Structured approach to the elicitation of expert beliefs for a Bayesian‐designed clinical trial: a case study

To quantify uncertainty in a formal manner, statisticians play a vital role in identifying a prior distribution for a Bayesian‐designed clinical trial. However, when expert beliefs are to be used to form the prior, the literature is sparse on how feasible and how reliable it is to elicit beliefs from experts. For late‐stage clinical trials, high importance is placed on reliability; however, feasibility may be equally important in early‐stage trials. This article describes a case study to assess how feasible it is to conduct an elicitation session in a structured manner and to form a probability distribution that would be used in a hypothetical early‐stage trial. The case study revealed that by using a structured approach to planning, training and conduct, it is feasible to elicit expert beliefs and form a probability distribution in a timely manner. We argue that by further increasing the published accounts of elicitation of expert beliefs in drug development, there will be increased confidence in the feasibility of conducting elicitation sessions. Furthermore, this will lead to wider dissemination of the pertinent issues on how to quantify uncertainty to both practicing statisticians and others involved with designing trials in a Bayesian manner. Copyright © 2013 John Wiley & Sons, Ltd.     

Applications of Bayesian statistical methodology to clinical trial design: A case study of a phase 2 trial with an interim futility assessment in patients with knee osteoarthritis

Development of new pharmacological treatments for osteoarthritis that address unmet medical needs in a competitive market place is challenging. Bayesian approaches to trial design offer advantages in defining treatment benefits by addressing clinically relevant magnitude of effects relative to comparators and in optimizing efficiency in analysis. Such advantages are illustrated by a motivating case study, a proof of concept, and dose finding study in patients with osteoarthritis. Patients with osteoarthritis were randomized to receive placebo, celecoxib, or 1 of 4 doses of galcanezumab. Primary outcome measure was change from baseline WOMAC pain after 8 weeks of treatment. Literature review of clinical trials with targeted comparator therapies quantified treatment effects versus placebo. Two success criteria were defined: one to address superiority to placebo with adequate precision and another to ensure a clinically relevant treatment effect. Trial simulations used a Bayesian dose response and longitudinal model. An interim analysis for futility was incorporated. Simulations indicated the study had ≥85% power to detect a 14‐mm improvement and ≤1% risk for a placebo‐like drug to pass. The addition of the second success criterion substantially reduced the risk of an inadequate, weakly efficacious drug proceeding to future development. The study was terminated at the interim analysis due to inadequate analgesic efficacy. A Bayesian approach using probabilistic statements enables clear understanding of success criteria, leading to informed decisions for study conduct. Incorporating an interim analysis can effectively reduce sample size, save resources, and minimize exposure of patients to an inadequate treatment.     

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta‐analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study‐to‐study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide‐induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the “3Rs initiative” to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd.     

A COMPARISON OF THE IMPRECISE BETA CLASS, THE RANDOMIZED PLAY-THE-WINNER RULE AND THE TRIANGULAR TEST FOR CLINICAL TRIALS WITH BINARY RESPONSES

This paper develops clinical trial designs that compare two treatments with a binary outcome. The imprecise beta class (IBC), a class of beta probability distributions, is used in a robust Bayesian framework to calculate posterior upper and lower expectations for treatment success rates using accumulating data. The posterior expectation for the difference in success rates can be used to decide when there is sufficient evidence for randomized treatment allocation to cease. This design is formally related to the randomized play‐the‐winner (RPW) design, an adaptive allocation scheme where randomization probabilities are updated sequentially to favour the treatment with the higher observed success rate. A connection is also made between the IBC and the sequential clinical trial design based on the triangular test. Theoretical and simulation results are presented to show that the expected sample sizes on the truly inferior arm are lower using the IBC compared with either the triangular test or the RPW design, and that the IBC performs well against established criteria involving error rates and the expected number of treatment failures.     

Leveraging historical data into oncology development programs: Two case studies of phase 2 Bayesian augmented control trial designs

Leveraging historical data into the design and analysis of phase 2 randomized controlled trials can improve efficiency of drug development programs. Such approaches can reduce sample size without loss of power. Potential issues arise when the current control arm is inconsistent with historical data, which may lead to biased estimates of treatment efficacy, loss of power, or inflated type 1 error. Consideration as to how to borrow historical information is important, and in particular, adjustment for prognostic factors should be considered. This paper will illustrate two motivating case studies of oncology Bayesian augmented control (BAC) trials. In the first example, a glioblastoma study, an informative prior was used for the control arm hazard rate. Sample size savings were 15% to 20% by using a BAC design. In the second example, a pancreatic cancer study, a hierarchical model borrowing method was used, which enabled the extent of borrowing to be determined by consistency of observed study data with historical studies. Supporting Bayesian analyses also adjusted for prognostic factors. Incorporating historical data via Bayesian trial design can provide sample size savings, reduce study duration, and enable a more scientific approach to development of novel therapies by avoiding excess recruitment to a control arm. Various sensitivity analyses are necessary to interpret results. Current industry efforts for data transparency have meaningful implications for access to patient‐level historical data, which, while not critical, is helpful to adjust for potential imbalances in prognostic factors.     

Decision‐making in a phase II clinical trial: a new approach combining Bayesian and frequentist concepts

The aim of a phase II clinical trial is to decide whether or not to develop an experimental therapy further through phase III clinical evaluation. In this paper, we present a Bayesian approach to the phase II trial, although we assume that subsequent phase III clinical trials will have standard frequentist analyses. The decision whether to conduct the phase III trial is based on the posterior predictive probability of a significant result being obtained. This fusion of Bayesian and frequentist techniques accepts the current paradigm for expressing objective evidence of therapeutic value, while optimizing the form of the phase II investigation that leads to it. By using prior information, we can assess whether a phase II study is needed at all, and how much or what sort of evidence is required. The proposed approach is illustrated by the design of a phase II clinical trial of a multi‐drug resistance modulator used in combination with standard chemotherapy in the treatment of metastatic breast cancer. Copyright © 2005 John Wiley & Sons, Ltd     

Sample size re‐estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter–based sample size re‐estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta‐analytic‐predictive approach. To incorporate external information into the sample size re‐estimation, we propose to update the meta‐analytic‐predictive prior based on the results of the internal pilot study and to re‐estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re‐estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior‐data conflict is present, incorporating external information into the sample size re‐estimation improves the operating characteristics compared to the traditional approach. In the case of a prior‐data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re‐estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re‐estimation, the potential gains should be balanced against the risks.     

Effect of reporting bias in the analysis of spontaneous reporting data

It is well‐known that a spontaneous reporting system suffers from significant under‐reporting of adverse drug reactions from the source population. The existing methods do not adjust for such under‐reporting for the calculation of measures of association between a drug and the adverse drug reaction under study. Often there is direct and/or indirect information on the reporting probabilities. This work incorporates the reporting probabilities into existing methodologies, specifically to Bayesian confidence propagation neural network and DuMouchel's empirical Bayesian methods, and shows how the two methods lead to biased results in the presence of under‐reporting. Considering all the cases to be reported, the association measure for the source population can be estimated by using only exposure information through a reference sample from the source population. Copyright © 2014 John Wiley & Sons, Ltd.     

Case study in the Bayesian analysis of a cost‐effectiveness trial in the evaluation of health care technologies: Depression

We present a case study based on a depression study that will illustrate the use of Bayesian statistics in the economic evaluation of cost‐effectiveness data, demonstrate the benefits of the Bayesian approach (whilst honestly recognizing any deficiencies) with respect to frequentist methods, and provide details of using the methods, including computer code where appropriate. Copyright © 2003 John Wiley & Sons, Ltd.     

Bayesian sample size determination for phase IIA clinical trials using historical data and semi‐parametric prior's elicitation

The Simon's two‐stage design is the most commonly applied among multi‐stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre‐trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two‐stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B‐splines. The motivating example is the planning of the phase IIA two‐stage trial on anti‐HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.     

Decision‐making in early clinical drug development

This paper illustrates an approach to setting the decision framework for a study in early clinical drug development. It shows how the criteria for a go and a stop decision are calculated based on pre‐specified target and lower reference values. The framework can lead to a three‐outcome approach by including a consider zone; this could enable smaller studies to be performed in early development, with other information either external to or within the study used to reach a go or stop decision. In this way, Phase I/II trials can be geared towards providing actionable decision‐making rather than the traditional focus on statistical significance. The example provided illustrates how the decision criteria were calculated for a Phase II study, including an interim analysis, and how the operating characteristics were assessed to ensure the decision criteria were robust. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian single-arm phase II trial designs with time-to-event endpoints

For the cancer clinical trials with immunotherapy and molecularly targeted therapy, time-to-event endpoint is often a desired endpoint. In this paper, we present an event-driven approach for Bayesian one-stage and two-stage single-arm phase II trial designs. Two versions of Bayesian one-stage designs were proposed with executable algorithms and meanwhile, we also develop theoretical relationships between the frequentist and Bayesian designs. These findings help investigators who want to design a trial using Bayesian approach have an explicit understanding of how the frequentist properties can be achieved. Moreover, the proposed Bayesian designs using the exact posterior distributions accommodate the single-arm phase II trials with small sample sizes. We also proposed an optimal two-stage approach, which can be regarded as an extension of Simon's two-stage design with the time-to-event endpoint. Comprehensive simulations were conducted to explore the frequentist properties of the proposed Bayesian designs and an R package BayesDesign can be assessed via R CRAN for convenient use of the proposed methods.     

Outcome-adaptive allocation with natural lead-in for three-group trials with binary outcomes

ABSTRACT

Just as Bayes extensions of the frequentist optimal allocation design have been developed for the two-group case, we provide a Bayes extension of optimal allocation in the three-group case. We use the optimal allocations derived by Jeon and Hu [Optimal adaptive designs for binary response trials with three treatments. Statist Biopharm Res. 2010;2(3):310–318] and estimate success probabilities for each treatment arm using a Bayes estimator. We also introduce a natural lead-in design that allows adaptation to begin as early in the trial as possible. Simulation studies show that the Bayesian adaptive designs simultaneously increase the power and expected number of successfully treated patients compared to the balanced design. And compared to the standard adaptive design, the natural lead-in design introduced in this study produces a higher expected number of successes whilst preserving power.     

On Parametric Bootstrapping and Bayesian Prediction

Abstract.  We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback–Leibler divergence. Finally, we give some examples.     

Estimation of the intensity function of an inhomogeneous Poisson process with a change‐point

Recent work on point processes includes studying posterior convergence rates of estimating a continuous intensity function. In this article, convergence rates for estimating the intensity function and change‐point are derived for the more general case of a piecewise continuous intensity function. We study the problem of estimating the intensity function of an inhomogeneous Poisson process with a change‐point using non‐parametric Bayesian methods. An Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain estimates of the intensity function and the change‐point which is illustrated using simulation studies and applications. The Canadian Journal of Statistics 47: 604–618; 2019 © 2019 Statistical Society of Canada     

Bayesian Binomial Regression: Predicting Survival at a Trauma Center

Standard methods for analyzing binomial regression data rely on asymptotic inferences. Bayesian methods can be performed using simple computations, and they apply for any sample size. We provide a relatively complete discussion of Bayesian inferences for binomial regression with emphasis on inferences for the probability of “success.” Furthermore, we illustrate diagnostic tools, perform model selection among nonnested models, and examine the sensitivity of the Bayesian methods.     

Bayesian adaptive linearization method for phase I drug combination trials with dimension reduction

Many phase I drug combination designs have been proposed to find the maximum tolerated combination (MTC). Due to the two‐dimension nature of drug combination trials, these designs typically require complicated statistical modeling and estimation, which limit their use in practice. In this article, we propose an easy‐to‐implement Bayesian phase I combination design, called Bayesian adaptive linearization method (BALM), to simplify the dose finding for drug combination trials. BALM takes the dimension reduction approach. It selects a subset of combinations, through a procedure called linearization, to convert the two‐dimensional dose matrix into a string of combinations that are fully ordered in toxicity. As a result, existing single‐agent dose‐finding methods can be directly used to find the MTC. In case that the selected linear path does not contain the MTC, a dose‐insertion procedure is performed to add new doses whose expected toxicity rate is equal to the target toxicity rate. Our simulation studies show that the proposed BALM design performs better than competing, more complicated combination designs.     

Decision‐making in drug development using a composite definition of success

Evidence‐based quantitative methodologies have been proposed to inform decision‐making in drug development, such as metrics to make go/no‐go decisions or predictions of success, identified with statistical significance of future clinical trials. While these methodologies appropriately address some critical questions on the potential of a drug, they either consider the past evidence without predicting the outcome of the future trials or focus only on efficacy, failing to account for the multifaceted aspects of a successful drug development. As quantitative benefit‐risk assessments could enhance decision‐making, we propose a more comprehensive approach using a composite definition of success based not only on the statistical significance of the treatment effect on the primary endpoint but also on its clinical relevance and on a favorable benefit‐risk balance in the next pivotal studies. For one drug, we can thus study several development strategies before starting the pivotal trials by comparing their predictive probability of success. The predictions are based on the available evidence from the previous trials, to which new hypotheses on the future development could be added. The resulting predictive probability of composite success provides a useful summary to support the discussions of the decision‐makers. We present a fictive, but realistic, example in major depressive disorder inspired by a real decision‐making case.