently, adaptive phase II/III clinical trials are typically carried out with a strict two‐stage design. The first stage is a learning stage called phase II, and the second stage is a confirmatory stage called phase III. Following phase II analysis, inefficacious or harmful dose arms are dropped, then one or two promising dose arms are selected for the second stage. However, there are often situations in which researchers are in dilemma to make ‘go or no‐go’ decision and/or to select ‘best’ dose arm(s), as data from the first stage may not provide sufficient information for their decision making. In this case, it is challenging to follow a strict two‐stage plan. Therefore, we propose a varying‐stage adaptive phase II/III clinical trial design, in which we consider whether there is a need to have an intermediate stage to obtain more data, so that a more informative decision could be made. Hence, the number of further investigational stages in our design is determined on the basis of data accumulated to the interim analysis. With respect to adaptations, we consider dropping dose arm(s), switching another plausible endpoint as the primary study endpoint, re‐estimating sample size, and early stopping for futility. We use an adaptive combination test to perform final analyses. By applying closed testing procedure, we control family‐wise type I error rate at the nominal level of α in the strong sense. We delineate other essential design considerations including the threshold parameters and the proportion of alpha allocated in the two‐stage versus three‐stage setting. Copyright © 2013 John Wiley & Sons, Ltd.