A Bayesian dose‐finding design for phase I/II clinical trials with nonignorable dropouts

Phase I/II trials utilize both toxicity and efficacy data to achieve efficient dose finding. However, due to the requirement of assessing efficacy outcome, which often takes a long period of time to be evaluated, the duration of phase I/II trials is often longer than that of the conventional dose‐finding trials. As a result, phase I/II trials are susceptible to the missing data problem caused by patient dropout, and the missing efficacy outcomes are often nonignorable in the sense that patients who do not experience treatment efficacy are more likely to drop out of the trial. We propose a Bayesian phase I/II trial design to accommodate nonignorable dropouts. We treat toxicity as a binary outcome and efficacy as a time‐to‐event outcome. We model the marginal distribution of toxicity using a logistic regression and jointly model the times to efficacy and dropout using proportional hazard models to adjust for nonignorable dropouts. The correlation between times to efficacy and dropout is modeled using a shared frailty. We propose a two‐stage dose‐finding algorithm to adaptively assign patients to desirable doses. Simulation studies show that the proposed design has desirable operating characteristics. Our design selects the target dose with a high probability and assigns most patients to the target dose. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive group sequential design for phase II clinical trials: A Bayesian decision theoretic approach

Bayesian decision theoretic approaches (BDTAs) have been widely studied in the literature as tools for designing and conducting phase II clinical trials. However, full Bayesian approaches that consider multiple endpoints are lacking. Since the monitoring of toxicity is a major goal of phase II trials, we propose an adaptive group sequential design using a BDTA, which characterizes efficacy and toxicity as correlated bivariate binary endpoints. We allow trade‐off between the two endpoints. Interim evaluations are conducted group sequentially, but the number of interim looks and the size of each group are chosen adaptively based on current observations. We utilize a loss function consisting of two components: the loss associated with accruing, treating, and monitoring patients, and the loss associated with making incorrect decisions. The performance of our Bayesian modeling, and the operating characteristics of decision rules under a wide range of loss function parameters are evaluated using seven scenarios in a simulation study. Our method is illustrated in the context of a single‐arm phase II trial of bevacizumab, gemcitabine, and oxaliplatin in patients with metastatic pancreatic adenocarcinoma. Copyright © 2009 John Wiley & Sons, Ltd.     

A Bayesian adaptive phase I/II platform trial design for pediatric immunotherapy trials

Immunotherapy is the most promising new cancer treatment for various pediatric tumors and has resulted in an unprecedented surge in the number of novel immunotherapeutic treatments that need to be evaluated in clinical trials. Most phase I/II trial designs have been developed for evaluating only one candidate treatment at a time, and are thus not optimal for this task. To address these issues, we propose a Bayesian phase I/II platform trial design, which accounts for the unique features of immunotherapy, thereby allowing investigators to continuously screen a large number of immunotherapeutic treatments in an efficient and seamless manner. The elicited numerical utility is adopted to account for the risk‐benefit trade‐off and to quantify the desirability of the dose. During the trial, inefficacious or overly toxic treatments are adaptively dropped from the trial and the promising treatments are graduated from the trial to the next stage of development. Once an experimental treatment is dropped or graduated, the next available new treatment can be immediately added and tested. Extensive simulation studies have demonstrated the desirable operating characteristics of the proposed design.     

Bayesian two-stage designs for phase II clinical trials

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

Accounting for patient heterogeneity in phase II clinical trials

Phase II clinical trials typically are single-arm studies conducted to decide whether an experimental treatment is sufficiently promising, relative to standard treatment, to warrant further investigation. Many methods exist for conducting phase II trials under the assumption that patients are homogeneous. In the presence of patient heterogeneity, however, these designs are likely to draw incorrect conclusions. We propose a class of model-based Bayesian designs for single-arm phase II trials with a binary or time-to-event outcome and two or more prognostic subgroups. The designs' early stopping rules are subgroup specific and allow the possibility of terminating some subgroups while continuing others, thus providing superior results when compared with designs that ignore treatment-subgroup interactions. Because our formulation requires informative priors on standard treatment parameters and subgroup main effects, and non-informative priors on experimental treatment parameters and treatment-subgroup interactions, we provide an algorithm for computing prior hyperparameter values. A simulation study is presented and the method is illustrated by a chemotherapy trial in acute leukemia.     

Adaptive two-stage designs in phase II clinical trials

Two-stage designs have been widely used in phase II clinical trials. Such designs are desirable because they allow a decision to be made on whether a treatment is effective or not after the accumulation of the data at the end of each stage. Optimal fixed two-stage designs, where the sample size at each stage is fixed in advance, were proposed by Simon when the primary outcome is a binary response. This paper proposes an adaptive two-stage design which allows the sample size at the second stage to depend on the results at the first stage. Using a Bayesian decision-theoretic construct, we derive optimal adaptive two-stage designs; the optimality criterion being minimum expected sample size under the null hypothesis. Comparisons are made between Simon's two-stage fixed design and the new design with respect to this optimality criterion.     

A Bayesian predictive two-stage design for phase II clinical trials

In this paper, we propose a Bayesian two-stage design for phase II clinical trials, which represents a predictive version of the single threshold design (STD) recently introduced by Tan and Machin. The STD two-stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre-specified target value and assuming that the observed response rate is slightly higher than the target. Unlike the STD, we do not refer to a fixed experimental outcome, but take into account the uncertainty about future data. In both stages, the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value. Such a probability is expressed in terms of prior predictive distributions of the data. The performance of the design is based on the distinction between analysis and design priors, recently introduced in the literature. The properties of the method are studied when all the design parameters vary.     

BOP2: Bayesian optimal design for phase II clinical trials with simple and complex endpoints

We propose a flexible Bayesian optimal phase II (BOP2) design that is capable of handling simple (e.g., binary) and complicated (e.g., ordinal, nested, and co‐primary) endpoints under a unified framework. We use a Dirichlet‐multinomial model to accommodate different types of endpoints. At each interim, the go/no‐go decision is made by evaluating a set of posterior probabilities of the events of interest, which is optimized to maximize power or minimize the number of patients under the null hypothesis. Unlike other existing Bayesian designs, the BOP2 design explicitly controls the type I error rate, thereby bridging the gap between Bayesian designs and frequentist designs. In addition, the stopping boundary of the BOP2 design can be enumerated prior to the onset of the trial. These features make the BOP2 design accessible to a wide range of users and regulatory agencies and particularly easy to implement in practice. Simulation studies show that the BOP2 design has favorable operating characteristics with higher power and lower risk of incorrectly terminating the trial than some existing Bayesian phase II designs. The software to implement the BOP2 design is freely available at www.trialdesign.org . Copyright © 2017 John Wiley & Sons, Ltd.     

A Bayesian dose finding design for dual endpoint phase I trials

We propose a dose-finding weighted design for an early clinical trial which aims to determine the optimal dose, selected on the basis of both efficacy and toxicity, to be used in patients entering subsequent studies in a drug development process. The goal is to identify the optimal dose, while using a minimal number of subjects. For each dose under test, a decision table is defined with a utility value attached to each possible decision. The relationship between the utility and the target probability for each outcome is shown. A Dirichlet prior is used and we illustrate the process of maximizing the expected utility under the resulting posterior distribution to find the optimal decision at each stage of the trial. We show how this affects the eventual choice of optimal dose in various scenarios. Properties of our design are discussed and compared with a current standard design.     

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.     

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 Bayesian predictive strategy for an adaptive two‐stage design in phase II clinical trials

Phase II clinical trials are typically designed as two‐stage studies, in order to ensure early termination of the trial if the interim results show that the treatment is ineffective. Most of two‐stage designs, developed under both a frequentist and a Bayesian framework, select the second stage sample size before observing the first stage data. This may cause some paradoxical situations during the practical carrying out of the trial. To avoid these potential problems, we suggest a Bayesian predictive strategy to derive an adaptive two‐stage design, where the second stage sample size is not selected in advance, but depends on the first stage result. The criterion we propose is based on a modification of a Bayesian predictive design recently presented in the literature (see (Statist. Med. 2008; 27 :1199–1224)). The distinction between analysis and design priors is essential for the practical implementation of the procedure: some guidelines for choosing these prior distributions are discussed and their impact on the required sample size is examined. Copyright © 2010 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.     

Bayesian decision theoretic two-stage design in phase II clinical trials with survival endpoint

In this paper, we consider two-stage designs with failure-time endpoints in single-arm phase II trials. We propose designs in which stopping rules are constructed by comparing the Bayes risk of stopping at stage I with the expected Bayes risk of continuing to stage II using both the observed data in stage I and the predicted survival data in stage II. Terminal decision rules are constructed by comparing the posterior expected loss of a rejection decision versus an acceptance decision. Simple threshold loss functions are applied to time-to-event data modeled either parametrically or nonparametrically, and the cost parameters in the loss structure are calibrated to obtain desired type I error and power. We ran simulation studies to evaluate design properties including types I and II errors, probability of early stopping, expected sample size, and expected trial duration and compared them with the Simon two-stage designs and a design, which is an extension of the Simon's designs with time-to-event endpoints. An example based on a recently conducted phase II sarcoma trial illustrates the method.     

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

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

Bayesian decision sequential analysis with survival endpoint in phase II clinical trials

Chen and Chaloner (Statist. Med. 2006; 25 :2956–2966. DOI: 10.1002/sim.2429 ) present a Bayesian stopping rule for a single‐arm clinical trial with a binary endpoint. In some cases, earlier stopping may be possible by basing the stopping rule on the time to a binary event. We investigate the feasibility of computing exact, Bayesian, decision‐theoretic time‐to‐event stopping rules for a single‐arm group sequential non‐inferiority trial relative to an objective performance criterion. For a conjugate prior distribution, exponential failure time distribution, and linear and threshold loss structures, we obtain the optimal Bayes stopping rule by backward induction. We compute frequentist operating characteristics of including Type I error, statistical power, and expected run length. We also briefly address design issues. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian hierarchical EMAX model for dose-response in early phase efficacy clinical trials

A primary goal of a phase II dose-ranging trial is to identify a correct dose before moving forward to a phase III confirmatory trial. A correct dose is one that is actually better than control. A popular model in phase II is an independent model that puts no structure on the dose-response relationship. Unfortunately, the independent model does not efficiently use information from related doses. One very successful alternate model improves power using a pre-specified dose-response structure. Past research indicates that EMAX models are broadly successful and therefore attractive for designing dose-response trials. However, there may be instances of slight risk of nonmonotone trends that need to be addressed when planning a clinical trial design. We propose to add hierarchical parameters to the EMAX model. The added layer allows information about the treatment effect in one dose to be “borrowed” when estimating the treatment effect in another dose. This is referred to as the hierarchical EMAX model. Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, and it has a fixed schedule for randomization. The second design is Bayesian but adaptive, and it uses response adaptive randomization. In this article, a randomized trial of patients with severe traumatic brain injury is provided as a motivating example.     

Optimal adaptive two‐stage designs for early phase II clinical trials

Simon's optimal two‐stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints. With this approach, the second‐stage sample size is fixed when the trial passes the first stage with sufficient activity. Adaptive designs, such as those due to Banerjee and Tsiatis (2006) and Englert and Kieser (2013), are flexible in the sense that the second‐stage sample size depends on the response from the first stage, and these designs are often seen to reduce the expected sample size under the null hypothesis as compared with Simon's approach. An unappealing trait of the existing designs is that they are not associated with a second‐stage sample size, which is a non‐increasing function of the first‐stage response rate. In this paper, an efficient intelligent process, the branch‐and‐bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected. The proposed optimal design is observed to have smaller expected sample sizes compared to Simon's optimal design, and the maximum total sample size of the proposed adaptive design is very close to that from Simon's method. The proposed optimal adaptive two‐stage design is recommended for use in practice to improve the flexibility and efficiency of early phase therapeutic development. Copyright © 2015 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.     

Competing designs for drug combination in phase I dose‐finding clinical trials

The aim of phase I combination dose‐finding studies in oncology is to estimate one or several maximum tolerated doses (MTDs) from a set of available dose levels of two or more agents. Combining several agents can indeed increase the overall anti‐tumor action but at the same time also increase the toxicity. It is, however, unreasonable to assume the same dose–toxicity relationship for the combination as for the simple addition of each single agent because of a potential antagonist or synergistic effect. Therefore, using single‐agent dose‐finding methods for combination therapies is not appropriate. In recent years, several authors have proposed novel dose‐finding designs for combination studies, which use either algorithm‐based or model‐based methods. The aim of our work was to compare, via a simulation study, six dose‐finding methods for combinations proposed in recent years. We chose eight scenarios that differ in terms of the number and location of the true MTD(s) in the combination space. We then compared the performance of each design in terms of correct combination selection, patient allocation, and mean number of observed toxicities during the trials. Our results showed that the model‐based methods performed better than the algorithm‐based ones. However, none of the compared model‐based designs gave consistently better results than the others. Copyright © 2014 John Wiley & Sons, Ltd.