The continual reassessment method in cancer phase i clinical trials: A simulation study

In cancer studies, the aim of phase I clinical trials is to identify an appropriate dose for experimentation in phase II and III studies. The continual reassessment method (CRM) has been developed recently and presented as the method of choice in the design and analysis of such phase I studies. However, to implement the method, some methodological and practical considerations must be addressed. This paper examines, through a simulation study, the sensitivity of CRM both to the initial modelling of the dose-toxicity relationship and the prior. It appears that the performance of CRM can be improved by using vague priors and initial tuning of the model to allow flexibility.     

Bridging continual reassessment method for phase I clinical trials in different ethnic populations

Accumulating evidence shows that the conventional one‐size‐fits‐all dose‐finding paradigm is problematic when applied to different ethnic populations. Because of inter‐ethnic heterogeneity, the dosage established in a landmark trial for a certain population may not be generalizable to a different ethnic population, and a follow‐up bridge trial is often needed to find the maximum tolerated dose for the new population. We propose the bridging continual reassessment method (B‐CRM) to facilitate dose finding for such follow‐up bridge trials. The B‐CRM borrows information from the landmark trial through a novel estimate of the dose‐toxicity curve and accommodates the inter‐ethnic heterogeneity using the Bayesian model averaging approach. Extensive simulation studies show that the B‐CRM has desirable operating characteristics with a high probability to select the target dose. This article focuses on ethnic heterogeneity, but the proposed method can be directly used to handle other types of patient heterogeneity, for example, patient subgroups defined by prognostic factors or biomarkers. The software to implement the B‐CRM design is available for free download at http://odin.mdacc.tmc.edu/~yyuan/ . Copyright © 2015 John Wiley & Sons, Ltd.     

Heterogeneity in phase I clinical trials: prior elicitation and computation using the continual reassessment method

Heterogeneity in a phase I clinical trial patient population may lead to distinctly different dose-response relationships along covariate values. For a given target probability of toxicity, this implies different maximum tolerated doses (MTDs) for each distinct subpopulation. Within the framework of O'Quigley, Pepe and Fisher's (1990) continual reassessment method, we propose the notion of average and patient-specific MTDs by augmenting the dose--response model with other covariates to account for such differences. A method to elicit prior distributions on the dose and other covariate parameters are proposed, based on the predictive approach of Ibrahim and Laud (1994), Laud and Ibrahim (1995), and Ibrahim, Ryan and Chen (1998). This approach relies on prior predictions for the response vector y(0) and a quantity a(0) specifying uncertainty in y(0). Then, y(0) and a(0) are used to specify a prior for the regression coefficients in a semi-automatic fashion. The elicitation scheme for y(0) uses results from previous phase I cancer clinical trials. The average and patient-specific MTDs and an elicitation method are demonstrated in logistic regression examples.     

A comparison of model choices for the continual reassessment method in phase I cancer trials

Determination of the maximum tolerated dose (MTD) is the main objective of phase I trials. Trials are typically carried out with restricted sample sizes. Model‐based approaches proposed to identify the MTD (including the Continual Reassessment Method or CRM) suppose a simple model for the dose‐toxicity relation. At this early stage of clinical development, the true family of models is not known and several proposals have been done. Asymptotic convergence of the recommendation to the true MTD can be obtained with a one‐parameter model even in case of model misspecification. Nevertheless, operating characteristics with finite sample sizes can be largely affected by the choice of the model. In this paper, we evaluate and compare several models in a simulation framework. This framework includes a large class of dose‐toxicity relations against which to test the competing models, an ‘optimal’ method that provides efficient non‐parametric estimates of the probability of dose limiting toxicity to serve as a benchmark and as a graphic representation. In particular we explore the use of a one‐parameter versus a two‐parameter model, we compare the power and the logistic models and finally we investigate the impact of dose recoding on the operating characteristics. Comparisons are carried out with both a likelihood approach and a Bayesian approach for model estimations. We show that average performances of a one‐parameter model are superior and that the power model has good operating characteristics. Some models can speed up dose escalation and lead to more aggressive designs. We derive some behavior related to the choice of model and insist on the use of simulations under several scenarios before the initiation of each new trial in order to determine the best model to be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Practical modifications to the time-to-event continual reassessment method for phase I cancer trials with fast patient accrual and late-onset toxicities

The goal of phase I cancer trials is to determine the highest dose of a treatment regimen with an acceptable toxicity rate. Traditional designs for phase I trials, such as the Continual Reassessment Method (CRM) and the 3 + 3 design, require each patient or a cohort of patients to be fully evaluated for the dose-limiting toxicity (DLT) before new patients can be enrolled. As such, the trial duration may be prohibitively long. The Time-to-Event Continual Reassessment Method (TITE-CRM, Cheung and Chappell, 2000) circumvents this limitation by allowing staggered patient accrual without the need for complete DLT follow-up of previously treated patients. However, in the setting of fast patient accrual and late-onset toxicities, the TITE-CRM results in overly aggressive dose escalation and exposes a considerable number of patients to toxic doses. We examine a modification to the TITE-CRM proposed by the original TITE-CRM creator and propose an alternative approach useful in this setting by incorporating an accrual suspension rule. A simulation study designed based on a neuro-oncology trial indicates that the modified methods provide a much improved degree of safety than the TITE-CRM while maintaining desirable design accuracy. The practical aspects of the proposed designs are discussed. The modifications presented are useful when planning phase I trials involving chemoradiation therapy.     

The continual reassessment method: comparison of Bayesian stopping rules for dose-ranging studies

The continual reassessment method (CRM) provides a Bayesian estimation of the maximum tolerated dose (MTD) in phase I clinical trials and is also used to estimate the minimal efficacy dose (MED) in phase II clinical trials. In this paper we propose Bayesian stopping rules for the CRM, based on either posterior or predictive probability distributions that can be applied sequentially during the trial. These rules aim at early detection of either the mis-choice of dose range or a prefixed gain in the point estimate or accuracy of estimated probability of response associated with the MTD (or MED). They were compared through a simulation study under six situations that could represent the underlying unknown dose-response (either toxicity or failure) relationship, in terms of sample size, probability of correct selection and bias of the response probability associated to the MTD (or MED). Our results show that the stopping rules act correctly, with early stopping by using the two first rules based on the posterior distribution when the actual underlying dose-response relationship is far from that initially supposed, while the rules based on predictive gain functions provide a discontinuation of inclusions whatever the actual dose-response curve after 20 patients on average, that is, depending mostly on the accumulated data. The stopping rules were then applied to a data set from a dose-ranging phase II clinical trial aiming at estimating the MED dose of midazolam in the sedation of infants during cardiac catheterization. All these findings suggest the early use of the two first rules to detect a mis-choice of dose range, while they confirm the requirement of including at least 20 patients at the same dose to reach an accurate estimate of MTD (MED). A two-stage design is under study.     

Some practical improvements in the continual reassessment method for phase I studies

The Continual Reassessment Method (CRM) is a Bayesian phase I design whose purpose is to estimate the maximum tolerated dose of a drug that will be used in subsequent phase II and III studies. Its acceptance has been hindered by the greater duration of CRM designs compared to standard methods, as well as by concerns with excessive experimentation at high dosage levels, and with more frequent and severe toxicity. This paper presents the results of a simulation study in which one assigns more than one subject at a time to each dose level, and each dose increase is limited to one level. We show that these modifications address all of the most serious criticisms of the CRM, reducing the duration of the trial by 50–67 per cent, reducing toxicity incidence by 20–35 per cent, and lowering toxicity severity. These are achieved with minimal effects on accuracy. Most important, based on our experience at our institution, such modifications make the CRM acceptable to clinical investigators.     

A trivariate continual reassessment method for phase I/II trials of toxicity,efficacy, and surrogate efficacy

Recently, many Bayesian methods have been developed for dose finding when simultaneously modeling both toxicity and efficacy outcomes in a blended phase I/II fashion. A further challenge arises when all the true efficacy data cannot be obtained quickly after the treatment so that surrogate markers are instead used (e.g., in cancer trials). We propose a framework to jointly model the probabilities of toxicity, efficacy, and surrogate efficacy given a particular dose. Our trivariate binary model is specified as a composition of two bivariate binary submodels. In particular, we extend the bivariate continual reassessment method (CRM), as well as utilize a particular Gumbel copula. The resulting trivariate algorithm utilizes all the available data at any given time point and can flexibly stop the trial early for either toxicity or efficacy. Our simulation studies demonstrate that our proposed method can successfully improve dosage targeting efficiency and guard against excess toxicity over a variety of true model settings and degrees of surrogacy. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive design improvements in the continual reassessment method for phase I studies.

The continual reassessment method (CRM) enables full and efficient use of all data and prior information available in a phase I study. However, despite a number of recent enhancements to the method, its acceptance in actual clinical practice has been hampered by several practical difficulties. In this paper, we consider several further refinements in the context of phase I oncology trials. In particular, we allow the trial to stop when the width of the posterior 95 per cent probability interval for the maximum tolerated dose (MTD) becomes sufficiently narrow (that is, when the information accumulating from the trial data reaches a prespecified level). We employ a simulation study to evaluate five such stopping rules under three alternative states of prior knowledge regarding the MTD (accurate, too low and too high). Our results suggest our adaptive designs preserve the CRM's estimation ability while offering the possibility of earlier stopping of the trial.     

Bayesian methods for phase I clinical trials.

Phase I clinical trials are conducted to determine the dose-response curve of a new drug with respect to toxic side effects and, in particular, to estimate the maximum tolerated dose (MTD). In this paper we take a Bayesian approach to the problem of making inferences about the MTD. Working with broad classes of priors, we obtain the posterior distribution of the MTD and study its properties. We also address the question of providing updated assessments of the risk of toxicity for new patients entering the study at a specific dose level. These assessments would be useful in deciding issues of study management and ethics. Our analysis pays particular attention to the sensitivity of the inferences and risk assessments to the choice of prior and the choice of model for the dose-response relationship.     

A Bayesian design for phase I cancer therapeutic vaccine trials

Phase I clinical trials are the first step in drug development to test a new drug or drug combination on humans. Typical designs of Phase I trials use toxicity as the primary endpoint and aim to find the maximum tolerable dosage. However, these designs are poorly applicable for the development of cancer therapeutic vaccines because the expected safety concerns for these vaccines are not as much as cytotoxic agents. The primary objectives of a cancer therapeutic vaccine phase I trial thus often include determining whether the vaccine shows biologic activity and the minimum dose necessary to achieve a full immune or even clinical response. In this paper, we propose a new Bayesian phase I trial design that allows simultaneous evaluation of safety and immunogenicity outcomes. We demonstrate the proposed clinical trial design by both a numeric study and a therapeutic human papillomavirus vaccine trial.     

Posterior maximization and averaging for Bayesian working model choice in the continual reassessment method

The continual reassessment method (CRM) is a method for estimating the maximum tolerated dose in a dose-finding study. Traditionally, use is made of a single working model or 'skeleton' idealizing an underlying true dose-toxicity relationship. This working model is chosen either by discussion with investigators or published data, before the beginning of the trial or simply on the basis of operating characteristics. To overcome the arbitrariness of the choice of such a single working model, Yin and Yuan (biJ. Am. Statist. Assoc. 2009; 104:954-968) propose a model averaging over a set of working models. Here, instead of averaging, we investigate some alternative Bayesian model criteria that maximize the posterior distribution. We propose three adaptive model-selecting CRMs using the Bayesian model selection criteria, in which we specify in advance a collection of candidate working models for the dose-toxicity relationship, especially initial guesses of toxicity probabilities, and adaptively select the only one working model among the candidates updated by using the original CRM for each working model, based on the posterior model probability, the posterior predictive loss or the deviance information criteria, during the course of the trial. These approaches were compared via a simulation study with the model averaging approach.     

Flexible Bayesian methods for cancer phase I clinical trials. Dose escalation with overdose control

We examine a large class of prior distributions to model the dose-response relationship in cancer phase I clinical trials. We parameterize the dose-toxicity model in terms of the maximum tolerated dose (MTD) gamma and the probability of dose limiting toxicity (DLT) at the initial dose rho(0). The MTD is estimated using the EWOC (escalation with overdose control) method of Babb et al. We show through simulations that a candidate joint prior for (rho0,gamma) with negative a priori correlation structure results in a safer trial than the one that assumes independent priors for these two parameters while keeping the efficiency of the estimate of the MTD essentially unchanged.     

Application of the continual reassessment method to a phase I dose-finding trial in Japanese patients: East meets West

After cancer-related phase I dose-finding trials are completed in Western countries, further phase I trials are often conducted to determine recommended doses (RDS) for Japanese patients. This may be due to concerns about possible differences in treatment tolerability between Caucasians and Japanese. In most of these, a conventional '3 +3' cohort study design is used in making dose escalation decisions, possibly due to its relatively easy implementation. Since its proposal by O'Quigleybiet al. (1990; Biometrics, 46:33-48), the continual reassessment method (CRM) has been used increasingly in cancer-related phase I dose-finding studies as an alternative to '3 +3' designs. One of the principal advantages of applying a Bayesian CRM may be the utilization of all available prior information to estimate RDS through prior distributions that are assumed for model parameters representing the dose-toxicity relationship. In this paper, we present an application of the Bayesian CRM to a phase I dose-finding study in Japanese patients with advanced breast cancer using an informative prior elicited from clinical investigators. In some settings, it may be appropriate to use an informative prior that reflects the accurate and comprehensive previous knowledge of clinical investigators. On the other hand, for a model-based Bayesian outcome-adaptive clinical trial, it is necessary to establish sufficiently vague priors so that accumulating data dominate decisions as the amount of observed data increases. Thus, we retrospectively investigated the relative strength of the prior using a recently proposed method to compute a prior effective sample size.     

Bayesian interim analysis of phase II cancer clinical trials

Many popular sequential phase II clinical trial designs optimize some criterion subject to constraints on the error probabilities at null and alternative values of the response rate. Such designs may forfeit optimality if one fails to conduct analyses strictly according to plan. Moreover, a decision, say, to accept the experimental therapy at one interim analysis does not necessarily imply the same degree of evidence as the same decision when made at another analysis. I propose an alternative design that bases decisions on the ability of the data to persuade either a sceptic or an enthusiast. My standard of evidence, called the persuasion probability, is based on the Bayesian posterior probability that the experimental treatment is superior to the standard. The design calls for termination at any interim analysis at which an observed persuasion probability exceeds its critical value. I investigate the standards of evidence implied by some frequentist procedures and calculate frequentist properties of persuasion-probability designs. © 1997 John Wiley & Sons, Ltd.     

Bayesian hybrid dose-finding design in phase I oncology clinical trials

In oncology, dose escalation is often carried out to search for the maximum tolerated dose (MTD) in phase I clinical trials. We propose a Bayesian hybrid dose-finding method that inherits the robustness of model-free methods and the efficiency of model-based methods. In the Bayesian hypothesis testing framework, we compute the Bayes factor and adaptively assign a dose to each cohort of patients based on the adequacy of the dose-toxicity information that has been collected thus far. If the data observed at the current treatment dose are adequately informative about the toxicity probability of this dose (e.g. whether this dose is below or above the MTD), we make the decision of dose assignment (e.g. either to escalate or to de-escalate the dose) directly without assuming a parametric dose-toxicity curve. If the observed data at the current dose are not sufficient to deliver such a definitive decision, we resort to a parametric dose-toxicity curve, such as that of the continual reassessment method (CRM), in order to borrow strength across all the doses under study to guide dose assignment. We examine the properties of the hybrid design through extensive simulation studies, and also compare the new method with the CRM and the '3 + 3' design. The simulation results show that our design is more robust than parametric model-based methods and more efficient than nonparametric model-free methods.     

Bayesian two-stage designs for phase II clinical trials

Many different statistical designs have been used in phase II clinical trials. The majority of these are based on frequentist statistical approaches. Bayesian methods provide a good alternative to frequentist approaches as they allow for the incorporation of relevant prior information and the presentation of the trial results in a manner which, some feel, is more intuitive and helpful. In this paper, we propose two new Bayesian designs for phase II clinical trials. These designs have been developed specifically to make them as user friendly and as familiar as possible to those who have had experience working with two-stage frequentist phase II designs. Thus, unlike many of the Bayesian designs already proposed in the literature, our designs do not require a distribution for the response rate of the currently used drug or the explicit specification of utility or loss functions. We study the properties of our designs and compare them with the Simon two-stage optimal and minimax designs. We also apply them to an example of two recently concluded phase II trials conducted at the National Cancer Centre in Singapore. Sample size tables for the designs are given.     

Competing designs for phase I clinical trials: a review

Phase I clinical trials are typically small, uncontrolled studies designed to determine a maximum tolerated dose of a drug which will be used in further testing. Two divergent schools have developed in designing phase I clinical trials. The first defines the maximum tolerated dose as a statistic computed from data, and hence it is identified, rather than estimated. The second defines the maximum tolerated dose as a parameter of a monotonic dose-response curve, and hence is estimated. We review techniques from both philosophies. The goal is to present these methods in a single package, to compare them from philosophical and statistical grounds, to hopefully clear up some common misconceptions, and to make a few recommendations. This paper is not a review of simulation studies of these designs, nor does it present any new simulations comparing these designs.     

On some applications of Bayesian methods in cancer clinical trials.

The NCCTG randomized controlled clinical trial for the treatment of advanced colorectal carcinoma is a wonderful case study of the dynamic interplay between scientific learning and statistical inference. Ethical concerns for minimizing the number of patients assigned to an inferior treatment and interest in identifying subsets of patients for whom a treatment is most likely efficacious pose challenging problems for the practice of statistics. In the first part of this paper, I comment on the applications of Bayesian methods to these problems in the NCCTG trial as presented by Freedman and Spieglehalter and Dixon and Simon, respectively. In the second part of this paper, I discuss and illustrate a Bayesian approach to model sensitivity analysis with a particular focus on model specification and criticism. The Bayesian approach provides a formal methodology to assess the sensitivity of inferences to the inputs into an analysis so that it is possible to investigate the consequences of the specification of the model. I apply these methods to the specification and criticism of a class of survival models for the analysis of survival times in the NCCTG trial.