Improvements to the Escalation with Overdose Control design and a comparison with the restricted Continual Reassessment Method

The Escalation with Overdose Control (EWOC) design for cancer dose finding clinical trials is a variation of the Continual Reassessment Method (CRM) that was proposed to overcome the limitation of the original CRM of exposing patients to high toxic doses. The properties of EWOC have been studied to some extent, but some aspects of the design are not well studied, and its performance is not fully understood. Comparisons of the EWOC design to the most commonly used modified CRM designs have not yet been performed, and the advantages of EWOC over the modified CRM designs are unclear. In this paper, we assess the properties of the EWOC design and of the restricted CRM and some variations of these designs. We show that EWOC has several weaknesses that CRM does not have that make it impractical to use in its original formulation. We propose modified EWOC designs that address some of the weaknesses and that have some desirable statistical properties compared with the original EWOC design, the restricted CRM design, and the 3 + 3 design. However, their statistical properties are sensitive to correct specification of the prior distribution of their parameters and hence nevertheless will need to be used with some caution. The restricted CRM design is shown to have more stable performance across a wider family of dose‐toxicity curves than EWOC and therefore may be a preferable general choice in cancer clinical research.     

Theoretical study of the continual reassessment method

The continual reassessment method (CRM) was first introduced by O’Quigley et al. [1990. Continual reassessment method: a practical design for Phase I clinical trials in cancer. Biometrics 46, 33–48]. Many articles followed adding to the original ideas, among which are articles by Babb et al. [1998. Cancer Phase I clinical trials: efficient dose escalation with overdose control. Statist. Med. 17, 1103–1120], Braun [2002. The bivariate-continual reassessment method. Extending the CRM to phase I trials of two competing outcomes. Controlled Clin. Trials 23, 240–256], Chevret [1993. The continual reassessment method in cancer phase I clinical trials: a simulation study. Statist. Med. 12, 1093–1108], Faries [1994. Practical modifications of the continual reassessment method for phase I cancer clinical trials. J. Biopharm. Statist. 4, 147–164], Goodman et al. [1995. Some practical improvements in the continual reassessment method for phase I studies. Statist. Med. 14, 1149–1161], Ishizuka and Ohashi [2001. The continual reassessment method and its applications: a Bayesian methodology for phase I cancer clinical trials. Statist. Med. 20, 2661–2681], Legedeza and Ibrahim [2002. Longitudinal design for phase I trials using the continual reassessment method. Controlled Clin. Trials 21, 578–588], Mahmood [2001. Application of preclinical data to initiate the modified continual reassessment method for maximum tolerated dose-finding trial. J. Clin. Pharmacol. 41, 19–24], Moller [1995. An extension of the continual reassessment method using a preliminary up and down design in a dose finding study in cancer patients in order to investigate a greater number of dose levels. Statist. Med. 14, 911–922], O’Quigley [1992. Estimating the probability of toxicity at the recommended dose following a Phase I clinical trial in cancer. Biometrics 48, 853–862], O’Quigley and Shen [1996. Continual reassessment method: a likelihood approach. Biometrics 52, 163–174], O’Quigley et al. (1999), O’Quigley et al. [2002. Non-parametric optimal design in dose finding studies. Biostatistics 3, 51–56], O’Quigley and Paoletti [2003. Continual reassessment method for ordered groups. Biometrics 59, 429–439], Piantodosi et al., 1998. [1998 Practical implementation of a modified continual reassessment method for dose-finding trials. Cancer Chemother. Pharmacol. 41, 429–436] and Whitehead and Williamson [1998. Bayesian decision procedures based on logistic regression models for dose-finding studies. J. Biopharm. Statist. 8, 445–467]. The method is broadly described by Storer [1989. Design and analysis of Phase I clinical trials. Biometrics 45, 925–937]. Whether likelihood or Bayesian based, inference poses particular theoretical difficulties in view of working models being under-parameterized. Nonetheless CRM models have proven themselves to be of practical use and, in this work, the aim is to turn the spotlight on the main theoretical ideas underpinning the approach, obtaining results which can provide guidance in practice. Stemming from this theoretical framework are a number of results and some further development, in particular the way to structure a randomized allocation of subjects as well as a more robust approach to the problem of dealing with patient heterogeneity.     

Incorporating historical information to improve phase I clinical trials

Incorporating historical data has a great potential to improve the efficiency of phase I clinical trials and to accelerate drug development. For model-based designs, such as the continuous reassessment method (CRM), this can be conveniently carried out by specifying a “skeleton,” that is, the prior estimate of dose limiting toxicity (DLT) probability at each dose. In contrast, little work has been done to incorporate historical data into model-assisted designs, such as the Bayesian optimal interval (BOIN), Keyboard, and modified toxicity probability interval (mTPI) designs. This has led to the misconception that model-assisted designs cannot incorporate prior information. In this paper, we propose a unified framework that allows for incorporating historical data into model-assisted designs. The proposed approach uses the well-established “skeleton” approach, combined with the concept of prior effective sample size, thus it is easy to understand and use. More importantly, our approach maintains the hallmark of model-assisted designs: simplicity—the dose escalation/de-escalation rule can be tabulated prior to the trial conduct. Extensive simulation studies show that the proposed method can effectively incorporate prior information to improve the operating characteristics of model-assisted designs, similarly to model-based designs.     

Robust EM Continual Reassessment Method in Oncology Dose Finding

The continual reassessment method (CRM) is a commonly used dose-finding design for phase I clinical trials. Practical applications of this method have been restricted by two limitations: (1) the requirement that the toxicity outcome needs to be observed shortly after the initiation of the treatment; and (2) the potential sensitivity to the prespecified toxicity probability at each dose. To overcome these limitations, we naturally treat the unobserved toxicity outcomes as missing data, and use the expectation-maximization (EM) algorithm to estimate the dose toxicity probabilities based on the incomplete data to direct dose assignment. To enhance the robustness of the design, we propose prespecifying multiple sets of toxicity probabilities, each set corresponding to an individual CRM model. We carry out these multiple CRMs in parallel, across which model selection and model averaging procedures are used to make more robust inference. We evaluate the operating characteristics of the proposed robust EM-CRM designs through simulation studies and show that the proposed methods satisfactorily resolve both limitations of the CRM. Besides improving the MTD selection percentage, the new designs dramatically shorten the duration of the trial, and are robust to the prespecification of the toxicity probabilities.     

Designs foe phase i cancer clinical trials with differentiation of graded toxicity

For phase I cancer clinical trials, toxicity is a major concern. Commonly, toxicity is categorized to five levels of severity. In addition to the traditional standard dose-escaiation design, the Continual Reassessment Method (CRM) provides a promising alternative to estimate the maximum tolerated dose of a drug. However, in both standard design (STD) and CRM, the severity level of toxicity on grade 3/4 of a previous patient's response would not be a differentiated factor for the next dose level assignment. In this study, we extend the procedure incorporating the idea of unequal weights on the assessments of grade 3 and grade 4 toxicity in the dose escalation. The simulation results show that the proposed extended procedures by taking the impact of grade 4 toxicity into account, both for STD and CRM, reduce the chance of recommendation to the higher dose levels. Similar trends are observed for patient allocation to the higher levels. Additionally, for CRM which performs more accurately on the estimation of maximum tolerated dose (MTD), the proposed extended CRM maintains the same characteristic.     

Specifications of a continual reassessment method design for phase I trials of combined drugs

In studies of combinations of agents in phase I oncology trials, the dose–toxicity relationship may not be monotone for all combinations, in which case the toxicity probabilities follow a partial order. The continual reassessment method for partial orders (PO‐CRM) is a design for phase I trials of combinations that leans upon identifying possible complete orders associated with the partial order. This article addresses some practical design considerations not previously undertaken when describing the PO‐CRM. We describe an approach in choosing a proper subset of possible orderings, formulated according to the known toxicity relationships within a matrix of combination therapies. Other design issues, such as working model selection and stopping rules, are also discussed. We demonstrate the practical ability of PO‐CRM as a phase I design for combinations through its use in a recent trial designed at the University of Virginia Cancer Center. Copyright © 2013 John Wiley & Sons, Ltd.     

Convergence properties of sequential Bayesian D-optimal designs

We establish convergence properties of sequential Bayesian optimal designs. In particular, for sequential D-optimality under a general nonlinear location-scale model for binary experiments, we establish posterior consistency, consistency of the design measure, and the asymptotic normality of posterior following the design. We illustrate our results in the context of a particular application in the design of phase I clinical trials, namely a sequential design of Haines et al. [2003. Bayesian optimal designs for phase I clinical trials. Biometrics 59, 591–600] that incorporates an ethical constraint on overdosing.     

Performance of phase-I dose finding designs with and without a run-in intra-patient dose escalation stage

Dose-finding designs for phase-I trials aim to determine the recommended phase-II dose (RP2D) for further phase-II drug development. If the trial includes patients for whom several lines of standard therapy failed or if the toxicity of the investigated agent does not necessarily increase with dose, optimal dose-finding designs should limit the frequency of treatment with suboptimal doses. We propose a two-stage design strategy with a run-in intra-patient dose escalation part followed by a more traditional dose-finding design. We conduct simulation studies to compare the 3 + 3 design, the Bayesian Optimal Interval Design (BOIN) and the Continual Reassessment Method (CRM) with and without intra-patient dose escalation. The endpoints are accuracy, sample size, safety, and therapeutic efficiency. For scenarios where the correct RP2D is the highest dose, inclusion of an intra-patient dose escalation stage generally increases accuracy and therapeutic efficiency. However, for scenarios where the correct RP2D is below the highest dose, intra-patient dose escalation designs lead to increased risk of overdosing and an overestimation of RP2D. The magnitude of the change in operating characteristics after including an intra-patient stage is largest for the 3 + 3 design, decreases for the BOIN and is smallest for the CRM.     

Patient-specific dose finding in phase I clinical trials

This article proposes an extension of the continual reassessment method to determine the maximum tolerated dose (MTD) in the presence of patients' heterogeneity in phase I clinical trials. To start with a simple case, we consider the covariate as a binary variable representing two groups of patients. A logistic regression model is used to establish the dose–response relationship and the design is based on the Bayesian framework. Simulation studies for six plausible dose–response scenarios show that the proposed design is likely to determine the MTD more accurately than the design that does not take covariate into consideration.     

Escalation strategies for combination therapy Phase I trials

Phase I clinical trials aim to identify a maximum tolerated dose (MTD), the highest possible dose that does not cause an unacceptable amount of toxicity in the patients. In trials of combination therapies, however, many different dose combinations may have a similar probability of causing a dose‐limiting toxicity, and hence, a number of MTDs may exist. Furthermore, escalation strategies in combination trials are more complex, with possible escalation/de‐escalation of either or both drugs. This paper investigates the properties of two existing proposed Bayesian adaptive models for combination therapy dose‐escalation when a number of different escalation strategies are applied. We assess operating characteristics through a series of simulation studies and show that strategies that only allow ‘non‐diagonal’ moves in the escalation process (that is, both drugs cannot increase simultaneously) are inefficient and identify fewer MTDs for Phase II comparisons. Such strategies tend to escalate a single agent first while keeping the other agent fixed, which can be a severe restriction when exploring dose surfaces using a limited sample size. Meanwhile, escalation designs based on Bayesian D‐optimality allow more varied experimentation around the dose space and, consequently, are better at identifying more MTDs. We argue that for Phase I combination trials it is sensible to take forward a number of identified MTDs for Phase II experimentation so that their efficacy can be directly compared. Researchers, therefore, need to carefully consider the escalation strategy and model that best allows the identification of these MTDs. Copyright © 2012 John Wiley & Sons, Ltd.     

AIDE: Adaptive intrapatient dose escalation designs to accelerate Phase I clinical trials

Designing Phase I clinical trials is challenging when accrual is slow or sample size is limited. The corresponding key question is: how to efficiently and reliably identify the maximum tolerated dose (MTD) using a sample size as small as possible? We propose model-assisted and model-based designs with adaptive intrapatient dose escalation (AIDE) to address this challenge. AIDE is adaptive in that the decision of conducting intrapatient dose escalation depends on both the patient's individual safety data, as well as other enrolled patient's safety data. When both data indicate reasonable safety, a patient may perform intrapatient dose escalation, generating toxicity data at more than one dose. This strategy not only provides patients the opportunity to receive higher potentially more effective doses, but also enables efficient statistical learning of the dose-toxicity profile of the treatment, which dramatically reduces the required sample size. Simulation studies show that the proposed designs are safe, robust, and efficient to identify the MTD with a sample size that is substantially smaller than conventional interpatient dose escalation designs. Practical considerations are provided and R code for implementing AIDE is available upon request.     

Dose finding when the target dose is on a plateau of a dose–response curve: comparison of fully sequential designs

Consider the problem of estimating a dose with a certain response rate. Many multistage dose‐finding designs for this problem were originally developed for oncology studies where the mean dose–response is strictly increasing in dose. In non‐oncology phase II dose‐finding studies, the dose–response curve often plateaus in the range of interest, and there are several doses with the mean response equal to the target. In this case, it is usually of interest to find the lowest of these doses because higher doses might have higher adverse event rates. It is often desirable to compare the response rate at the estimated target dose with a placebo and/or active control. We investigate which of the several known dose‐finding methods developed for oncology phase I trials is the most suitable when the dose–response curve plateaus. Some of the designs tend to spread the allocation among the doses on the plateau. Others, such as the continual reassessment method and the t‐statistic design, concentrate allocation at one of the doses with the t‐statistic design selecting the lowest dose on the plateau more frequently. Copyright © 2013 John Wiley & Sons, Ltd.     

抗肿瘤药物贝叶斯Ⅰ期临床试验设计方法比较研究

Ⅰ期临床试验的主要目的是探索药物毒性最大耐受剂量MTD,而MTD估计的准确与否将影响之后的Ⅱ期和Ⅲ期临床试验研究的结果.抗肿瘤药物Ⅰ期试验的特点是直接对病人进行试验,且样本量较小,这对构造估计精确度高并具有安全性保障要求的统计设计方法提出了挑战.回顾三种常用的Ⅰ期试验设计方法有:3+3设计、CRM设计和mTPI设计.3+3设计是应用较为广泛的传统方法,后两者是当前常用的贝叶斯自适应试验设计方法.通过大量模拟研究对三种方法从最优分配、安全性和估计MTD精确性三方面给以全面考察,并结合中国实际得出mTPI设计是比较适合推荐的Ⅰ期临床试验设计方法的结论.     

A Three-Stage Bayesian Adaptive Phase I/II Design and Simulation Studies

Instead of using traditional separate phase I and II trials, in this article, we propose using a parallel three-stage phase I/II design, incorporating a dose expansion approach to flexibly evaluate the safety and efficacy of dose levels, and to select the optimal dose. In the proposed design, both the toxicity and efficacy responses are binary endpoints. A 3+3-based procedure is used for initial period of dose escalation at stage 1; at this level, the dose can be expanded to stage 2 for exploratory efficacy studies of phase IIa, while simultaneously, the safety testing can advance to a higher dose level. A beta-binomial model is used to model the efficacy responses. There are two placebo-controlled randomization interim monitoring analyses at stage 2 to select the promising doses to be recommended to stage 3 for further efficacy studies of phase IIb. An adaptive randomization approach is used to assign more patients to doses with higher efficacy levels at stage 3. We examine the properties of the proposed design through extensive simulation studies by using R programming language, and also compare the new design with the conventional design and a competing adaptive Bayesian design. The simulation results show that our design can efficiently assign more patients to doses with higher efficacy levels and is superior to the two competing designs in terms of total sample size reduction.     

Cumulative cohort design for dose-finding

We introduce a new design for dose-finding in the context of toxicity studies for which it is assumed that toxicity increases with dose. The goal is to identify the maximum tolerated dose, which is taken to be the dose associated with a prespecified “target” toxicity rate. The decision to decrease, increase or repeat a dose for the next subject depends on how far an estimated toxicity rate at the current dose is from the target. The size of the window within which the current dose will be repeated is obtained based on the theory of Markov chains as applied to group up-and-down designs. But whereas the treatment allocation rule in Markovian group up-and-down designs is only based on information from the current cohort of subjects, the treatment allocation rule for the proposed design is based on the cumulative information at the current dose. We then consider an extension of this new design for clinical trials in which the subject's outcome is not known immediately. The new design is compared to the continual reassessment method.     

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

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

Generalized phase I-II designs to increase long term therapeutic success rate

Designs for early phase dose finding clinical trials typically are either phase I based on toxicity, or phase I-II based on toxicity and efficacy. These designs rely on the implicit assumption that the dose of an experimental agent chosen using these short-term outcomes will maximize the agent's long-term therapeutic success rate. In many clinical settings, this assumption is not true. A dose selected in an early phase oncology trial may give suboptimal progression-free survival or overall survival time, often due to a high rate of relapse following response. To address this problem, a new family of Bayesian generalized phase I-II designs is proposed. First, a conventional phase I-II design based on short-term outcomes is used to identify a set of candidate doses, rather than selecting one dose. Additional patients then are randomized among the candidates, patients are followed for a predefined longer time period, and a final dose is selected to maximize the long-term therapeutic success rate, defined in terms of duration of response. Dose-specific sample sizes in the randomization are determined adaptively to obtain a desired level of selection reliability. The design was motivated by a phase I-II trial to find an optimal dose of natural killer cells as targeted immunotherapy for recurrent or treatment-resistant B-cell hematologic malignancies. A simulation study shows that, under a range of scenarios in the context of this trial, the proposed design has much better performance than two conventional phase I-II designs.     

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. Copyright © 2014 John Wiley & Sons, Ltd.     

Curtailed two-stage designs with two dependent binary endpoints

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs.     

TITE‐BOIN‐ET: Time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on both efficacy and toxicity outcomes

One of the primary purposes of an oncology dose‐finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de‐escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late‐onset outcomes. To solve these issues, we propose the time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on cumulative and pending data of both efficacy and toxicity. The new design, named “TITE‐BOIN‐ET” design, is nonparametric and a model‐assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose‐finding trials compared with the model‐based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE‐BOIN‐ET design has advantages compared with the model‐based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE‐BOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose‐finding trials.