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.

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.

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 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.

A phase I study of sirolimus in combination with metronomic therapy (CHOAnome) in children with recurrent or refractory solid and brain tumors

BACKGROUND/PURPOSE

To determine the maximum tolerated dose, toxicities, and response of sirolimus combined with oral metronomic therapy in pediatric patients with recurrent and refractory solid and brain tumors.

PROCEDURE

Patients younger than 30 years of age with recurrent, refractory, or high-risk solid and brain tumors were eligible. Patients received six-week cycles of sirolimus with twice daily celecoxib, and alternating etoposide and cyclophosphamide every three weeks, with Bayesian dose escalation over four dose levels (NCT01331135).

RESULTS

Eighteen patients were enrolled: four on dose level (DL) 1, four on DL2, eight on DL3, and two on DL4. Diagnoses included solid tumors (Ewing sarcoma, osteosarcoma, malignant peripheral nerve sheath tumor, rhabdoid tumor, retinoblastoma) and brain tumors (glioblastoma multiforme [GBM], diffuse intrinsic pontine glioma, high-grade glioma [HGG], medulloblastoma, ependymoma, anaplastic astrocytoma, low-grade infiltrative astrocytoma, primitive neuroectodermal tumor, nongerminomatous germ cell tumor]. One dose-limiting toxicity (DLT; grade 4 neutropenia) was observed on DL2, two DLTs (grade 3 abdominal pain and grade 3 mucositis) on DL3, and two DLTs (grade 3 dehydration and grade 3 mucositis) on DL4. The recommended phase II dose of sirolimus was 2 mg/m² (DL3). Best response was stable disease (SD) in eight patients, and partial response (PR) in one patient with GBM. A patient with HGG was removed from the study with SD and developed PR without further therapy. Western blot analysis showed inhibition of phospho-S6 kinase in all patients during the first cycle of therapy.

CONCLUSION

The combination of sirolimus with metronomic chemotherapy is well tolerated in children. A phase II trial of this combination is ongoing.

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.

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.

A dynamic stopping rule for phase I clinical trials

This paper investigates a stopping rule to be utilised in phase I clinical trials. The motivation is to develop a dynamic rule so that a trial stops early if the maximum tolerated dose lies towards the beginning of a dose region. Also, it will employ many patients if the maximum tolerated dose lies towards the end of a dose region. A two-parameter logistic model is assumed for the dose-response data. A trial is stopped early before reaching the maximum number of patients when the width of the Bayesian posterior probability interval of the slope parameter meets a desired value. Instead of setting a pre-specified width to stop at, we determine it based on the parameter estimate obtained after a reasonable number of steps in a trial. Simulation studies of six plausible dose-response scenarios show that the proposed stopping rule is capable of limiting the number of patients to be recruited depending on the underlying scenario. Although the rule is applied to a D-optimum design here, it will be equally applicable to other model-based designs.

Motivating sample sizes in adaptive Phase I trials via Bayesian posterior credible intervals

In contrast with typical Phase III clinical trials, there is little existing methodology for determining the appropriate numbers of patients to enroll in adaptive Phase I trials. And, as stated by Dennis Lindley in a more general context, "[t]he simple practical question of 'What size of sample should I take' is often posed to a statistician, and it is a question that is embarrassingly difficult to answer." Historically, simulation has been the primary option for determining sample sizes for adaptive Phase I trials, and although useful, can be problematic and time-consuming when a sample size is needed relatively quickly. We propose a computationally fast and simple approach that uses Beta distributions to approximate the posterior distributions of DLT rates of each dose and determines an appropriate sample size through posterior coverage rates. We provide sample sizes produced by our methods for a vast number of realistic Phase I trial settings and demonstrate that our sample sizes are generally larger than those produced by a competing approach that is based upon the nonparametric optimal design.

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.

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.

Sample size formulae for the Bayesian continual reassessment method

BACKGROUND

In the planning of a dose finding study, a primary design objective is to maintain high accuracy in terms of the probability of selecting the maximum tolerated dose. While numerous dose finding methods have been proposed in the literature, concrete guidance on sample size determination is lacking.

PURPOSE

With a motivation to provide quick and easy calculations during trial planning, we present closed form formulae for sample size determination associated with the use of the Bayesian continual reassessment method (CRM).

METHODS

We examine the sampling distribution of a nonparametric optimal design and exploit it as a proxy to empirically derive an accuracy index of the CRM using linear regression.

RESULTS

We apply the formulae to determine the sample size of a phase I trial of PTEN-long in pancreatic cancer patients and demonstrate that the formulae give results very similar to simulation. The formulae are implemented by an R function 'getn' in the package 'dfcrm'.

LIMITATIONS

The results are developed for the Bayesian CRM and should be validated by simulation when used for other dose finding methods.

CONCLUSIONS

The analytical formulae we propose give quick and accurate approximation of the required sample size for the CRM. The approach used to derive the formulae can be applied to obtain sample size formulae for other dose finding methods.