Dose‐escalation strategies which use subgroup information

Dose‐escalation trials commonly assume a homogeneous trial population to identify a single recommended dose of the experimental treatment for use in future trials. Wrongly assuming a homogeneous population can lead to a diluted treatment effect. Equally, exclusion of a subgroup that could in fact benefit from the treatment can cause a beneficial treatment effect to be missed. Accounting for a potential subgroup effect (ie, difference in reaction to the treatment between subgroups) in dose‐escalation can increase the chance of finding the treatment to be efficacious in a larger patient population. A standard Bayesian model‐based method of dose‐escalation is extended to account for a subgroup effect by including covariates for subgroup membership in the dose‐toxicity model. A stratified design performs well but uses available data inefficiently and makes no inferences concerning presence of a subgroup effect. A hypothesis test could potentially rectify this problem but the small sample sizes result in a low‐powered test. As an alternative, the use of spike and slab priors for variable selection is proposed. This method continually assesses the presence of a subgroup effect, enabling efficient use of the available trial data throughout escalation and in identifying the recommended dose(s). A simulation study, based on real trial data, was conducted and this design was found to be both promising and feasible.     

A simulation study of methods for selecting subgroup‐specific doses in phase 1 trials

Patient heterogeneity may complicate dose‐finding in phase 1 clinical trials if the dose‐toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively,it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem,we consider a generalization of the continual reassessment method on the basis of a hierarchical Bayesian dose‐toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup‐specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to 3 alternative approaches,on the basis of nonhierarchical models,that make different types of assumptions about within‐subgroup dose‐toxicity curves. The simulations show that the hierarchical model‐based method is recommended in settings where the dose‐toxicity curves are exchangeable between subgroups. We present practical guidelines for application and provide computer programs for trial simulation and conduct.     

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.     

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.     

Effect of design specifications in dose‐finding trials for combination therapies in oncology

Model‐based dose‐finding methods for a combination therapy involving two agents in phase I oncology trials typically include four design aspects namely, size of the patient cohort, three‐parameter dose‐toxicity model, choice of start‐up rule, and whether or not to include a restriction on dose‐level skipping. The effect of each design aspect on the operating characteristics of the dose‐finding method has not been adequately studied. However, some studies compared the performance of rival dose‐finding methods using design aspects outlined by the original studies. In this study, we featured the well‐known four design aspects and evaluated the impact of each independent effect on the operating characteristics of the dose‐finding method including these aspects. We performed simulation studies to examine the effect of these design aspects on the determination of the true maximum tolerated dose combinations as well as exposure to unacceptable toxic dose combinations. The results demonstrated that the selection rates of maximum tolerated dose combinations and UTDCs vary depending on the patient cohort size and restrictions on dose‐level skipping However, the three‐parameter dose‐toxicity models and start‐up rules did not affect these parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Improving early phase oncology clinical trial design: The case for finding the optimal biological dose

Historically early phase oncology drug development programmes have been based on the belief that “more is better”. Furthermore, rule-based study designs such as the “3 + 3” design are still often used to identify the MTD. Phillips and Clark argue that newer Bayesian model-assisted designs such as the BOIN design should become the go to designs for statisticians for MTD finding. This short communication goes one stage further and argues that Bayesian model-assisted designs such as the BOIN12 which balances risk-benefit should be included as one of the go to designs for early phase oncology trials, depending on the study objectives. Identifying the optimal biological dose for future research for many modern targeted drugs, immunotherapies, cell therapies and vaccine therapies can save significant time and resources.     

A Bayesian optimal interval design for dose optimization with a randomization scheme based on pharmacokinetics outcomes in oncology

The primary objective of an oncology dose-finding trial for novel therapies, such as molecularly targeted agents and immune-oncology therapies, is to identify the optimal dose (OD) that is tolerable and therapeutically beneficial for subjects in subsequent clinical trials. Pharmacokinetic (PK) information is considered an appropriate indicator for evaluating the level of drug intervention in humans from a pharmacological perspective. Several novel anticancer agents have been shown to have significant exposure-efficacy relationships, and some PK information has been considered an important predictor of efficacy. This paper proposes a Bayesian optimal interval design for dose optimization with a randomization scheme based on PK outcomes in oncology. A simulation study shows that the proposed design has advantages compared to the other designs in the percentage of correct OD selection and the average number of patients allocated to OD in various realistic settings.     

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.     

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.     

Coherence principles in interval‐based dose finding

This paper studies the notion of coherence in interval‐based dose‐finding methods. An incoherent decision is either (a) a recommendation to escalate the dose following an observed dose‐limiting toxicity or (b) a recommendation to deescalate the dose following a non–dose‐limiting toxicity. In a simulated example, we illustrate that the Bayesian optimal interval method and the Keyboard method are not coherent. We generated dose‐limiting toxicity outcomes under an assumed set of true probabilities for a trial of n=36 patients in cohorts of size 1, and we counted the number of incoherent dosing decisions that were made throughout this simulated trial. Each of the methods studied resulted in 13/36 (36%) incoherent decisions in the simulated trial. Additionally, for two different target dose‐limiting toxicity rates, 20% and 30%, and a sample size of n=30 patients, we randomly generated 100 dose‐toxicity curves and tabulated the number of incoherent decisions made by each method in 1000 simulated trials under each curve. For each method studied, the probability of incurring at least one incoherent decision during the conduct of a single trial is greater than 75%. Coherency is an important principle in the conduct of dose‐finding trials. Interval‐based methods violate this principle for cohorts of size 1 and require additional modifications to overcome this shortcoming. Researchers need to take a closer look at the dose assignment behavior of interval‐based methods when using them to plan dose‐finding studies.     

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.     

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.     

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.     

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.     

Dynamic ordering design for dose finding in drug-combination trials

Drug-combination studies have become increasingly popular in oncology. One of the critical concerns in phase I drug-combination trials is the uncertainty in toxicity evaluation. Most of the existing phase I designs aim to identify the maximum tolerated dose (MTD) by reducing the two-dimensional searching space to one dimension via a prespecified model or splitting the two-dimensional space into multiple one-dimensional subspaces based on the partially known toxicity order. Nevertheless, both strategies often lead to complicated trials which may either be sensitive to model assumptions or induce longer trial durations due to subtrial split. We develop two versions of dynamic ordering design (DOD) for dose finding in drug-combination trials, where the dose-finding problem is cast in the Bayesian model selection framework. The toxicity order of dose combinations is continuously updated via a two-dimensional pool-adjacent-violators algorithm, and then the dose assignment for each incoming cohort is selected based on the optimal model under the dynamic toxicity order. We conduct extensive simulation studies to evaluate the performance of DOD in comparison with four other commonly used designs under various scenarios. Simulation results show that the two versions of DOD possess competitive performances in terms of correct MTD selection as well as safety, and we apply both versions of DOD to two real oncology trials for illustration.     

Dose finding with continuous outcome in phase I oncology trials

The goal of a phase I clinical trial in oncology is to find a dose with acceptable dose‐limiting toxicity rate. Often, when a cytostatic drug is investigated or when the maximum tolerated dose is defined using a toxicity score, the main endpoint in a phase I trial is continuous. We propose a new method to use in a dose‐finding trial with continuous endpoints. The new method selects the right dose on par with other methods and provides more flexibility in assigning patients to doses in the course of the trial when the rate of accrual is fast relative to the follow‐up time. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Phase I trial design for drug combinations with Bayesian model averaging

Various statistical models have been proposed for two‐dimensional dose finding in drug‐combination trials. However, it is often a dilemma to decide which model to use when conducting a particular drug‐combination trial. We make a comprehensive comparison of four dose‐finding methods, and for fairness, we apply the same dose‐finding algorithm under the four model structures. Through extensive simulation studies, we compare the operating characteristics of these methods in various practical scenarios. The results show that different models may lead to different design properties and that no single model performs uniformly better in all scenarios. As a result, we propose using Bayesian model averaging to overcome the arbitrariness of the model specification and enhance the robustness of the design. We assign a discrete probability mass to each model as the prior model probability and then estimate the toxicity probabilities of combined doses in the Bayesian model averaging framework. During the trial, we adaptively allocated each new cohort of patients to the most appropriate dose combination by comparing the posterior estimates of the toxicity probabilities with the prespecified toxicity target. The simulation results demonstrate that the Bayesian model averaging approach is robust under various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimating the variance for heterogeneity in arm‐based network meta‐analysis

Network meta‐analysis can be implemented by using arm‐based or contrast‐based models. Here we focus on arm‐based models and fit them using generalized linear mixed model procedures. Full maximum likelihood (ML) estimation leads to biased trial‐by‐treatment interaction variance estimates for heterogeneity. Thus, our objective is to investigate alternative approaches to variance estimation that reduce bias compared with full ML. Specifically, we use penalized quasi‐likelihood/pseudo‐likelihood and hierarchical (h) likelihood approaches. In addition, we consider a novel model modification that yields estimators akin to the residual maximum likelihood estimator for linear mixed models. The proposed methods are compared by simulation, and 2 real datasets are used for illustration. Simulations show that penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood reduce bias and yield satisfactory coverage rates. Sum‐to‐zero restriction and baseline contrasts for random trial‐by‐treatment interaction effects, as well as a residual ML‐like adjustment, also reduce bias compared with an unconstrained model when ML is used, but coverage rates are not quite as good. Penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood are therefore recommended.