Bayesian Adaptive Randomization and Trial Monitoring with Predictive Probability for Time-to-Event Endpoint

There has been much development in Bayesian adaptive designs in clinical trials. In the Bayesian paradigm, the posterior predictive distribution characterizes the future possible outcomes given the currently observed data. Based on the interim time-to-event data, we develop a new phase II trial design by combining the strength of both Bayesian adaptive randomization and the predictive probability. By comparing the mean survival times between patients assigned to two treatment arms, more patients are assigned to the better treatment on the basis of adaptive randomization. We continuously monitor the trial using the predictive probability for early termination in the case of superiority or futility. We conduct extensive simulation studies to examine the operating characteristics of four designs: the proposed predictive probability adaptive randomization design, the predictive probability equal randomization design, the posterior probability adaptive randomization design, and the group sequential design. Adaptive randomization designs using predictive probability and posterior probability yield a longer overall median survival time than the group sequential design, but at the cost of a slightly larger sample size. The average sample size using the predictive probability method is generally smaller than that of the posterior probability design.     

Biomarker-Defined Subgroup Selection Adaptive Design for Phase III Confirmatory Trial with Time-to-Event Data: Comparing Group Sequential and Various Adaptive Enrichment Designs

Predictive and prognostic biomarkers play an important role in personalized medicine to determine strategies for drug evaluation and treatment selection. In the context of continuous biomarkers, identification of an optimal cutoff for patient selection can be challenging due to limited information on biomarker predictive value, the biomarker’s distribution in the intended use population, and the complexity of the biomarker relationship to clinical outcomes. As a result, prespecified candidate cutoffs may be rationalized based on biological and practical considerations. In this context, adaptive enrichment designs have been proposed with interim decision rules to select a biomarker-defined subpopulation to optimize study performance. With a group sequential design as a reference, the performance of several proposed adaptive designs are evaluated and compared under various scenarios (e.g., sample size, study power, enrichment effects) where type I error rates are well controlled through closed testing procedures and where subpopulation selections are based upon the predictive probability of trial success. It is found that when the treatment is more effective in a subpopulation, these adaptive designs can improve study power substantially. Furthermore, we identified one adaptive design to have generally higher study power than the other designs under various scenarios.     

Subgroup-Based Adaptive (SUBA) Designs for Multi-arm Biomarker Trials

Targeted therapies based on biomarker profiling are becoming a mainstream direction of cancer research and treatment. Depending on the expression of specific prognostic biomarkers, targeted therapies assign different cancer drugs to subgroups of patients even if they are diagnosed with the same type of cancer by traditional means, such as tumor location. For example, Herceptin is only indicated for the subgroup of patients with HER2+ breast cancer, but not other types of breast cancer. However, subgroups like HER2+ breast cancer with effective targeted therapies are rare, and most cancer drugs are still being applied to large patient populations that include many patients who might not respond or benefit. Also, the response to targeted agents in humans is usually unpredictable. To address these issues, we propose subgroup-based adaptive (SUBA), designs that simultaneously search for prognostic subgroups and allocate patients adaptively to the best subgroup-specific treatments throughout the course of the trial. The main features of SUBA include the continuous reclassification of patient subgroups based on a random partition model and the adaptive allocation of patients to the best treatment arm based on posterior predictive probabilities. We compare the SUBA design with three alternative designs including equal randomization, outcome-adaptive randomization, and a design based on a probit regression. In simulation studies, we find that SUBA compares favorably against the alternatives.     

An optimal Bayesian predictive probability design for phase II clinical trials with simple and complicated endpoints

Most existing phase II clinical trial designs focus on conventional chemotherapy with binary tumor response as the endpoint. The advent of novel therapies, such as molecularly targeted agents and immunotherapy, has made the endpoint of phase II trials more complicated, often involving ordinal, nested, and coprimary endpoints. We propose a simple and flexible Bayesian optimal phase II predictive probability (OPP) design that handles binary and complex endpoints in a unified way. The Dirichlet-multinomial model is employed to accommodate different types of endpoints. At each interim, given the observed interim data, we calculate the Bayesian predictive probability of success, should the trial continue to the maximum planned sample size, and use it to make the go/no-go decision. The OPP design controls the type I error rate, maximizes power or minimizes the expected sample size, and is easy to implement, because the go/no-go decision boundaries can be enumerated and included in the protocol before the onset of the trial. Simulation studies show that the OPP design has satisfactory operating characteristics.     

Bayesian treatment screening and selection using subgroup-specific utilities of response and toxicity

A Bayesian design is proposed for randomized phase II clinical trials that screen multiple experimental treatments compared to an active control based on ordinal categorical toxicity and response. The underlying model and design account for patient heterogeneity characterized by ordered prognostic subgroups. All decision criteria are subgroup specific, including interim rules for dropping unsafe or ineffective treatments, and criteria for selecting optimal treatments at the end of the trial. The design requires an elicited utility function of the two outcomes that varies with the subgroups. Final treatment selections are based on posterior mean utilities. The methodology is illustrated by a trial of targeted agents for metastatic renal cancer, which motivated the design methodology. In the context of this application, the design is evaluated by computer simulation, including comparison to three designs that conduct separate trials within subgroups, or conduct one trial while ignoring subgroups, or base treatment selection on estimated response rates while ignoring toxicity.     

Personalized medicine using DNA biomarkers: a review

Biomarkers are of increasing importance for personalized medicine, with applications including diagnosis, prognosis, and selection of targeted therapies. Their use is extremely diverse, ranging from pharmacodynamics to treatment monitoring. Following a concise review of terminology, we provide examples and current applications of three broad categories of biomarkers-DNA biomarkers, DNA tumor biomarkers, and other general biomarkers. We outline clinical trial phases for identifying and validating diagnostic and prognostic biomarkers. Predictive biomarkers, more generally termed companion diagnostic tests predict treatment response in terms of efficacy and/or safety. We consider suitability of clinical trial designs for predictive biomarkers, including a detailed discussion of validation study designs, with emphasis on interpretation of study results. We specifically discuss the interpretability of treatment effects if a large set of DNA biomarker profiles is available and the number of therapies is identical to the number of different profiles.     

A nonparametric Bayesian basket trial design

Targeted therapies on the basis of genomic aberrations analysis of the tumor have shown promising results in cancer prognosis and treatment. Regardless of tumor type, trials that match patients to targeted therapies for their particular genomic aberrations have become a mainstream direction of therapeutic management of patients with cancer. Therefore, finding the subpopulation of patients who can most benefit from an aberration‐specific targeted therapy across multiple cancer types is important. We propose an adaptive Bayesian clinical trial design for patient allocation and subpopulation identification. We start with a decision theoretic approach, including a utility function and a probability model across all possible subpopulation models. The main features of the proposed design and population finding methods are the use of a flexible nonparametric Bayesian survival regression based on a random covariate‐dependent partition of patients, and decisions based on a flexible utility function that reflects the requirement of the clinicians appropriately and realistically, and the adaptive allocation of patients to their superior treatments. Through extensive simulation studies, the new method is demonstrated to achieve desirable operating characteristics and compares favorably against the alternatives.     

Performance of Biomarker-Based Subgroup Selection Rules in Adaptive Enrichment Designs

In the planning stage of a clinical trial investigating a potentially targeted therapy, there is commonly a high degree of uncertainty whether the treatment is more efficient (or efficient only) in a subgroup compared to the whole population. Recently developed adaptive designs enable to allow for an efficacy assessment both for the whole population and a subgroup and to select the target population mid-course based on interim results (see, e.g., Wang et al., Pharm Stat 6:227–244, 2007, Brannath et al., Stat Med 28:1445–1463, 2009, Wang et al., Biom J 51:358–374, 2009, Jenkins et al., Pharm Stat 10:347–356, 2011, Friede et al., Stat Med 31:4309–4120, 2012). Frequently, predictive biomarkers are used in these trials for identifying patients more likely to benefit from a drug. We consider the situation that the selection of the patient population is based on a biomarker and where the diagnostics that evaluates the biomarker may be perfect, i.e., with 100 % sensitivity and specificity, or not. The performance of the applied subset selection rule is crucial for the overall characteristics of the design. In the setting of an adaptive enrichment design, we evaluate the properties of subgroup selection rules in terms of type I error rate and power by taking into account decision rules with a fixed ad hoc threshold and optimal decision rules developed for the situation of uncertain assumptions. In a simulation study, we demonstrate that designs with optimal decision rules are under certain assumptions more powerful as compared to those with ad hoc decision rules. Throughout the results, a strong impact of sensitivity and specificity of the biomarker on both type I error rate and power is observed.     

Bayesian adaptive biased-coin designs for clinical trials with normal responses

Adaptive designs are used in phase III clinical trials for skewing the allocation pattern toward the better treatments. We use optimum design theory to derive a skewed Bayesian biased-coin procedure for sequential designs with continuous responses. The skewed designs are used to provide adaptive designs, the performance of which is studied numerically and theoretically. Important properties are loss and the proportion of allocation to the better treatment.     

Design considerations for two-stage enrichment clinical trials

When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a “phase III-like” trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment trials.     

Bayesian enrichment strategies for randomized discontinuation trials

We propose optimal choice of the design parameters for random discontinuation designs (RDD) using a Bayesian decision-theoretic approach. We consider applications of RDDs to oncology phase II studies evaluating activity of cytostatic agents. The design consists of two stages. The preliminary open-label stage treats all patients with the new agent and identifies a possibly sensitive subpopulation. The subsequent second stage randomizes, treats, follows, and compares outcomes among patients in the identified subgroup, with randomization to either the new or a control treatment. Several tuning parameters characterize the design: the number of patients in the trial, the duration of the preliminary stage, and the duration of follow-up after randomization. We define a probability model for tumor growth, specify a suitable utility function, and develop a computational procedure for selecting the optimal tuning parameters.     

Bayesian personalized treatment selection strategies that integrate predictive with prognostic determinants

The evolution of “informatics” technologies has the potential to generate massive databases, but the extent to which personalized medicine may be effectuated depends on the extent to which these rich databases may be utilized to advance understanding of the disease molecular profiles and ultimately integrated for treatment selection, necessitating robust methodology for dimension reduction. Yet, statistical methods proposed to address challenges arising with the high‐dimensionality of omics‐type data predominately rely on linear models and emphasize associations deriving from prognostic biomarkers. Existing methods are often limited for discovering predictive biomarkers that interact with treatment and fail to elucidate the predictive power of their resultant selection rules. In this article, we present a Bayesian predictive method for personalized treatment selection that is devised to integrate both the treatment predictive and disease prognostic characteristics of a particular patient's disease. The method appropriately characterizes the structural constraints inherent to prognostic and predictive biomarkers, and hence properly utilizes these complementary sources of information for treatment selection. The methodology is illustrated through a case study of lower grade glioma. Theoretical considerations are explored to demonstrate the manner in which treatment selection is impacted by prognostic features. Additionally, simulations based on an actual leukemia study are provided to ascertain the method's performance with respect to selection rules derived from competing methods.     

An adaptive two-stage design with treatment selection using the conditional error function approach

As an approach to combining the phase II dose finding trial and phase III pivotal trials, we propose a two-stage adaptive design that selects the best among several treatments in the first stage and tests significance of the selected treatment in the second stage. The approach controls the type I error defined as the probability of selecting a treatment and claiming its significance when the selected treatment is indifferent from placebo, as considered in Bischoff and Miller (2005). Our approach uses the conditional error function and allows determining the conditional type I error function for the second stage based on information observed at the first stage in a similar way to that for an ordinary adaptive design without treatment selection. We examine properties such as expected sample size and stage-2 power of this design with a given type I error and a maximum stage-2 sample size under different hypothesis configurations. We also propose a method to find the optimal conditional error function of a simple parametric form to improve the performance of the design and have derived optimal designs under some hypothesis configurations. Application of this approach is illustrated by a hypothetical example.     

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well‐being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate‐adjusted response‐adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well‐being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response‐adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well‐being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.     

A Bayesian platform trial design to simultaneously evaluate multiple drugs in multiple indications with mixed endpoints

In the era of targeted therapies and immunotherapies, the traditional drug development paradigm of testing one drug at a time in one indication has become increasingly inefficient. Motivated by a real-world application, we propose a master-protocol–based Bayesian platform trial design with mixed endpoints (PDME) to simultaneously evaluate multiple drugs in multiple indications, where different subsets of efficacy measures (eg, objective response and landmark progression-free survival) may be used by different indications as single or multiple endpoints. We propose a Bayesian hierarchical model to accommodate mixed endpoints and reflect the trial structure of indications that are nested within treatments. We develop a two-stage approach that first clusters the indications into homogeneous subgroups and then applies the Bayesian hierarchical model to each subgroup to achieve precision information borrowing. Patients are enrolled in a group-sequential way and adaptively assigned to treatments according to their efficacy estimates. At each interim analysis, the posterior probabilities that the treatment effect exceeds prespecified clinically relevant thresholds are used to drop ineffective treatments and “graduate” effective treatments. Simulations show that the PDME design has desirable operating characteristics compared to existing method.     

Auto-adaptive Alpha Allocation: A Strategy to Mitigate Risk on Study Assumptions

In some clinical development programs, there are potential biomarkers with promising but uncertain predictive effect, while the probability of success in the overall population cannot be readily dismissed. It is risky to focus only on the overall population, or just the biomarker subpopulation. In 2009, Chen and Beckman proposed a Bayesian decision framework to optimize the type I error rate (alpha) allocation in a Phase III clinical study with possible predictive subset effect. The utilization of internal data in this framework is of particular interest because it provides an opportunity to mitigate the potential risk of misspecified study assumptions using an auto-adaptive strategy. In this paper, we examine this auto-adaptive strategy in detail through extensive numerical case studies and provide guidance on the appropriate use of partial current trial (internal) data in this data-driven optimization framework. We show that internal data can be used to inform the alpha allocation to hypothesis testing in the overall population and the subgroup. The resulting adaptive testing strategy is robust with respect to the uncertainty in the predictive subgroup effect and biomarker prevalence.     

A Bayesian basket trial design that borrows information across strata based on the similarity between the posterior distributions of the response probability

Basket trials simultaneously evaluate the effect of one or more drugs on a defined biomarker, genetic alteration, or molecular target in a variety of disease subtypes, often called strata. A conventional approach for analyzing such trials is an independent analysis of each of the strata. This analysis is inefficient as it lacks the power to detect the effect of drugs in each stratum. To address these issues, various designs for basket trials have been proposed, centering on designs using Bayesian hierarchical models. In this article, we propose a novel Bayesian basket trial design that incorporates predictive sample size determination, early termination for inefficacy and efficacy, and the borrowing of information across strata. The borrowing of information is based on the similarity between the posterior distributions of the response probability. In general, Bayesian hierarchical models have many distributional assumptions along with multiple parameters. By contrast, our method has prior distributions for response probability and two parameters for similarity of distributions. The proposed design is easier to implement and less computationally demanding than other Bayesian basket designs. Through a simulation with various scenarios, our proposed design is compared with other designs including one that does not borrow information and one that uses a Bayesian hierarchical model.     

Development of a Drug-Response Modeling Framework to Identify Cell Line Derived Translational Biomarkers That Can Predict Treatment Outcome to Erlotinib or Sorafenib

Development of drug responsive biomarkers from pre-clinical data is a critical step in drug discovery, as it enables patient stratification in clinical trial design. Such translational biomarkers can be validated in early clinical trial phases and utilized as a patient inclusion parameter in later stage trials. Here we present a study on building accurate and selective drug sensitivity models for Erlotinib or Sorafenib from pre-clinical in vitro data, followed by validation of individual models on corresponding treatment arms from patient data generated in the BATTLE clinical trial. A Partial Least Squares Regression (PLSR) based modeling framework was designed and implemented, using a special splitting strategy and canonical pathways to capture robust information for model building. Erlotinib and Sorafenib predictive models could be used to identify a sub-group of patients that respond better to the corresponding treatment, and these models are specific to the corresponding drugs. The model derived signature genes reflect each drug’s known mechanism of action. Also, the models predict each drug’s potential cancer indications consistent with clinical trial results from a selection of globally normalized GEO expression datasets.     

Expression of hormone receptors predicts survival and platinum sensitivity of high-grade serous ovarian cancer

High-grade serous ovarian cancer (HGSOC) has abundant expression of hormone receptors, including androgen receptor (AR), estrogen receptor α (ER), and progesterone receptor (PR). The effects of hormone receptors on prognosis of HGSOC were first evaluated in online databases. Their prognostic values were then explored and validated in our inhouse TJ-cohort (92 HGSOC patients) and in a validation cohort (33 HGSOC patients), wherein hormone receptors were detected immunohistochemically. High expression of hormone receptors denoted longer progression-free survival (PFS), overall survival (OS), and platinum-free interval (PFI). Platinum-sensitive patients had higher expression of hormone receptors than their counterparts. Correlation analysis revealed significant positive correlations between hormone receptors expression and survival. AR, ER, and PR had predictive and prognostic values, alone and in combination. By receiver operating characteristic curve (ROC) analysis, co-expression of AR, ER, and PR had an improved predictive performance with an area under the curve (AUC) value of 0.945. Expression of hormone receptors predicts survival and platinum sensitivity of HGSOC. AR, ER, and PR might be feasible prognostic biomarkers for HGSOC by immunohistochemical analysis.     

Population-Enrichment Adaptive Design Strategy for an Event-Driven Vaccine Efficacy Trial

A population-enrichment adaptive design allows a prospective use for study population selection. It has the flexibility allowing pre-specified modifications to an ongoing trial to mitigate the potential risk associated with the assumptions made at design stage. In this way, the trial can potentially encompass a broader target patient population, and move forward only with the subpopulations that appear to be benefiting from the treatment. Our work is motivated by a Phase III event-driven vaccine efficacy trial. Two target patient subpopulations were enrolled with the assumption that vaccine efficacy can be demonstrated based on the combined population. It is recognized due to the nature of patients’ underlying conditions, one subpopulation might respond to the treatment better than the other. To maximize the probability of demonstrating vaccine efficacy in at least one patient population while taking advantage of combining two subpopulations in one single trial, an adaptive design strategy with potential population enrichment is developed. Specifically, if the observed vaccine efficacy at interim for one subpopulation is not promising to warrant carrying forward, the population may be enriched with the other subpopulation with better performance. Simulations were conducted to evaluate the operational characteristics from a selection of interim analysis plans. This population-enrichment design provides a more efficient way as compared to the conventional approaches when targeting multiple subpopulations. If executed and planned with caution, this strategy can provide a greater chance of success of the trial and help maintain scientific and regulatory rigors.