Characterization of dose‐response for count data using a generalized MCP‐Mod approach in an adaptive dose‐ranging trial

Understanding the dose–response relationship is a key objective in Phase II clinical development. Yet, designing a dose‐ranging trial is a challenging task, as it requires identifying the therapeutic window and the shape of the dose–response curve for a new drug on the basis of a limited number of doses. Adaptive designs have been proposed as a solution to improve both quality and efficiency of Phase II trials as they give the possibility to select the dose to be tested as the trial goes. In this article, we present a ‘shapebased’ two‐stage adaptive trial design where the doses to be tested in the second stage are determined based on the correlation observed between efficacy of the doses tested in the first stage and a set of pre‐specified candidate dose–response profiles. At the end of the trial, the data are analyzed using the generalized MCP‐Mod approach in order to account for model uncertainty. A simulation study shows that this approach gives more precise estimates of a desired target dose (e.g. ED70) than a single‐stage (fixed‐dose) design and performs as well as a two‐stage D‐optimal design. We present the results of an adaptive model‐based dose‐ranging trial in multiple sclerosis that motivated this research and was conducted using the presented methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

An alternative phase II/III design for continuous endpoints

The success rate of drug development has been declined dramatically in recent years and the current paradigm of drug development is no longer functioning. It requires a major undertaking on breakthrough strategies and methodology for designs to minimize sample sizes and to shorten duration of the development. We propose an alternative phase II/III design based on continuous efficacy endpoints, which consists of two stages: a selection stage and a confirmation stage. For the selection stage, a randomized parallel design with several doses with a placebo group is employed for selection of doses. After the best dose is chosen, the patients of the selected dose group and placebo group continue to enter the confirmation stage. New patients will also be recruited and randomized to receive the selected dose or placebo group. The final analysis is performed with the cumulative data of patients from both stages. With the pre‐specified probabilities of rejecting the drug at each stage, sample sizes and critical values for both stages can be determined. As it is a single trial with controlling overall type I and II error rates, the proposed phase II/III adaptive design may not only reduce the sample size but also improve the success rate. An example illustrates the applications of the proposed phase II/III adaptive design. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of Bayesian hierarchical models for phase I/II clinical trials in oncology

Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade‐offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving‐reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.     

Bayesian phase II adaptive randomization by jointly modeling time-to-event efficacy and binary toxicity

In oncology, toxicity is typically observable shortly after a chemotherapy treatment, whereas efficacy, often characterized by tumor shrinkage, is observable after a relatively long period of time. In a phase II clinical trial design, we propose a Bayesian adaptive randomization procedure that accounts for both efficacy and toxicity outcomes. We model efficacy as a time-to-event endpoint and toxicity as a binary endpoint, sharing common random effects in order to induce dependence between the bivariate outcomes. More generally, we allow the randomization probability to depend on patients’ specific covariates, such as prognostic factors. Early stopping boundaries are constructed for toxicity and futility, and a superior treatment arm is recommended at the end of the trial. Following the setup of a recent renal cancer clinical trial at M. D. Anderson Cancer Center, we conduct extensive simulation studies under various scenarios to investigate the performance of the proposed method, and compare it with available Bayesian adaptive randomization procedures.     

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.     

Stopping for efficacy in single-arm phase II clinical trials

Phase II clinical trials investigate whether a new drug or treatment has sufficient evidence of effectiveness against the disease under study. Two-stage designs are popular for phase II since they can stop in the first stage if the drug is ineffective. Investigators often face difficulties in determining the target response rates, and adaptive designs can help to set the target response rate tested in the second stage based on the number of responses observed in the first stage. Popular adaptive designs consider two alternate response rates, and they generally minimise the expected sample size at the maximum uninterested response rate. Moreover, these designs consider only futility as the reason for early stopping and have high expected sample sizes if the provided drug is effective. Motivated by this problem, we propose an adaptive design that enables us to terminate the single-arm trial at the first stage for efficacy and conclude which alternate response rate to choose. Comparing the proposed design with a popular adaptive design from literature reveals that the expected sample size decreases notably if any of the two target response rates are correct. In contrast, the expected sample size remains almost the same under the null hypothesis.     

Bayesian randomized clinical trials: A decision‐theoretic sequential design

The authors propose a Bayesian decision‐theoretic framework justifying randomization in clinical trials. Noting that the decision maker is often unable or unwilling to specify a unique utility function, they develop a sequential myopic design that includes randomization justified by the consideration of a set of utility functions. Randomization is introduced over all nondominated treatments, allowing for interim removal of treatments and early stopping. The authors illustrate their approach in the context of a study to find the optimal dose of pegylated interferon for platinum resistant ovarian cancer. They also develop an algorithm to implement their methodology in a phase II clinical trial comparing several competing experimental treatments.     

Bayesian adaptive dose‐escalation designs for simultaneously estimating the optimal and maximum safe dose based on safety and efficacy

The main purpose of dose‐escalation trials is to identify the dose(s) that is/are safe and efficacious for further investigations in later studies. In this paper, we introduce dose‐escalation designs that incorporate both the dose‐limiting events and dose‐limiting toxicities (DLTs) and indicative responses of efficacy into the procedure. A flexible nonparametric model is used for modelling the continuous efficacy responses while a logistic model is used for the binary DLTs. Escalation decisions are based on the combination of the probabilities of DLTs and expected efficacy through a gain function. On the basis of this setup, we then introduce 2 types of Bayesian adaptive dose‐escalation strategies. The first type of procedures, called “single objective,” aims to identify and recommend a single dose, either the maximum tolerated dose, the highest dose that is considered as safe, or the optimal dose, a safe dose that gives optimum benefit risk. The second type, called “dual objective,” aims to jointly estimate both the maximum tolerated dose and the optimal dose accurately. The recommended doses obtained under these dose‐escalation procedures provide information about the safety and efficacy profile of the novel drug to facilitate later studies. We evaluate different strategies via simulations based on an example constructed from a real trial on patients with type 2 diabetes, and the use of stopping rules is assessed. We find that the nonparametric model estimates the efficacy responses well for different underlying true shapes. The dual‐objective designs give better results in terms of identifying the 2 real target doses compared to the single‐objective designs.     

Bayesian adaptive dose‐escalation procedures for binary and continuous responses utilizing a gain function

One of the main aims of early phase clinical trials is to identify a safe dose with an indication of therapeutic benefit to administer to subjects in further studies. Ideally therefore, dose‐limiting events (DLEs) and responses indicative of efficacy should be considered in the dose‐escalation procedure. Several methods have been suggested for incorporating both DLEs and efficacy responses in early phase dose‐escalation trials. In this paper, we describe and evaluate a Bayesian adaptive approach based on one binary response (occurrence of a DLE) and one continuous response (a measure of potential efficacy) per subject. A logistic regression and a linear log‐log relationship are used respectively to model the binary DLEs and the continuous efficacy responses. A gain function concerning both the DLEs and efficacy responses is used to determine the dose to administer to the next cohort of subjects. Stopping rules are proposed to enable efficient decision making. Simulation results shows that our approach performs better than taking account of DLE responses alone. To assess the robustness of the approach, scenarios where the efficacy responses of subjects are generated from an E _max model, but modelled by the linear log–log model are also considered. This evaluation shows that the simpler log–log model leads to robust recommendations even under this model showing that it is a useful approximation to the difficulty in estimating E _max model. Additionally, we find comparable performance to alternative approaches using efficacy and safety for dose‐finding. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive Bayesian compound designs for dose finding studies

We consider the problem of how to efficiently and safely design dose finding studies. Both current and novel utility functions are explored using Bayesian adaptive design methodology for the estimation of a maximum tolerated dose (MTD). In particular, we explore widely adopted approaches such as the continual reassessment method and minimizing the variance of the estimate of an MTD. New utility functions are constructed in the Bayesian framework and are evaluated against current approaches. To reduce computing time, importance sampling is implemented to re-weight posterior samples thus avoiding the need to draw samples using Markov chain Monte Carlo techniques. Further, as such studies are generally first-in-man, the safety of patients is paramount. We therefore explore methods for the incorporation of safety considerations into utility functions to ensure that only safe and well-predicted doses are administered. The amalgamation of Bayesian methodology, adaptive design and compound utility functions is termed adaptive Bayesian compound design (ABCD). The performance of this amalgamation of methodology is investigated via the simulation of dose finding studies. The paper concludes with a discussion of results and extensions that could be included into our approach.     

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.     

Bayesian adaptive linearization method for phase I drug combination trials with dimension reduction

Many phase I drug combination designs have been proposed to find the maximum tolerated combination (MTC). Due to the two‐dimension nature of drug combination trials, these designs typically require complicated statistical modeling and estimation, which limit their use in practice. In this article, we propose an easy‐to‐implement Bayesian phase I combination design, called Bayesian adaptive linearization method (BALM), to simplify the dose finding for drug combination trials. BALM takes the dimension reduction approach. It selects a subset of combinations, through a procedure called linearization, to convert the two‐dimensional dose matrix into a string of combinations that are fully ordered in toxicity. As a result, existing single‐agent dose‐finding methods can be directly used to find the MTC. In case that the selected linear path does not contain the MTC, a dose‐insertion procedure is performed to add new doses whose expected toxicity rate is equal to the target toxicity rate. Our simulation studies show that the proposed BALM design performs better than competing, more complicated combination designs.     

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.     

Incorporating historical information to improve dose optimization design with toxicity and efficacy endpoints: iBOIN-ET

In modern oncology drug development, adaptive designs have been proposed to identify the recommended phase 2 dose. The conventional dose finding designs focus on the identification of maximum tolerated dose (MTD). However, designs ignoring efficacy could put patients under risk by pushing to the MTD. Especially in immuno-oncology and cell therapy, the complex dose-toxicity and dose-efficacy relationships make such MTD driven designs more questionable. Additionally, it is not uncommon to have data available from other studies that target on similar mechanism of action and patient population. Due to the high variability from phase I trial, it is beneficial to borrow historical study information into the design when available. This will help to increase the model efficiency and accuracy and provide dose specific recommendation rules to avoid toxic dose level and increase the chance of patient allocation at potential efficacious dose levels. In this paper, we propose iBOIN-ET design that uses prior distribution extracted from historical studies to minimize the probability of decision error. The proposed design utilizes the concept of skeleton from both toxicity and efficacy data, coupled with prior effective sample size to control the amount of historical information to be incorporated. Extensive simulation studies across a variety of realistic settings are reported including a comparison of iBOIN-ET design to other model based and assisted approaches. The proposed novel design demonstrates the superior performances in percentage of selecting the correct optimal dose (OD), average number of patients allocated to the correct OD, and overdosing control during dose escalation process.     

Adaptive Isotonic Estimation of the Minimum Effective and Peak Doses in the Presence of Covariates

We consider a problem of estimating the minimum effective and peak doses in the presence of covariates. We propose a sequential strategy for subject assignment that includes an adaptive randomization component to balance the allocation to placebo and active doses with respect to covariates. We conclude that either adjusting for covariates in the model or balancing allocation with respect to covariates is required to avoid bias in the target dose estimation. We also compute optimal allocation to estimate the minimum effective and peak doses in discrete dose space using isotonic regression.     

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.     

Bayesian optimization design for dose-finding based on toxicity and efficacy outcomes in phase I/II clinical trials

In phase I trials, the main goal is to identify a maximum tolerated dose under an assumption of monotonicity in dose–response relationships. On the other hand, such monotonicity is no longer applied to biologic agents because a different mode of action from that of cytotoxic agents potentially draws unimodal or flat dose–efficacy curves. Therefore, biologic agents require an optimal dose that provides a sufficient efficacy rate under an acceptable toxicity rate instead of a maximum tolerated dose. Many trials incorporate both toxicity and efficacy data, and drugs with a variety of modes of actions are increasingly being developed; thus, optimal dose estimation designs have been receiving increased attention. Although numerous authors have introduced parametric model-based designs, it is not always appropriate to apply strong assumptions in dose–response relationships. We propose a new design based on a Bayesian optimization framework for identifying optimal doses for biologic agents in phase I/II trials. Our proposed design models dose–response relationships via nonparametric models utilizing a Gaussian process prior, and the uncertainty of estimates is considered in the dose selection process. We compared the operating characteristics of our proposed design against those of three other designs through simulation studies. These include an expansion of Bayesian optimal interval design, the parametric model-based EffTox design, and the isotonic design. In simulations, our proposed design performed well and provided results that were more stable than those from the other designs, in terms of the accuracy of optimal dose estimations and the percentage of correct recommendations.     

TSNP: A two-stage nonparametric phase I/II clinical trial design for immunotherapy

We develop a transparent and efficient two-stage nonparametric (TSNP) phase I/II clinical trial design to identify the optimal biological dose (OBD) of immunotherapy. We propose a nonparametric approach to derive the closed-form estimates of the joint toxicity–efficacy response probabilities under the monotonic increasing constraint for the toxicity outcomes. These estimates are then used to measure the immunotherapy's toxicity–efficacy profiles at each dose and guide the dose finding. The first stage of the design aims to explore the toxicity profile. The second stage aims to find the OBD, which can achieve the optimal therapeutic effect by considering both the toxicity and efficacy outcomes through a utility function. The closed-form estimates and concise dose-finding algorithm make the TSNP design appealing in practice. The simulation results show that the TSNP design yields superior operating characteristics than the existing Bayesian parametric designs. User-friendly computational software is freely available to facilitate the application of the proposed design to real trials. We provide comprehensive illustrations and examples about implementing the proposed design with associated software.     

Optimal and lead-in adaptive allocation for binary outcomes: A comparison of Bayesian methods

We compare posterior and predictive estimators and probabilities in response-adaptive randomization designs for two- and three-group clinical trials with binary outcomes. Adaptation based upon posterior estimates are discussed, as are two predictive probability algorithms: one using the traditional definition, the other using a skeptical distribution. Optimal and natural lead-in designs are covered. Simulation studies show that efficacy comparisons lead to more adaptation than center comparisons, though at some power loss, skeptically predictive efficacy comparisons and natural lead-in approaches lead to less adaptation but offer reduced allocation variability. Though nuanced, these results help clarify the power-adaptation trade-off in adaptive randomization.