Optimization of EWOC principle in BLRM design for phase 1 oncology trials

Bayesian logistic regression model (BLRM) is widely used to guide dose escalation decisions in phase 1 oncology trials. An important feature of BLRM design is the appealing safety performance due to its escalation with overdose control (EWOC). However, some recent literature indicates that BLRM with EWOC may have a relatively low probability to find the maximum tolerated dose (MTD) compared to some other dose escalation designs. This work discusses this design problem and proposes a practical solution to improve the performance of BLRM design. Specifically, we suggest increasing the EWOC cutoff from routine value 0.25 to a value between 0.3 and 0.4, which will increase the chance of finding the correct MTD with minimal compromise to overdosing risk. Our comparative simulation studies indicate that BLRM with an increased EWOC cutoff has comparable operating characteristics on the correct MTD selection and over-toxicity control as other dose escalation designs (BOIN, mTPI, keyboard, etc.). Moreover, we compare the methodology and operating characteristics of BLRM designs with various decision rules that allow more flexible overdosing control. A case study of dose escalation in a recent phase 1 oncology trial is provided to show how BLRM with optimal EWOC cutoff operates well in practice.

A Monte Carlo simulation study comparing the up and down, biased-coin up and down and continual reassessment methods used to estimate an effective dose (ED95 or ED90) in anaesthesiology research

Background

Dose-finding studies in anaesthesiology aim to target the effective dose (ED) of an anaesthetic agent in a specific population. The common dose-finding designs used are the up and down method (UDM), the biased-coin up and down (BCD), and the continual reassessment method (CRM). Although the advantages of CRM over the UDM and BCD methods have been described in the statistical literature in terms of precision and direct estimation of ED, CRM may also offer attractive properties from an ethical point of view.

Methods

Based on Monte Carlo simulations, this article aims to compare the three methods with regard to 1) their ability to find as close an estimate as possible for the ED95 or ED90 and 2) the total number of patients needed to treat and the number of failures.

Results

In contrast to BCD and UDM, CRM does find an estimate for ED95 and ED90. UDM underestimates both ED95 and ED90. BCD is close to the targeted EDs when the starting dose does not exceed the ED of interest, otherwise it overestimates it. CRM with cohorts of two patients is closest to the ED of interest independently of the starting doses. CRM requires between 20 and 50 observations, UDM should include 90 patients, and BCD 100 or 60 observations. Lastly, CRM is associated with fewer failures, compared with BCD and UDM.

Conclusions

Based on Monte Carlo simulations, our work suggests that the UDM is not an adequate dose-finding method because it underestimates the ED of interest. Compared with BCD, CRM offers the advantages of being more efficient, requires fewer patients to be included, and is associated with fewer failures.

A flexible dose-response modeling framework based on continuous toxicity outcomes in phase I cancer clinical trials

BACKGROUND

The past few decades have seen remarkable developments in dose-finding designs for phase I cancer clinical trials. While many of these designs rely on a binary toxicity response, there is an increasing focus on leveraging continuous toxicity responses. A continuous toxicity response pertains to a quantitative measure represented by real numbers. A higher value corresponds not only to an elevated likelihood of side effects for patients but also to an increased probability of treatment efficacy. This relationship between toxicity and dose is often nonlinear, necessitating flexibility in the quest to find an optimal dose.

METHODS

A flexible, fully Bayesian dose-finding design is proposed to capitalize on continuous toxicity information, operating under the assumption that the true shape of the dose-toxicity curve is nonlinear.

RESULTS

We conduct simulations of clinical trials across varying scenarios of non-linearity to evaluate the operational characteristics of the proposed design. Additionally, we apply the proposed design to a real-world problem to determine an optimal dose for a molecularly targeted agent.

CONCLUSIONS

Phase I cancer clinical trials, designed within a fully Bayesian framework with the utilization of continuous toxicity outcomes, offer an alternative approach to finding an optimal dose, providing unique benefits compared to trials designed based on binary toxicity outcomes.

Enhancement of Bayesian optimal interval design by accounting for overdose and underdose errors trade-offs

Model-assisted designs, a new class of dose-finding designs for determining the maximum tolerated dose (MTD), model only the dose-limiting toxicity (DLT) data observed at the current dose based on a simple binomial model and offer the boundaries of DLT for the determination of dose escalation, retention, or de-escalation before beginning the trials. The boundaries for dose-escalation and de-escalation decisions are relevant to the operating characteristics of the design. The well-known model-assisted design, Bayesian Optimal Interval (BOIN), selects these boundaries to minimize the probability of incorrect decisions at each dose allocation but does not distinguish between overdose and underdose allocations caused by incorrect decisions when calculating the probability of incorrect decisions. Distinguishing between overdose and underdose based on the decision error in the BOIN design is expected to increase the accuracy of MTD determination. In this study, we extended the BOIN design to account for the decision probabilities of incorrect overdose and underdose allocations separately. To minimize the two probabilities simultaneously, we propose utilizing multiple objective optimizations and formulating an approach for determining the boundaries for dose escalation and de-escalation. Comprehensive simulation studies using fixed and randomly generated scenarios of DLT probability demonstrated that the proposed method is superior or comparable to existing interval designs, along with notably better operating characteristics of the proposed method.

A Bayesian adaptive design for dual-agent phase I-II oncology trials integrating efficacy data across stages

Combination of several anticancer treatments has typically been presumed to have enhanced drug activity. Motivated by a real clinical trial, this paper considers phase I-II dose finding designs for dual-agent combinations, where one main objective is to characterize both the toxicity and efficacy profiles. We propose a two-stage Bayesian adaptive design that accommodates a change of patient population in-between. In stage I, we estimate a maximum tolerated dose combination using the escalation with overdose control (EWOC) principle. This is followed by a stage II, conducted in a new yet relevant patient population, to find the most efficacious dose combination. We implement a robust Bayesian hierarchical random-effects model to allow sharing of information on the efficacy across stages, assuming that the related parameters are either exchangeable or nonexchangeable. Under the assumption of exchangeability, a random-effects distribution is specified for the main effects parameters to capture uncertainty about the between-stage differences. The inclusion of nonexchangeability assumption further enables that the stage-specific efficacy parameters have their own priors. The proposed methodology is assessed with an extensive simulation study. Our results suggest a general improvement of the operating characteristics for the efficacy assessment, under a conservative assumption about the exchangeability of the parameters a priori.

qTPI: A quasi-toxicity probability interval design for phase I trials with multiple-grade toxicities

The common terminology criteria for adverse events by the National Cancer Institute has greatly facilitated the revolution of drug development and an increasing number of Phase I trials have started to collect multiple-grade toxicity endpoints. Appropriate and yet transparent Phase I statistical designs for multiple-grade toxicities are therefore in great needs. In this article, we propose a quasi-toxicity probability interval (qTPI) design that incorporates a quasi-continuous measure of the toxicity probability (q T P ) into the Bayesian theoretic framework of the interval based designs. Multiple-grade toxicity outcomes of each patient are mapped to q T P according to a severity weight matrix. Dose-toxicity curve underlying the dosing decisions in the qTPI design is continuously updated using accumulating trial data. Numerical simulations investigating the operating characteristics of qTPI show that qTPI achieved better safety, accuracy and reliability compared to designs that rely on binary toxicity data. Furthermore, parameter elicitation in qTPI is simple and does not involve multiple hypothetical cohorts specification. Finally, a hypothetical soft tissue sarcoma trial with six toxicity types and grade 0 to grade 4 severity grades is illustrated with patient-by-patient dose allocation under the qTPI design.

Combining cytotoxic agents with continuous dose levels in seamless phase I-II clinical trials

Phase I-II cancer clinical trial designs are intended to accelerate drug development. In cases where efficacy cannot be ascertained in a short period of time, it is common to divide the study in two stages: i) a first stage in which dose is escalated based only on toxicity data and we look for the maximum tolerated dose (MTD) set and ii) a second stage in which we search for the most efficacious dose within the MTD set. Current available approaches in the area of continuous dose levels involve fixing the MTD after stage I and discarding all collected stage I efficacy data. However, this methodology is clearly inefficient when there is a unique patient population present across stages. In this article, we propose a two-stage design for the combination of two cytotoxic agents assuming a single patient population across the entire study. In stage I, conditional escalation with overdose control (EWOC) is used to allocate successive cohorts of patients. In stage II, we employ an adaptive randomization approach to allocate patients to drug combinations along the estimated MTD curve, which is constantly updated. The proposed methodology is assessed with extensive simulations in the context of a real case study.

A dose-finding design for phase I clinical trials based on Bayesian stochastic approximation

Background

Current dose-finding designs for phase I clinical trials can correctly select the MTD in a range of 30–80% depending on various conditions based on a sample of 30 subjects. However, there is still an unmet need for efficiency and cost saving.

Methods

We propose a novel dose-finding design based on Bayesian stochastic approximation. The design features utilization of dose level information through local adaptive modelling and free assumption of toxicity probabilities and hyper-parameters. It allows a flexible target toxicity rate and varying cohort size. And we extend it to accommodate historical information via prior effective sample size. We compare the proposed design to some commonly used methods in terms of accuracy and safety by simulation.

Results

On average, our design can improve the percentage of correct selection to about 60% when the MTD resides at a early or middle position in the search domain and perform comparably to other competitive methods otherwise. A free online software package is provided to facilitate the application, where a simple decision tree for the design can be pre-printed beforehand.

Conclusion

The paper proposes a novel dose-finding design for phase I clinical trials. Applying the design to future cancer trials can greatly improve the efficiency, consequently save cost and shorten the development period.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01741-3.

Extending the Continual Reassessment Method to accommodate step-up dosing in Phase I trials

The Continual Reassessment Method (CRM) was developed for Phase I trials to identify a maximum‐tolerated dose of an agent using a design in which each participant is treated with a single administration of the agent. We propose an extension of the CRM in which participants receive multiple administrations of an agent using a so‐called step‐up dosing procedure in which participants receive one or more administrations of lower doses of the agent before they receive their penultimate dose. We use methods developed for the CRM to model the probability of DLT for each administration, which leads to the use of conditional probability models to model the joint probability of DLT across multiple administrations. We compare our approach to two existing methods that use time‐to‐event modeling methods for modeling the probability of DLT. We demonstrate through simulations that our approach has operating characteristics similar to existing methods, but due to its foundations in the CRM, ours is simpler to implement than existing approaches and is therefore more likely to be adopted in practice.

A nonparametric Bayesian method for dose finding in drug combinations cancer trials

We propose an adaptive design for early-phase drug-combination cancer trials with the goal of estimating the maximum tolerated dose (MTD). A nonparametric Bayesian model, using beta priors truncated to the set of partially ordered dose combinations, is used to describe the probability of dose limiting toxicity (DLT). Dose allocation between successive cohorts of patients is estimated using a modified continual reassessment scheme. The updated probabilities of DLT are calculated with a Gibbs sampler that employs a weighting mechanism to calibrate the influence of data vs the prior. At the end of the trial, we recommend one or more dose combinations as the MTD based on our proposed algorithm. We apply our method to a Phase I clinical trial of CB-839 and Gemcitabine that motivated this nonparametric design. The design operating characteristics indicate that our method is comparable with existing methods.

Vincristine Sulfate Liposome Injection with Bendamustine and Rituximab as First-Line Therapy for B-Cell Lymphomas: A Phase I Study

Background

We conducted an investigator-initiated, phase I trial of vincristine sulfate liposomal injection (VSLI) in combination with bendamustine and rituximab (BR) for indolent B-cell (BCL) or mantle cell lymphoma.

Methods

Participants received 6 cycles of standard BR with VSLI at patient-specific dose determined by the Escalation with Overdose Control (EWOC) model targeting 33% probability of dose-limiting toxicity (DLT). Maximum tolerated dose (MTD) was the primary endpoint; secondary endpoints included rates of adverse events (AEs), overall response rate (ORR), and complete response (CR). Vincristine sulfate liposomal injection is FDA approved for the treatment of patients with recurrent Philadelphia chromosome-negative (Ph−) acute lymphoblastic leukemia (ALL).

Results

Among 10 enrolled patients, VSLI was escalated from 1.80 to 2.24 mg/m², with one DLT (ileus) at 2.04 mg/m². Two patients discontinued VSLI early. The most common AE included lymphopenia (100%), constipation, nausea, infusion reaction (each 60%), neutropenia, and peripheral neuropathy (50%). Grade 3/4 AE included lymphopenia (90%), neutropenia (20%), and ileus (10%), with prolonged grade ≥2 lymphopenia observed in most patients. Calculated MTD for VSLI was 2.25 mg/m² (95% Bayesian credible interval: 2.00-2.40). Overall response was 100% with 50% CR. With median follow-up 26 months, 4/10 patients experienced recurrence and 1 died.

Conclusion

Vincristine sulfate liposomal injection at 2.25 mg/m² can be safely combined with BR for indolent B-cell lymphoma, but given observed toxicities and recurrences, we did not pursue an expanded cohort.

Clinical Trials Registration Number: ClinicalTrials.gov identifier NCT02257242.

Exposure driven dose escalation design with overdose control: Concept and first real life experience in an oncology phase I trial

Background

Methods

Results

Conclusion

•

Formally leverage pharmacokinetic data and modeling in dose escalation studies.

•

Suitable for molecules with potential non-linear pharmacokinetic.

•

Smarter dose escalation and more informative recommended phase 2 dose.

An adaptive gBOIN design with shrinkage boundaries for phase I dose-finding trials

Background

With the emergence of molecularly targeted agents and immunotherapies, the landscape of phase I trials in oncology has been changed. Though these new therapeutic agents are very likely induce multiple low- or moderate-grade toxicities instead of DLT, most of the existing phase I trial designs account for the binary toxicity outcomes. Motivated by a pediatric phase I trial of solid tumor with a continuous outcome, we propose an adaptive generalized Bayesian optimal interval design with shrinkage boundaries, gBOINS, which can account for continuous, toxicity grades endpoints and regard the conventional binary endpoint as a special case.

Result

The proposed gBOINS design enjoys convergence properties, e.g., the induced interval shrinks to the toxicity target and the recommended dose converges to the true maximum tolerated dose with increased sample size.

Conclusion

The proposed gBOINS design is transparent and simple to implement. We show that the gBOINS design has the desirable finite property of coherence and large-sample property of consistency. Numerical studies show that the proposed gBOINS design yields good performance and is comparable with or superior to the competing design.

Probability-of-decision interval 3+3 (POD-i3+3) design for phase I dose finding trials with late-onset toxicity

Late-onset toxicities often occur in phase I trials investigating novel immunotherapy and molecular targeted therapies. For trials with cohort based designs (such as modified toxicity probability interval, Bayesian optimal interval, and i3+3), patients are often turned away since the current cohort are still being followed without definite dose-limiting toxicities, which results in prolonged trial duration and waste of patient resources. In this paper, we incorporate a probability-of-decision framework into the i3+3 design and allow real-time dosing inference when the next patient becomes available. Both follow-up time for the pending patients and time to dose-limiting toxicities for the observed patients are used in calculating the posterior probability of each possible dosing decision. An intensive simulation study is conducted to evaluate the operating characteristics of the newly proposed probability-of-decision-i3+3 design under various dosing scenarios and patient accrual settings. Results show that the probability-of-decision-i3+3 design achieves comparable safety and reliability performances but much shorter trial duration compared to the complete designs.

Is more better? An analysis of toxicity and response outcomes from dose-finding clinical trials in cancer

BACKGROUND

The overwhelming majority of dose-escalation clinical trials use methods that seek a maximum tolerable dose, including rule-based methods like the 3+3, and model-based methods like CRM and EWOC. These methods assume that the incidences of efficacy and toxicity always increase as dose is increased. This assumption is widely accepted with cytotoxic therapies. In recent decades, however, the search for novel cancer treatments has broadened, increasingly focusing on inhibitors and antibodies. The rationale that higher doses are always associated with superior efficacy is less clear for these types of therapies.

METHODS

We extracted dose-level efficacy and toxicity outcomes from 115 manuscripts reporting dose-finding clinical trials in cancer between 2008 and 2014. We analysed the outcomes from each manuscript using flexible non-linear regression models to investigate the evidence supporting the monotonic efficacy and toxicity assumptions.

RESULTS

We found that the monotonic toxicity assumption was well-supported across most treatment classes and disease areas. In contrast, we found very little evidence supporting the monotonic efficacy assumption.

CONCLUSIONS

Our conclusion is that dose-escalation trials routinely use methods whose assumptions are violated by the outcomes observed. As a consequence, dose-finding trials risk recommending unjustifiably high doses that may be harmful to patients. We recommend that trialists consider experimental designs that allow toxicity and efficacy outcomes to jointly determine the doses given to patients and recommended for further study.

Bayesian optimization design for finding a maximum tolerated dose combination in phase I clinical trials

The development of combination therapies has become commonplace because potential synergistic benefits are expected for resistant patients of single-agent treatment. In phase I clinical trials, the underlying premise is toxicity increases monotonically with increasing dose levels. This assumption cannot be applied in drug combination trials, however, as there are complex drug-drug interactions. Although many parametric model-based designs have been developed, strong assumptions may be inappropriate owing to little information available about dose-toxicity relationships. No standard solution for finding a maximum tolerated dose combination has been established. With these considerations, we propose a Bayesian optimization design for identifying a single maximum tolerated dose combination. Our proposed design utilizing Bayesian optimization guides the next dose by a balance of information between exploration and exploitation on the nonparametrically estimated dose-toxicity function, thereby allowing us to reach a global optimum with fewer evaluations. We evaluate the proposed design by comparing it with a Bayesian optimal interval design and with the partial-ordering continual reassessment method. The simulation results suggest that the proposed design works well in terms of correct selection probabilities and dose allocations. The proposed design has high potential as a powerful tool for use in finding a maximum tolerated dose combination.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades

We propose a Bayesian adaptive design for early phase drug combination cancer trials incorporating ordinal grade of toxicities. Parametric models are used to describe the relationship between the dose combinations and the probabilities of the ordinal toxicities under the proportional odds assumption. Trial design proceeds by treating cohorts of two patients simultaneously receiving different dose combinations. Specifically, at each stage of the trial, we seek the dose of one agent by minimizing the Bayes risk with respect to a loss function given the current dose of the other agent. We consider two types of loss functions corresponding to the Continual Reassessment Method (CRM) and Escalation with Overdose Control (EWOC). At the end of the trial, we estimate the MTD curve as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD by comparing this design to the one that uses a binary indicator of DLT. The methodology is further adapted to the case of a pre-specified discrete set of dose combinations.

Fractional design: An alternative paradigm for late-onset toxicities in oncology dose-finding studies

Late-onset (LO) toxicities often arise in the new era of phase I oncology dose-finding trials with targeted agents or immunotherapies. The current LO toxicities modelling is often formulated in a weighted likelihood framework, where the time-to-event continual reassessment method (TITE-CRM) is commonly used. The TITE-CRM uses the patient exposure time as a weight for the censored observation, while there is large uncertainty on which weight function to be used. As an alternative, the fractional scheme formulates an efficient and robust paradigm to address LO toxicity issues in dose finding. We review the fractional continual reassessment method (fCRM) and compare its operating characteristics with those of the TITE-CRM as well as other competitive designs via extensive simulation studies based on both the fixed and randomly generated scenarios. The fCRM is shown to possess desirable operating characteristics in identifying the maximum tolerated dose (MTD) and deliver competitive performances in comparison with other designs. It provides an alternative efficient and robust paradigm for interpreting and addressing LO toxicities in the new era of phase I dose-finding trials in precision oncology. A real trial example is used to illustrate the practical use of the fCRM design.

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.

A Bayesian seamless phase I-II trial design with two stages for cancer clinical trials with drug combinations

The use of drug combinations in clinical trials is increasingly common during the last years since a more favorable therapeutic response may be obtained by combining drugs. In phase I clinical trials, most of the existing methodology recommends a one unique dose combination as "optimal," which may result in a subsequent failed phase II clinical trial since other dose combinations may present higher treatment efficacy for the same level of toxicity. We are particularly interested in the setting where it is necessary to wait a few cycles of therapy to observe an efficacy outcome and the phase I and II population of patients are different with respect to treatment efficacy. Under these circumstances, it is common practice to implement two-stage designs where a set of maximum tolerated dose combinations is selected in a first stage, and then studied in a second stage for treatment efficacy. In this article we present a new two-stage design for early phase clinical trials with drug combinations. In the first stage, binary toxicity data is used to guide the dose escalation and set the maximum tolerated dose combinations. In the second stage, we take the set of maximum tolerated dose combinations recommended from the first stage, which remains fixed along the entire second stage, and through adaptive randomization, we allocate subsequent cohorts of patients in dose combinations that are likely to have high posterior median time to progression. The methodology is assessed with extensive simulations and exemplified with a real trial.

2D (2 Dimensional) TEQR design for Determining the optimal Dose for safety and efficacy

Designs, such as the Eff-Tox, OBD (optimal biological dose), STEIN (simple efficacy toxicity interval), and TEPI (toxicity efficacy probability interval) designs, have been proposed to determine the optimal dose of a new oncology drug using both efficacy and toxicity. The goal of these designs is to select the optimal drug dose for further phase trials more accurately than dose finding designs that only consider toxicity, such as the 3 + 3, TEQR (toxicity equivalence range), mTPI (modified toxicity probability interval), and EWOC (escalation with overdose control) designs. We propose a new frequentist design for optimal dose selection, the 2D TEQR design, that is easier to understand and simpler to implement than the TEPI, Eff-Tox, STEIN and OBD designs, as it is based on the empirical or observed toxicity and efficacy rates and does not require specialized computations. We compare the performance of this new design with those of the TEPI, STEIN, Eff-Tox and OBD Isotonic designs. Although for the same sample size and cohort size, the frequentist 2D TEQR design is less accurate than the Bayesian TEPI design and also the STEIN design in selecting the optimal dose, the accuracy of optimal dose selection of the 2D TEQR design can be increased, in many cases, with a moderate increase in cohort size. The 2D TEQR design is as accurate as or more accurate than the Eff-Tox design in optimal dose selection, and better than the OBD Isotonic design, unless there is a clear peak in the true response rates, in which case the OBD Isotonic design performs better than the other 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.

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

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

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.

Two-stage design for phase I-II cancer clinical trials using continuous dose combinations of cytotoxic agents

We present a two-stage phase I/II design of a combination of two drugs in cancer clinical trials. The goal is to estimate safe dose combination regions with a desired level of efficacy. In stage I, conditional escalation with overdose control is used to allocate dose combinations to successive cohorts of patients and the maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. In stage II, we propose a Bayesian adaptive design for conducting the phase II trial to determine dose combination regions along the MTD curve with a desired level of efficacy. The methodology is evaluated by extensive simulations and application to a real trial.

Comparison between continuous and discrete doses for model based designs in cancer dose finding

Despite of an extensive statistical literature showing that discretizing continuous variables results in substantial loss of information, categorization of continuous variables has been a common practice in clinical research and in cancer dose finding (phase I) clinical trials. The objective of this study is to quantify the loss of information incurred by using a discrete set of doses to estimate the maximum tolerated dose (MTD) in phase I trials, instead of a continuous dose support. Escalation With Overdose Control and Continuous Reassessment Method were used because they are model-based designs where dose can be specified either as continuous or as a set of discrete levels. Five equally spaced sets of doses with different interval lengths and three sample sizes with sixteen scenarios were evaluated to compare the operating characteristics between continuous and discrete dose designs by Monte Carlo simulation. Loss of information was quantified by safety and efficiency measures. We conclude that if there is insufficient knowledge about the true MTD value, as commonly happens in phase I clinical trials, a continuous dose scheme minimizes information loss. If one is required to implement a design using discrete doses, then a scheme with 9 to 11 doses may yield similar results to the continuous dose scheme.

Uniformly most powerful Bayesian interval design for phase I dose-finding trials

Interval designs have recently attracted much attention in phase I clinical trials because of their simplicity and desirable finite-sample performance. However, existing interval designs typically cannot converge to the optimal dose level since their intervals do not shrink to the target toxicity probability as the sample size increases. The uniformly most powerful Bayesian test (UMPBT) is an objective Bayesian hypothesis testing procedure, which results in the largest probability that the Bayes factor against null hypothesis exceeds the evidence threshold for all possible values of the data generating parameter. On the basis of the rejection region of UMPBT, we develop the uniformly most powerful Bayesian interval (UMPBI) design for phase I dose-finding trials. The proposed UMPBI design enjoys convergence properties because the induced interval indeed shrinks to the toxicity target and the recommended dose converges to the true maximum tolerated dose as the sample size increases. Moreover, it possesses an optimality property that the probability of incorrect decisions is minimized. We conduct simulation studies to demonstrate the competitive finite-sample operating characteristics of the UMPBI in comparison with other existing interval designs. As an illustration, we apply the UMPBI design to a panitumumab and standard gemcitabine-based chemoradiation combination trial.

Extensions of the mTPI and TEQR designs to include non-monotone efficacy in addition to toxicity for optimal dose determination for early phase immunotherapy oncology trials

With the emergence of immunotherapy and other novel therapies, the traditional assumption that the efficacy of the study drug increases monotonically with dose levels is not always true. Therefore, dose-finding methods evaluating only toxicity data may not be adequate. In this paper, we have first compared the Modified Toxicity Probability Interval (mTPI) and Toxicity Equivalence Range (TEQR) dose-finding oncology designs for safety with identical stopping rules; we have then extended both designs to include efficacy in addition to safety – we determine the optimal dose for safety and efficacy using these designs by applying isotonic regression to the observed toxicity and efficacy rates, once the early phase trial is completed. We consider multiple types of underlying dose response curves, i.e., monotonically increasing, plateau, or umbrella-shaped. We conduct simulation studies to investigate the operating characteristics of the two proposed designs and compare them to existing designs. We found that the extended mTPI design selects the optimal dose for safety and efficacy more accurately than the other designs for most of the scenarios considered.

A Bayesian Adaptive Design in Cancer Phase I Trials using Dose Combinations in the Presence of a Baseline Covariate

A Bayesian adaptive design for dose finding of a combination of two drugs in cancer phase I clinical trials that takes into account patients heterogeneity thought to be related to treatment susceptibility is described. The estimation of the maximum tolerated dose (MTD) curves is a function of a baseline covariate using two cytotoxic agents. A logistic model is used to describe the relationship between the doses, baseline covariate, and the probability of dose limiting toxicity (DLT). Trial design proceeds by treating cohorts of two patients simultaneously using escalation with overdose control (EWOC), where at each stage of the trial, the next dose combination corresponds to the α quantile of the current posterior distribution of the MTD of one of two agents at the current dose of the other agent and the next patient's baseline covariate value. The MTD curves are estimated as function of Bayes estimates of the model parameters at the end of trial. Average DLT, pointwise average bias, and percent of dose recommendation at dose combination neighborhoods around the true MTD are compared to the design that uses the covariate to the one that ignores the baseline characteristic. We also examine the performance of the approach under model misspecifications for the true dose-toxicity relationship. The methodology is further illustrated by the case of a pre-specified discrete set of dose combinations.

A Bayesian adaptive design for cancer phase I trials using a flexible range of doses

We present a Bayesian adaptive design for dose finding in cancer phase I clinical trials. The goal is to estimate the maximum tolerated dose (MTD) after possible modification of the dose range during the trial. Parametric models are used to describe the relationship between the dose and the probability of dose-limiting toxicity (DLT). We investigate model reparameterization in terms of the probabilities of DLT at the minimum and maximum available doses at the start of the trial. Trial design proceeds using escalation with overdose control (EWOC), where at each stage of the trial we seek the dose of the agent such that the posterior probability of exceeding the MTD of this agent is bounded by a feasibility bound. At any time during the trial, we test whether the MTD is below or above the minimum and maximum doses, respectively. If during the trial there is evidence that the MTD is outside the range of doses, we extend the range of doses and complete the trial with the planned sample size. At the end of the trial, a Bayes estimate of the MTD is proposed. We evaluate design operating characteristics in terms of safety of the trial design and efficiency of the MTD estimate under various scenarios and model misspecification. The methodology is further compared to the original EWOC design. We showed by comprehensive simulation studies that the proposed method is safe and can estimate the MTD more efficiently than the original EWOC design.

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.

Systematic comparison of the statistical operating characteristics of various Phase I oncology designs

Dose finding Phase I oncology designs can be broadly categorized as rule based, such as the 3 + 3 and the accelerated titration designs, or model based, such as the CRM and Eff-Tox designs. This paper systematically reviews and compares through simulations several statistical operating characteristics, including the accuracy of maximum tolerated dose (MTD) selection, the percentage of patients assigned to the MTD, over-dosing, under-dosing, and the trial dose-limiting toxicity (DLT) rate, of eleven rule-based and model-based Phase I oncology designs that target or pre-specify a DLT rate of ∼0.2, for three sets of true DLT probabilities. These DLT probabilities are generated at common dosages from specific linear, logistic, and log-logistic dose-toxicity curves. We find that all the designs examined select the MTD much more accurately when there is a clear separation between the true DLT rate at the MTD and the rates at the dose level immediately above and below it, such as for the DLT rates generated using the chosen logistic dose-toxicity curve; the separations in these true DLT rates depend, in turn, not only on the functional form of the dose-toxicity curve but also on the investigated dose levels and the parameter set-up. The model based mTPI, TEQR, BOIN, CRM and EWOC designs perform well and assign the greatest percentages of patients to the MTD, and also have a reasonably high probability of picking the true MTD across the three dose-toxicity curves examined. Among the rule-based designs studied, the 5 + 5 a design picks the MTD as accurately as the model based designs for the true DLT rates generated using the chosen log-logistic and linear dose-toxicity curves, but requires enrolling a higher number of patients than the other designs. We also find that it is critical to pick a design that is aligned with the true DLT rate of interest. Further, we note that Phase I trials are very small in general and hence may not provide accurate estimates of the MTD. Thus our work provides a map for planning Phase I oncology trials or developing new ones.

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.

Incoherent dose-escalation in phase I trials using the escalation with overdose control approach

A desirable property of any dose-escalation strategy for phase I oncology trials is coherence: if the previous patient experienced a toxicity, a higher dose is not recommended for the next patient; similarly, if the previous patient did not experience a toxicity, a lower dose is not recommended for the next patient. The escalation with overdose control (EWOC) approach is a model-based design that has been applied in practice, under which the dose assigned to the next patient is the one that, given all available data, has a posterior probability of exceeding the maximum tolerated dose equal to a pre-specified value known as the feasibility bound. Several methodological and applied publications have considered the EWOC approach with both feasibility bounds fixed and increasing throughout the trial. Whilst the EWOC approach with fixed feasibility bound has been proven to be coherent, some proposed methods of increasing the feasibility bound regardless of toxicity outcomes of patients can lead to incoherent dose-escalation. This paper formalises a proof that incoherent dose-escalation can occur if the feasibility bound is increased without consideration of preceding toxicity outcomes, and shows via simulation studies that only small increases in the feasibility bound are required for incoherent dose-escalations to occur.

A Bayesian adaptive design for estimating the maximum tolerated dose curve using drug combinations in cancer phase I clinical trials

We present a cancer phase I clinical trial design of a combination of two drugs with the goal of estimating the maximum tolerated dose curve in the two-dimensional Cartesian plane. A parametric model is used 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 the probabilities of toxicities at dose combinations corresponding to the minimum and maximum doses available in the trial and the interaction parameter. Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC), 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. The maximum tolerated dose curve is estimated as a function of Bayes estimates of the model parameters. Performance of the trial is studied by evaluating its design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD curve and under model misspecifications for the true dose-toxicity relationship. The method is further extended to accommodate discrete dose combinations and compared with previous approaches under several scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

Escalation with Overdose Control is More Efficient and Safer than Accelerated Titration for Dose Finding

The standard 3 + 3 or "modified Fibonacci" up-and-down (MF-UD) method of dose escalation is by far the most used design in dose-finding cancer trials. However, MF-UD has always shown inferior performance when compared with its competitors regarding number of patients treated at optimal doses. A consequence of using less effective designs is that more patients are treated with doses outside the therapeutic window. In June 2012, the U S Food and Drug Administration (FDA) rejected the proposal to use Escalation with Overdose Control (EWOC), an established dose-finding method which has been extensively used in FDA-approved first in human trials and imposed a variation of the MF-UD, known as accelerated titration (AT) design. This event motivated us to perform an extensive simulation study comparing the operating characteristics of AT and EWOC. We show that the AT design has poor operating characteristics relative to three versions of EWOC under several practical scenarios. From the clinical investigator's perspective, lower bias and mean square error make EWOC designs preferable than AT designs without compromising safety. From a patient's perspective, uniformly higher proportion of patients receiving doses within an optimal range of the true MTD makes EWOC designs preferable than AT designs.

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.

Escalation with overdose control using time to toxicity for cancer phase I clinical trials

Escalation with overdose control (EWOC) is a Bayesian adaptive phase I clinical trial design that produces consistent sequences of doses while controlling the probability that patients are overdosed. However, this design does not take explicitly into account the time it takes for a patient to exhibit dose limiting toxicity (DLT) since the occurrence of DLT is ascertained within a predetermined window of time. Models to estimate the Maximum Tolerated Dose (MTD) that use the exact time when the DLT occurs are expected to be more precise than those where the variable of interest is categorized as presence or absence of DLT, given that information is lost in the process of categorization of the variable. We develop a class of parametric models for time to toxicity data in order to estimate the MTD efficiently, and present extensive simulations showing that the method has good design operating characteristics relative to the original EWOC and a version of time to event EWOC (TITE-EWOC) which allocates weights to account for the time it takes for a patient to exhibit DLT. The methodology is exemplified by a cancer phase I clinical trial we designed in order to estimate the MTD of Veliparib (ABT-888) in combination with fixed doses of gemcitabine and intensity modulated radiation therapy in patients with locally advanced, un-resectable pancreatic cancer.

A new approach to designing phase I-II cancer trials for cytotoxic chemotherapies

Recently, there has been much work on early phase cancer designs that incorporate both toxicity and efficacy data, called phase I-II designs because they combine elements of both phases. However, they do not explicitly address the phase II hypothesis test of H0 : p ≤ p0 , where p is the probability of efficacy at the estimated maximum tolerated dose η from phase I and p0 is the baseline efficacy rate. Standard practice for phase II remains to treat p as a fixed, unknown parameter and to use Simon's two-stage design with all patients dosed at η. We propose a phase I-II design that addresses the uncertainty in the estimate p=p(η) in H0 by using sequential generalized likelihood theory. Combining this with a phase I design that incorporates efficacy data, the phase I-II design provides a common framework that can be used all the way from the first dose of phase I through the final accept/reject decision about H0 at the end of phase II, utilizing both toxicity and efficacy data throughout. Efficient group sequential testing is used in phase II that allows for early stopping to show treatment effect or futility. The proposed phase I-II design thus removes the artificial barrier between phase I and phase II and fulfills the objectives of searching for the maximum tolerated dose and testing if the treatment has an acceptable response rate to enter into a phase III trial.

Escalation with overdose control using all toxicities and time to event toxicity data in cancer Phase I clinical trials

The primary purposes of Phase I cancer clinical trials are to determine the maximum tolerated dose (MTD) and the treatment schedule of a new drug. Phase I trials usually involve a small number of patients so that fully utilizing all toxicity information including time to event toxicity data is key to improving the trial efficiency and the accuracy of MTD estimation. Chen et al. proposed a novel normalized equivalent toxicity score (NETS) system to fully utilize multiple toxicities per patient instead of a binary indicator of dose limiting toxicity (DLT). Cheung and Chappell developed the time to toxicity event (TITE) approach to incorporate time to toxicity event data. Escalation with overdose control (EWOC) is an adaptive Bayesian Phase I design which can allow rapid dose escalation while controlling the probability of overdosing patients. In this manuscript, we use EWOC as a framework and integrate it with the NETS system and the TITE approach to develop an advanced Phase I design entitled EWOC-NETS-TITE. We have conducted simulation studies to compare its operating characteristics using selected derived versions of EWOC because EWOC itself has already been extensively compared with common Phase I designs [3]. Simulation results demonstrate that EWOC-NETS-TITE can substantially improve the trial efficiency and accuracy of MTD determination as well as allow patients to be entered in a staggered fashion to significantly shorten trial duration. Moreover, user-friendly software for EWOC-NETS-TITE is under development.