Cancer phase I clinical trials: efficient dose escalation with overdose control

We describe an adaptive dose escalation scheme for use in cancer phase I clinical trials. The method is fully adaptive, makes use of all the information available at the time of each dose assignment, and directly addresses the ethical need to control the probability of overdosing. It is designed to approach the maximum tolerated dose as fast as possible subject to the constraint that the predicted proportion of patients who receive an overdose does not exceed a specified value. We conducted simulations to compare the proposed method with four up-and-down designs, two stochastic approximation methods, and with a variant of the continual reassessment method. The results showed the proposed method effective as a means to control the frequency of overdosing. Relative to the continual reassessment method, our scheme overdosed a smaller proportion of patients, exhibited fewer toxicities and estimated the maximum tolerated dose with comparable accuracy. When compared to the non-parametric schemes, our method treated fewer patients at either subtherapeutic or severely toxic dose levels, treated more patients at optimal dose levels and estimated the maximum tolerated dose with smaller average bias and mean squared error. Hence, the proposed method is promising alternative to currently used cancer phase I clinical trial designs. © 1998 John Wiley & Sons, Ltd.     

Estimating the dose-toxicity curve in completed phase I studies

While there is an extensive amount of literature covering prospective designs for phase I trials, the methodology for analyzing these data is limited. Prospective designs select the maximum tolerated dose (MTD) through a dose escalation scheme based on a model or on empirical rules. For example, the '3 + 3' method (standard method: SM) assigns patients in cohorts of three and expands to six if one toxicity is observed. It has been shown previously that the MTD chosen by the SM may be low, possibly leading to a non-efficacious dose. Additionally, when deviation from the original trial design occurs, the rules for determining MTD might not be applicable. We hypothesize that a retrospective analysis would suggest an MTD that is more accurate than the one obtained by the SM. A weighted Continual Reassessment Method (CRM-w) has been suggested (Biometrics 2005; 61:749-756) for analyzing data obtained from designs other than the prospective Continual Reassessment Method (CRM). However, CRM-w has not been evaluated in trials that follow the SM design. In this study, we propose a method to analyze completed phase I trials and possibly confirm or amend the recommended phase II dose, based on a constrained maximum likelihood estimation (CMLE). A comparison of CRM-w, isotonic regression, and CMLE in analyzing simulated SM trials shows that CMLE more accurately selects the true MTD than SM, and is better or comparable to isotonic regression and CRM-w. Confidence intervals around the toxicity probabilities at each dose level are estimated using the cumulative toxicity data. A programming code is included.     

The continual reassessment method and its applications: a Bayesian methodology for phase I cancer clinical trials

We discuss the continual reassessment method (CRM) and its extension with practical applications in phase I and I/II cancer clinical trials. The CRM has been proposed as an alternative design of a traditional cohort design and its essential features are the sequential (continual) selection of a dose level for the next patients based on the dose-toxicity relationship and the updating of the relationship based on patients' response data using Bayesian calculation. The original CRM has been criticized because it often tends to allocate too toxic doses to many patients and our proposal for overcoming this practical problem is to monitor a posterior density function of the occurrence of the dose limiting toxicity (DLT) at each dose level. A simulation study shows that strategies based on our proposal allocate a smaller number of patients to doses higher than the maximum tolerated dose (MTD) compared with the original method while the mean squared error of the probability of the DLT occurrence at the MTD is not inflated. We present a couple of extensions of the CRM with real prospective applications: (i) monitoring efficacy and toxicity simultaneously in a combination phase I/II trial; (ii) combining the idea of pharmacokinetically guided dose escalation (PKGDE) and utilization of animal toxicity data in determining the prior distribution. A stopping rule based on the idea of separation among the DLT density functions is discussed in the first example and a strategy for determining the model parameter of the dose-toxicity relationship is suggested in the second example.     

Escalation with overdose control for phase I drug‐combination trials

Dose finding for combined drugs has grown rapidly in oncology drug development. The escalation with overdose control (EWOC) method is a popular model‐based dose‐finding approach to single‐agent phase I clinical trials. When two drugs are combined as a treatment, we propose a two‐dimensional EWOC design for dose finding on the basis of a four‐parameter logistic regression model. During trial conduct, we continuously update the posterior distribution of the maximum tolerated dose (MTD) combination to find the most appropriate dose combination for each cohort of patients. The probability that the next assigned dose combination exceeds the MTD combination can be controlled by a feasibility bound, which is based on a prespecified quantile level of the MTD distribution such as to reduce the possibility of overdosing. We determine dose escalation, de‐escalation, or staying at the same doses by searching the MTD combination along the rows and columns in a two‐drug combination matrix, respectively. We conduct simulation studies to examine the performance of the two‐dimensional EWOC design under various practical scenarios, and illustrate it with a trial example. Copyright © 2013 John Wiley & Sons, Ltd.     

Dose finding with drug combinations in cancer phase I clinical trials using conditional escalation with overdose control

We present a Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials. The goal is to estimate the maximum tolerated dose (MTD) as a curve in the two‐dimensional Cartesian plane. We use a logistic model to describe the relationship between the doses of the two agents and the probability of dose limiting toxicity. The model is re‐parameterized in terms of parameters clinicians can easily interpret. Trial design proceeds using univariate escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current dose of the other agent. At the end of the trial, an estimate of the MTD curve is proposed as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial design and percent of dose recommendation at dose combination neighborhoods around the true MTD curve. We also examine the performance of the approach under model misspecifications for the true dose–toxicity relationship. Copyright © 2014 John Wiley & Sons, Ltd.     

Toxicity‐dependent feasibility bounds for the escalation with overdose control approach in phase I cancer trials

Phase I trials of anti‐cancer therapies aim to identify a maximum tolerated dose (MTD), defined as the dose that causes unacceptable toxicity in a target proportion of patients. Both rule‐based and model‐based methods have been proposed for MTD recommendation. The escalation with overdose control (EWOC) approach is a model‐based design where the dose assigned to the next patient is one that, given all available data, has a posterior probability of exceeding the MTD equal to a pre‐specified value known as the feasibility bound. The aim is to conservatively dose‐escalate and approach the MTD, avoiding severe overdosing early on in a trial. The EWOC approach has been applied in practice with the feasibility bound either fixed or varying throughout a trial, yet some of the methods may recommend incoherent dose‐escalation, that is, an increase in dose after observing severe toxicity at the current dose. We present examples where varying feasibility bounds have been used in practice, and propose a toxicity‐dependent feasibility bound approach that guarantees coherent dose‐escalation and incorporates the desirable features of other EWOC approaches. We show via detailed simulation studies that the toxicity‐dependent feasibility bound approach provides improved MTD recommendation properties to the original EWOC approach for both discrete and continuous doses across most dose‐toxicity scenarios, with comparable performance to other approaches without recommending incoherent dose escalation. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

IMPROVED DESIGNS FOR DOSE ESCALATION STUDIES USING PHARMACOKINETIC MEASUREMENTS

We describe a method for incorporating pharmacokinetic (PK) data into dose escalation clinical trial designs. Doing so can improve the efficiency and accuracy of these studies. The method proposed uses a parametric dose response function that models the probability of response in each person with two effects: the dose of drug administered and an ancillary pharmacokinetic measurement. After treatment and observation of each subject (or group of subjects) for response, one calculates the dose to be administered to the next individual (or group) to yield the target probability of response from the current best estimate of the dose–response curve. This procedure is a variant of the continual reassesment method (CRM). Statistical simulations employing a logistic dose–response model (that is, we model the logit of the response probability as a linear combination of predictors), dose of drug, and the area under the time-concentration curve (AUC) demonstrate that the addition of pharmacokinetic information to the CRM is a practical and useful way to improve both dose–response modelling and the design of dose escalation studies.     

A robust two‐stage design identifying the optimal biological dose for phase I/II clinical trials

We propose a robust two‐stage design to identify the optimal biological dose for phase I/II clinical trials evaluating both toxicity and efficacy outcomes. In the first stage of dose finding, we use the Bayesian model averaging continual reassessment method to monitor the toxicity outcomes and adopt an isotonic regression method based on the efficacy outcomes to guide dose escalation. When the first stage ends, we use the Dirichlet‐multinomial distribution to jointly model the toxicity and efficacy outcomes and pick the candidate doses based on a three‐dimensional volume ratio. The selected candidate doses are then seamlessly advanced to the second stage for dose validation. Both toxicity and efficacy outcomes are continuously monitored so that any overly toxic and/or less efficacious dose can be dropped from the study as the trial continues. When the phase I/II trial ends, we select the optimal biological dose as the dose obtaining the minimal value of the volume ratio within the candidate set. An advantage of the proposed design is that it does not impose a monotonically increasing assumption on the shape of the dose–efficacy curve. We conduct extensive simulation studies to examine the operating characteristics of the proposed design. The simulation results show that the proposed design has desirable operating characteristics across different shapes of the underlying true dose–toxicity and dose–efficacy curves. The software to implement the proposed design is available upon request. Copyright © 2016 John Wiley & Sons, Ltd.     

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

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

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.     

An extension of the continual reassessment method using decision theory.

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q(*), of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q(*), a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q(*), that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q(*), among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.     

Improving safety of the continual reassessment method via a modified allocation rule

This article proposes a novel criterion for the allocation of patients in phase I dose-escalation clinical trials, aiming to find the maximum tolerated dose (MTD). Conventionally, using a model-based approach, the next patient is allocated to the dose with the toxicity estimate closest (in terms of the absolute or squared distance) to the maximum acceptable toxicity. This approach, however, ignores the uncertainty in point estimates and ethical concerns of assigning a lot of patients to overly toxic doses. In fact, balancing the trade-off between how accurately the MTD can be estimated and how many patients would experience adverse events is one of the primary challenges in phase I studies. Motivated by recent discussions in the theory of estimation in restricted parameter spaces, we propose a criterion that allows to balance these explicitly. The criterion requires a specification of one additional parameter only that has a simple and intuitive interpretation. We incorporate the proposed criterion into the one-parameter Bayesian continual reassessment method and show, using simulations, that it can result in similar accuracy on average as the original design, but with fewer toxic responses on average. A comparison with other model-based dose-escalation designs, such as escalation with overdose control and its modifications, demonstrates that the proposed design can result in either the same mean accuracy as alternatives but fewer toxic responses or in a higher mean accuracy but the same number of toxic responses. Therefore, the proposed design can provide a better trade-off between the accuracy and the number of patients experiencing adverse events, making the design a more ethical alternative over some of the existing methods for phase I trials.     

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.     

Three-dose-cohort designs in cancer phase I trials

Traditional designs for phase I clinical trials assign the same dose to patients in the same cohort. In this paper, we present a new class of designs for cancer phase I trials which initially rapidly escalate by allowing multiple doses (usually 3) to be assigned to each cohort of patients. The class of designs, called the LMH-CRM (an extension of the continual reassessment method (CRM) by administering different percentiles of the maximum tolerated dose (MTD), denoted 'low', 'medium', 'high'), is proven to be consistent and coherent (a commonsense property of phase I trials for dose escalation and de-escalation). Three designs (slow, moderate and fast) are derived based on different dose-escalation restrictions. Simulation results show that moderate and fast LMH-CRM combine the advantages of the CRM with one patient per cohort and three patients per cohort: it accurately estimates the MTD; controls overall toxicity rates; and is time efficient.     

Adaptive dose modification for phase I clinical trials

Most phase I dose‐finding methods in oncology aim to find the maximum‐tolerated dose from a set of prespecified doses. However, in practice, because of a lack of understanding of the true dose–toxicity relationship, it is likely that none of these prespecified doses are equal or reasonably close to the true maximum‐tolerated dose. To handle this issue, we propose an adaptive dose modification (ADM) method that can be coupled with any existing dose‐finding method to adaptively modify the dose, when it is needed, during the course of dose finding. To reflect clinical practice, we divide the toxicity probability into three regions: underdosing, acceptable, and overdosing regions. We adaptively add a new dose whenever the observed data suggest that none of the investigational doses are likely to be located in the acceptable region. The new dose is estimated via a nonparametric dose–toxicity model based on local polynomial regression. The simulation study shows that ADM substantially outperforms the similar existing method. We applied ADM to a phase I cancer trial. Copyright © 2016 John Wiley & Sons, Ltd.     

Two‐stage dose finding for cytostatic agents in phase I oncology trials

Conventional dose‐finding methods in oncology are mainly developed for cytotoxic agents with the aim of finding the maximum tolerated dose. In phase I clinical trials with cytostatic agents, such as targeted therapies, designs with toxicity endpoints alone may not work well. For cytostatic agents, the goal is often to find the most efficacious dose that is still tolerable, although these agents are typically less toxic than cytotoxic agents and their efficacy may not monotonically increase with the dose. To effectively differentiate doses for cytostatic agents, we develop a two‐stage dose‐finding procedure by first identifying the toxicity upper bound of the searching range through dose escalation and then determining the most efficacious dose through dose de‐escalation while toxicity is continuously monitored. In oncology, treatment efficacy often takes a relatively long period to exhibit compared with toxicity. To accommodate such delayed response, we model the time to the efficacy event by redistributing the mass of the censored observation to the right and compute the fractional contribution of the censored data. We evaluate the operating characteristics of the new dose‐finding design for cytostatic agents and demonstrate its satisfactory performance through simulation studies. Copyright © 2012 John Wiley & Sons, Ltd.     

Dose escalation trial designs based on a molecularly targeted endpoint

Traditional phase I dose-finding studies for chemotoxic agents base dose escalation on toxicity, with escalation continuing until unacceptable toxicity is observed. Recent development of molecularly targeted agents that have little or no toxicity in the therapeutic dose range has raised questions over the best study designs for phase I studies. Two types of designs are proposed and evaluated in this paper. In these designs, escalation is based on a binary response that indicates whether or not the agent has had the desired effect on the molecular target. One design is developed to ensure that if the true target response rate is low there will be a high probability of escalating and if the true target response rate is high there will be a low probability of escalating. The other design is developed to continue to escalate as long as the true response rate is increasing and to stop escalating when the response rate plateaus or decreases. A limited simulation study is performed and the designs are compared with respect to the dose level at the end of escalation and the number of patients treated on study.     

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.     

STEIN: A simple toxicity and efficacy interval design for seamless phase I/II clinical trials

Seamless phase I/II dose‐finding trials are attracting increasing attention nowadays in early‐phase drug development for oncology. Most existing phase I/II dose‐finding methods use sophisticated yet untestable models to quantify dose‐toxicity and dose‐efficacy relationships, which always renders them difficult to implement in practice. To simplify the practical implementation, we extend the Bayesian optimal interval design from maximum tolerated dose finding to optimal biological dose finding in phase I/II trials. In particular, optimized intervals for toxicity and efficacy are respectively derived by minimizing probabilities of incorrect classifications. If the pair of observed toxicity and efficacy probabilities at the current dose is located inside the promising region, we retain the current dose; if the observed probabilities are outside of the promising region, we propose an allocation rule by maximizing the posterior probability that the response rate of the next dose falls inside a prespecified efficacy probability interval while still controlling the level of toxicity. The proposed interval design is model‐free, thus is suitable for various dose‐response relationships. We conduct extensive simulation studies to demonstrate the small‐ and large‐sample performance of the proposed method under various scenarios. Compared to existing phase I/II dose‐finding designs, not only is our interval design easy to implement in practice, but it also possesses desirable and robust operating characteristics.     

Phase I/II adaptive design for drug combination oncology trials

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