Phase I/II adaptive design for drug combination oncology trials

Existing statistical methodology on dose finding for combination chemotherapies has focused on toxicity considerations alone in finding a maximum tolerated dose combination to recommend for further testing of efficacy in a phase II setting. Recently, there has been increasing interest in integrating phase I and phase II trials in order to facilitate drug development. In this article, we propose a new adaptive phase I/II method for dual‐agent combinations that takes into account both toxicity and efficacy after each cohort inclusion. The primary objective, both within and at the conclusion of the trial, becomes finding a single dose combination with an acceptable level of toxicity that maximizes efficacious response. We assume that there exist monotone dose–toxicity and dose–efficacy relationships among doses of one agent when the dose of other agent is fixed. We perform extensive simulation studies that demonstrate the operating characteristics of our proposed approach, and we compare simulated results to existing methodology in phase I/II design for combinations of agents. Copyright © 2014 John Wiley & Sons, Ltd.     

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 Bayesian adaptive phase I–II trial design for optimizing the schedule of therapeutic cancer vaccines

Phase I–II clinical trials refer to the class of designs that evaluate both the safety and efficacy of a novel therapeutic agent in a single trial. Typically, Phase I–II oncology trials take the form of dose‐escalation studies, where initial subjects are treated at the lowest dose level and subsequent subjects are treated at progressively higher doses until the optimal dose is identified. While dose‐escalation designs are well‐motivated in the case of traditional chemotherapeutic agents, an alternate approach may be considered for therapeutic cancer vaccines, where an investigator's main objective is to evaluate the safety and efficacy of a set of dosing schedules or adjuvant combinations rather than to compare the safety and efficacy of progressively higher dose levels. We present a two‐stage, Bayesian adaptive Phase I–II trial design to evaluate the safety and efficacy of therapeutic cancer vaccines. In the first stage, we determine whether a vaccination schedule achieves a minimum level of performance by comparing the toxicity and immune response rates to historical benchmarks. Vaccination schedules that achieve a minimum level of performance are compared using their magnitudes of immune response. If the superiority of a single schedule cannot be established after the first stage, Bayesian posterior predictive probabilities are used to determine the additional sample size required to identify the optimal vaccination schedule in a second stage. Copyright © 2016 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 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.     

An adaptive phase I design for identifying a biologically optimal dose for dual agent drug combinations

Historically, designs for dose seeking trials using chemotherapeutic drug combinations have been geared towards finding the maximum tolerated dose, with safety as the primary outcome. With target based agents whose dose-efficacy curves are unknown and dose-toxicity relationships may be minimal, alternative designs are needed. In this paper, we propose an extension to an adaptive single agent dose-finding design previously reported. A generalization of the continuation ratio model allowing separate toxicity and efficacy curves for each agent in a dual agent combination, generating a dose success surface for the combination, is proposed. A continual reassessment approach with a straightforward dose selection criterion using the accumulated data from all patients treated to that point is employed. Our simulation studies demonstrate favourable operating characteristics in terms of experimentation and recommendation rates, and the average sample size, under a variety of scenarios. The proposed approach allowing the incorporation of both the toxicity and efficacy of each agent into the identification of an optimal dosing region for a combination is novel and warrants further consideration.     

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.     

Using the time‐to‐event continual reassessment method in the presence of partial orders

The time‐to‐event continual reassessment method (TITE‐CRM) was proposed to handle the problem of long trial duration in Phase 1 trials as a result of late‐onset toxicities. Here, we implement the TITE‐CRM in dose‐finding trials of combinations of agents. When studying multiple agents, monotonicity of the dose–toxicity curve is not clearly defined. Therefore, the toxicity probabilities follow a partial order, meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial. A CRM design for partially ordered trials (PO‐CRM) was recently proposed. Simulation studies show that extending the TITE‐CRM to the partial order setting produces results similar to those of the PO‐CRM in terms of maximum tolerated dose recommendation yet reduces the duration of the trial. Copyright © 2012 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 dose‐finding approach based on shrunken predictive probability for combinations of two agents in phase I trials

We develop a novel dose‐finding method for two‐agent combination phase I trials on the basis of the shrunken predictive probability of toxicity. In this method, a shrinkage logistic regression model that allows distinct shrinkage multipliers for the coefficients of the main effects of two agents and their interaction on the probability of toxicity constructs the toxicity outcome. We also propose dose‐escalation/de‐escalation decision rules on the basis of the shrunken predictive probability of toxicity. Simulation studies under various patterns of monotonic dose‐response relationships for combinations of two agents demonstrated that the proposed method performed no worse than the existing two dose‐finding methods we selected. Copyright © 2013 John Wiley & Sons, Ltd.     

A product of independent beta probabilities dose escalation design for dual‐agent phase I trials

Dual‐agent trials are now increasingly common in oncology research, and many proposed dose‐escalation designs are available in the statistical literature. Despite this, the translation from statistical design to practical application is slow, as has been highlighted in single‐agent phase I trials, where a 3 + 3 rule‐based design is often still used. To expedite this process, new dose‐escalation designs need to be not only scientifically beneficial but also easy to understand and implement by clinicians. In this paper, we propose a curve‐free (nonparametric) design for a dual‐agent trial in which the model parameters are the probabilities of toxicity at each of the dose combinations. We show that it is relatively trivial for a clinician's prior beliefs or historical information to be incorporated in the model and updating is fast and computationally simple through the use of conjugate Bayesian inference. Monotonicity is ensured by considering only a set of monotonic contours for the distribution of the maximum tolerated contour, which defines the dose‐escalation decision process. Varied experimentation around the contour is achievable, and multiple dose combinations can be recommended to take forward to phase II. Code for R , Stata and Excel are available for implementation. © 2015 The Authors. Statistics in Medicine Published by 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.     

Dose‐finding designs using a novel quasi‐continuous endpoint for multiple toxicities

The aim of a phase I oncology trial is to identify a dose with an acceptable safety profile. Most phase I designs use the dose‐limiting toxicity, a binary endpoint, to assess the unacceptable level of toxicity. The dose‐limiting toxicity might be incomplete for investigating molecularly targeted therapies as much useful toxicity information is discarded. In this work, we propose a quasi‐continuous toxicity score, the total toxicity profile (TTP), to measure quantitatively and comprehensively the overall severity of multiple toxicities. We define the TTP as the Euclidean norm of the weights of toxicities experienced by a patient, where the weights reflect the relative clinical importance of each grade and toxicity type. We propose a dose‐finding design, the quasi‐likelihood continual reassessment method (CRM), incorporating the TTP score into the CRM, with a logistic model for the dose–toxicity relationship in a frequentist framework. Using simulations, we compared our design with three existing designs for quasi‐continuous toxicity score (the Bayesian quasi‐CRM with an empiric model and two nonparametric designs), all using the TTP score, under eight different scenarios. All designs using the TTP score to identify the recommended dose had good performance characteristics for most scenarios, with good overdosing control. For a sample size of 36, the percentage of correct selection for the quasi‐likelihood CRM ranged from 80% to 90%, with similar results for the quasi‐CRM design. These designs with TTP score present an appealing alternative to the conventional dose‐finding designs, especially in the context of molecularly targeted agents. Copyright © 2013 John Wiley & Sons, Ltd.     

Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment

Many dose–response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick‐breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome‐specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether. Copyright © 2013 John Wiley & Sons, Ltd.     

Model‐based phase I designs incorporating toxicity and efficacy for single and dual agent drug combinations: Methods and challenges

Novel therapies are challenging the standards of drug development. Agents with specific biologic targets, unknown dose‐efficacy curves, and limited toxicity mandate novel designs to identify biologically optimal doses. We review two model‐based designs that utilize either a proportional odds model or a continuation ratio model to identify an optimal dose of a single or two‐agent combination in a Phase I setting utilizing both toxicity and efficacy data. A continual reassessment method with straightforward dose selection criterion using accumulated data from all patients treated until that time point is employed while allowing for separate toxicity and efficacy curves for each drug in a two‐drug setting. The simulation studies demonstrate considerable promise, at least theoretically, in the ability of such model‐based designs to identify the optimal dose. Despite such favorable operating characteristics, there are several pragmatic challenges that hinder the routine implementation of such model‐based designs in practice. We review and offer practical solutions to potentially overcome some of these challenges. The acceptance and integration of these designs in practice may be quicker and easier if they are developed in concert with a clinical paradigm. Copyright © 2010 John Wiley & Sons, Ltd.     

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 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.     

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.     

A design for phase I trials in completely or partially ordered groups

We propose a design for dose finding for cytotoxic agents in completely or partially ordered groups of patients. By completely ordered groups, we mean that prior to the study, there is clinical information that would indicate that for a given dose, the groups can be ordered with respect to the probability of toxicity at that dose. With partially ordered groups, at a given dose, only some of the groups can be ordered with respect to the probability of toxicity at that dose. The method we propose includes elements of the parametric model used in the continual reassessment method combined with the Hwang‐Peddada order‐restricted estimation procedure. We evaluate the operating characteristics of these designs in a family of dose–toxicity curves representing complete and partial orders. Copyright © 2017 John Wiley & Sons, Ltd.     

Mixed‐effects Gaussian process functional regression models with application to dose–response curve prediction

We propose a new semiparametric model for functional regression analysis, combining a parametric mixed‐effects model with a nonparametric Gaussian process regression model, namely a mixed‐effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose–response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose–response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient‐specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.