The use of local and nonlocal priors in Bayesian test-based monitoring for single-arm phase II clinical trials

Bayesian sequential monitoring is widely used in adaptive phase II studies where the objective is to examine whether an experimental drug is efficacious. Common approaches for Bayesian sequential monitoring are based on posterior or predictive probabilities and Bayesian hypothesis testing procedures using Bayes factors. In the first part of the paper, we briefly show the connections between test-based (TB) and posterior probability-based (PB) sequential monitoring approaches. Next, we extensively investigate the choice of local and nonlocal priors for the TB monitoring procedure. We describe the pros and cons of different priors in terms of operating characteristics. We also develop a user-friendly Shiny application to implement the TB design.     

Bayesian optimization design for dose-finding based on toxicity and efficacy outcomes in phase I/II clinical trials

In phase I trials, the main goal is to identify a maximum tolerated dose under an assumption of monotonicity in dose–response relationships. On the other hand, such monotonicity is no longer applied to biologic agents because a different mode of action from that of cytotoxic agents potentially draws unimodal or flat dose–efficacy curves. Therefore, biologic agents require an optimal dose that provides a sufficient efficacy rate under an acceptable toxicity rate instead of a maximum tolerated dose. Many trials incorporate both toxicity and efficacy data, and drugs with a variety of modes of actions are increasingly being developed; thus, optimal dose estimation designs have been receiving increased attention. Although numerous authors have introduced parametric model-based designs, it is not always appropriate to apply strong assumptions in dose–response relationships. We propose a new design based on a Bayesian optimization framework for identifying optimal doses for biologic agents in phase I/II trials. Our proposed design models dose–response relationships via nonparametric models utilizing a Gaussian process prior, and the uncertainty of estimates is considered in the dose selection process. We compared the operating characteristics of our proposed design against those of three other designs through simulation studies. These include an expansion of Bayesian optimal interval design, the parametric model-based EffTox design, and the isotonic design. In simulations, our proposed design performed well and provided results that were more stable than those from the other designs, in terms of the accuracy of optimal dose estimations and the percentage of correct recommendations.     

Continuous event monitoring via a Bayesian predictive approach

In clinical trials, continuous monitoring of event incidence rate plays a critical role in making timely decisions affecting trial outcome. For example, continuous monitoring of adverse events protects the safety of trial participants, while continuous monitoring of efficacy events helps identify early signals of efficacy or futility. Because the endpoint of interest is often the event incidence associated with a given length of treatment duration (e.g., incidence proportion of an adverse event with 2 years of dosing), assessing the event proportion before reaching the intended treatment duration becomes challenging, especially when the event onset profile evolves over time with accumulated exposure. In particular, in the earlier part of the study, ignoring censored subjects may result in significant bias in estimating the cumulative event incidence rate. Such a problem is addressed using a predictive approach in the Bayesian framework. In the proposed approach, experts' prior knowledge about both the frequency and timing of the event occurrence is combined with observed data. More specifically, during any interim look, each event‐free subject will be counted with a probability that is derived using prior knowledge. The proposed approach is particularly useful in early stage studies for signal detection based on limited information. But it can also be used as a tool for safety monitoring (e.g., data monitoring committee) during later stage trials. Application of the approach is illustrated using a case study where the incidence rate of an adverse event is continuously monitored during an Alzheimer's disease clinical trial. The performance of the proposed approach is also assessed and compared with other Bayesian and frequentist methods via simulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of Bayesian hierarchical models for phase I/II clinical trials in oncology

Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade‐offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving‐reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.     

Sample size planning for phase II trials based on success probabilities for phase III

In recent years, high failure rates in phase III trials were observed. One of the main reasons is overoptimistic assumptions for the planning of phase III resulting from limited phase II information and/or unawareness of realistic success probabilities. We present an approach for planning a phase II trial in a time‐to‐event setting that considers the whole phase II/III clinical development programme. We derive stopping boundaries after phase II that minimise the number of events under side conditions for the conditional probabilities of correct go/no‐go decision after phase II as well as the conditional success probabilities for phase III. In addition, we give general recommendations for the choice of phase II sample size. Our simulations show that unconditional probabilities of go/no‐go decision as well as the unconditional success probabilities for phase III are influenced by the number of events observed in phase II. However, choosing more than 150 events in phase II seems not necessary as the impact on these probabilities then becomes quite small. We recommend considering aspects like the number of compounds in phase II and the resources available when determining the sample size. The lower the number of compounds and the lower the resources are for phase III, the higher the investment for phase II should be. Copyright © 2015 John Wiley & Sons, Ltd.     

Designing and analyzing clinical trials for personalized medicine via Bayesian models

Patients with different characteristics (e.g., biomarkers, risk factors) may have different responses to the same medicine. Personalized medicine clinical studies that are designed to identify patient subgroup treatment efficacies can benefit patients and save medical resources. However, subgroup treatment effect identification complicates the study design in consideration of desired operating characteristics. We investigate three Bayesian adaptive models for subgroup treatment effect identification: pairwise independent, hierarchical, and cluster hierarchical achieved via Dirichlet Process (DP). The impact of interim analysis and longitudinal data modeling on the personalized medicine study design is also explored. Interim analysis is considered since they can accelerate personalized medicine studies in cases where early stopping rules for success or futility are met. We apply integrated two-component prediction method (ITP) for longitudinal data simulation, and simple linear regression for longitudinal data imputation to optimize the study design. The designs' performance in terms of power for the subgroup treatment effects and overall treatment effect, sample size, and study duration are investigated via simulation. We found the hierarchical model is an optimal approach to identifying subgroup treatment effects, and the cluster hierarchical model is an excellent alternative approach in cases where sufficient information is not available for specifying the priors. The interim analysis introduction to the study design lead to the trade-off between power and expected sample size via the adjustment of the early stopping criteria. The introduction of the longitudinal modeling slightly improves the power. These findings can be applied to future personalized medicine studies with discrete or time-to-event endpoints.     

Empowering phase II clinical trials to reduce phase III failures

The large number of failures in phase III clinical trials, which occur at a rate of approximately 45%, is studied herein relative to possible countermeasures. First, the phenomenon of failures is numerically described. Second, the main reasons for failures are reported, together with some generic improvements suggested in the related literature. This study shows how statistics explain, but do not justify, the high failure rate observed. The rate of failures due to a lack of efficacy that are not expected, is considered to be at least 10%. Expanding phase II is the simplest and most intuitive way to reduce phase III failures since it can reduce phase III false negative findings and launches of phase III trials when the treatment is positive but suboptimal. Moreover, phase II enlargement is discussed using an economic profile. As resources for research are often limited, enlarging phase II should be evaluated on a case‐by‐case basis. Alternative strategies, such as biomarker‐based enrichments and adaptive designs, may aid in reducing failures. However, these strategies also have very low application rates with little likelihood of rapid growth.     

Stopping for efficacy in single-arm phase II clinical trials

Phase II clinical trials investigate whether a new drug or treatment has sufficient evidence of effectiveness against the disease under study. Two-stage designs are popular for phase II since they can stop in the first stage if the drug is ineffective. Investigators often face difficulties in determining the target response rates, and adaptive designs can help to set the target response rate tested in the second stage based on the number of responses observed in the first stage. Popular adaptive designs consider two alternate response rates, and they generally minimise the expected sample size at the maximum uninterested response rate. Moreover, these designs consider only futility as the reason for early stopping and have high expected sample sizes if the provided drug is effective. Motivated by this problem, we propose an adaptive design that enables us to terminate the single-arm trial at the first stage for efficacy and conclude which alternate response rate to choose. Comparing the proposed design with a popular adaptive design from literature reveals that the expected sample size decreases notably if any of the two target response rates are correct. In contrast, the expected sample size remains almost the same under the null hypothesis.     

Operating characteristics of a Simon two-stage phase II clinical trial design incorporating continuous toxicity monitoring

Phase II clinical trials are usually designed to measure efficacy, but safety is also an important end point. Previous authors recommended a method to monitor toxic events after each patient is enrolled, which is also known as continuously monitoring the toxicity. In this work, we investigate combining the usual Simon two-stage design to monitor response with the continuous toxicity monitoring methodology. Theoretical justification is given for the nominal size, probability of early termination, and average sample size under the null hypothesis of the combined testing procedure. A series of simulations are performed to investigate the performance of the combined procedure.     

Early stopping in seamless phase I/II clinical trials

In recent years, seamless phase I/II clinical trials have drawn much attention, as they consider both toxicity and efficacy endpoints in finding an optimal dose (OD). Engaging an appropriate number of patients in a trial is a challenging task. This paper attempts a dynamic stopping rule to save resources in phase I/II trials. That is, the stopping rule aims to save patients from unnecessary toxic or subtherapeutic doses. We allow a trial to stop early when widths of the confidence intervals for the dose-response parameters become narrower or when the sample size is equal to a predefined size, whichever comes first. The simulation study of dose-response scenarios in various settings demonstrates that the proposed stopping rule can engage an appropriate number of patients. Therefore, we suggest its use in clinical trials.     

Bayesian phase II adaptive randomization by jointly modeling time-to-event efficacy and binary toxicity

In oncology, toxicity is typically observable shortly after a chemotherapy treatment, whereas efficacy, often characterized by tumor shrinkage, is observable after a relatively long period of time. In a phase II clinical trial design, we propose a Bayesian adaptive randomization procedure that accounts for both efficacy and toxicity outcomes. We model efficacy as a time-to-event endpoint and toxicity as a binary endpoint, sharing common random effects in order to induce dependence between the bivariate outcomes. More generally, we allow the randomization probability to depend on patients’ specific covariates, such as prognostic factors. Early stopping boundaries are constructed for toxicity and futility, and a superior treatment arm is recommended at the end of the trial. Following the setup of a recent renal cancer clinical trial at M. D. Anderson Cancer Center, we conduct extensive simulation studies under various scenarios to investigate the performance of the proposed method, and compare it with available Bayesian adaptive randomization procedures.     

Sample size determination and treatment screening in two‐stage phase II clinical trials via ROC curve

In pharmaceutical‐related research, we usually use clinical trials methods to identify valuable treatments and compare their efficacy with that of a standard control therapy. Although clinical trials are essential for ensuring the efficacy and postmarketing safety of a drug, conducting clinical trials is usually costly and time‐consuming. Moreover, to allocate patients to the little therapeutic effect treatments is inappropriate due to the ethical and cost imperative. Hence, there are several 2‐stage designs in the literature where, for reducing cost and shortening duration of trials, they use the conditional power obtained from interim analysis results to appraise whether we should continue the lower efficacious treatments in the next stage. However, there is a lack of discussion about the influential impacts on the conditional power of a trial at the design stage in the literature. In this article, we calculate the optimal conditional power via the receiver operating characteristic curve method to assess the impacts on the quality of a 2‐stage design with multiple treatments and propose an optimal design using the minimum expected sample size for choosing the best or promising treatment(s) among several treatments under an optimal conditional power constraint. In this paper, we provide tables of the 2‐stage design subject to optimal conditional power for various combinations of design parameters and use an example to illustrate our methods.     

A Bayesian piecewise exponential phase II design for monitoring a time-to-event endpoint

A robust Bayesian design is presented for a single-arm phase II trial with an early stopping rule to monitor a time to event endpoint. The assumed model is a piecewise exponential distribution with non-informative gamma priors on the hazard parameters in subintervals of a fixed follow up interval. As an additional comparator, we also define and evaluate a version of the design based on an assumed Weibull distribution. Except for the assumed models, the piecewise exponential and Weibull model based designs are identical to an established design that assumes an exponential event time distribution with an inverse gamma prior on the mean event time. The three designs are compared by simulation under several log-logistic and Weibull distributions having different shape parameters, and for different monitoring schedules. The simulations show that, compared to the exponential inverse gamma model based design, the piecewise exponential design has substantially better performance, with much higher probabilities of correctly stopping the trial early, and shorter and less variable trial duration, when the assumed median event time is unacceptably low. Compared to the Weibull model based design, the piecewise exponential design does a much better job of maintaining small incorrect stopping probabilities in cases where the true median survival time is desirably large.     

Designs foe phase i cancer clinical trials with differentiation of graded toxicity

For phase I cancer clinical trials, toxicity is a major concern. Commonly, toxicity is categorized to five levels of severity. In addition to the traditional standard dose-escaiation design, the Continual Reassessment Method (CRM) provides a promising alternative to estimate the maximum tolerated dose of a drug. However, in both standard design (STD) and CRM, the severity level of toxicity on grade 3/4 of a previous patient's response would not be a differentiated factor for the next dose level assignment. In this study, we extend the procedure incorporating the idea of unequal weights on the assessments of grade 3 and grade 4 toxicity in the dose escalation. The simulation results show that the proposed extended procedures by taking the impact of grade 4 toxicity into account, both for STD and CRM, reduce the chance of recommendation to the higher dose levels. Similar trends are observed for patient allocation to the higher levels. Additionally, for CRM which performs more accurately on the estimation of maximum tolerated dose (MTD), the proposed extended CRM maintains the same characteristic.     

Utilizing Bayesian predictive power in clinical trial design

The Bayesian paradigm provides an ideal platform to update uncertainties and carry them over into the future in the presence of data. Bayesian predictive power (BPP) reflects our belief in the eventual success of a clinical trial to meet its goals. In this paper we derive mathematical expressions for the most common types of outcomes, to make the BPP accessible to practitioners, facilitate fast computations in adaptive trial design simulations that use interim futility monitoring, and propose an organized BPP-based phase II-to-phase III design framework.     

Impact of safety monitoring on error probabilities of binary efficacy outcome analyses in large phase III group sequential trials

In phase III clinical trials, some adverse events may not be rare or unexpected and can be considered as a primary measure for safety, particularly in trials of life-threatening conditions, such as stroke or traumatic brain injury. In some clinical areas, efficacy endpoints may be highly correlated with safety endpoints, yet the interim efficacy analyses under group sequential designs usually do not consider safety measures formally in the analyses. Furthermore, safety is often statistically monitored more frequently than efficacy measures. Because early termination of a trial in this situation can be triggered by either efficacy or safety, the impact of safety monitoring on the error probabilities of efficacy analyses may be nontrivial if the original design does not take the multiplicity effect into account. We estimate the actual error probabilities for a bivariate binary efficacy-safety response in large confirmatory group sequential trials. The estimated probabilities are verified by Monte Carlo simulation. Our findings suggest that type I error for efficacy analyses decreases as efficacy-safety correlation or between-group difference in the safety event rate increases. In addition, although power for efficacy is robust to misspecification of the efficacy-safety correlation, it decreases dramatically as between-group difference in the safety event rate increases.     

Bayesian sequential analysis for multiple-arm clinical trials

Use of full Bayesian decision-theoretic approaches to obtain optimal stopping rules for clinical trial designs typically requires the use of Backward Induction. However, the implementation of Backward Induction, apart from simple trial designs, is generally impossible due to analytical and computational difficulties. In this paper we present a numerical approximation of Backward Induction in a multiple-arm clinical trial design comparing k experimental treatments with a standard treatment where patient response is binary. We propose a novel stopping rule, denoted by τ ^p , as an approximation of the optimal stopping rule, using the optimal stopping rule of a single-arm clinical trial obtained by Backward Induction. We then present an example of a double-arm (k=2) clinical trial where we use a simulation-based algorithm together with τ ^p to estimate the expected utility of continuing and compare our estimates with exact values obtained by an implementation of Backward Induction. For trials with more than two treatment arms, we evaluate τ ^p by studying its operating characteristics in a three-arm trial example. Results from these examples show that our approximate trial design has attractive properties and hence offers a relevant solution to the problem posed by Backward Induction.     

Bayesian adaptive two-stage design for determining person-time in Phase II clinical trials with Poisson data

Adaptive clinical trial designs can often improve drug-study efficiency by utilizing data obtained during the course of the trial. We present a novel Bayesian two-stage adaptive design for Phase II clinical trials with Poisson-distributed outcomes that allows for person-observation-time adjustments for early termination due to either futility or efficacy. Our design is motivated by the adaptive trial from [9 V. Sambucini, A Bayesian predictive two-stage design for Phase II clinical trials, Stat. Med. 27 (2008), pp. 1199–1224. doi: 10.1002/sim.3021[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], which uses binomial data. Although many frequentist and Bayesian two-stage adaptive designs for count data have been proposed in the literature, many designs do not allow for person-time adjustments after the first stage. This restriction limits flexibility in the study design. However, our proposed design allows for such flexibility by basing the second-stage person-time on the first-stage observed-count data. We demonstrate the implementation of our Bayesian predictive adaptive two-stage design using a hypothetical Phase II trial of Immune Globulin (Intravenous).