Time-to-event analysis with treatment arm selection at interim

This paper discusses the application of an adaptive design for treatment arm selection in an oncology trial, with survival as the primary endpoint and disease progression as a key secondary endpoint. We carried out treatment arm selection at an interim analysis by using Bayesian predictive power combining evidence from the two endpoints. At the final analysis, we carried out a frequentist statistical test of efficacy on the survival endpoint. We investigated several approaches (Bonferroni approach, 'Dunnett-like' approach, a conditional error function approach and a combination p-value approach) with respect to their power and the precise conditions under which type I error control is attained.     

Evidence synthesis from aggregate recurrent event data for clinical trial design and analysis

Information from historical trials is important for the design, interim monitoring, analysis, and interpretation of clinical trials. Meta‐analytic models can be used to synthesize the evidence from historical data, which are often only available in aggregate form. We consider evidence synthesis methods for trials with recurrent event endpoints, which are common in many therapeutic areas. Such endpoints are typically analyzed by negative binomial regression. However, the individual patient data necessary to fit such a model are usually unavailable for historical trials reported in the medical literature. We describe approaches for back‐calculating model parameter estimates and their standard errors from available summary statistics with various techniques, including approximate Bayesian computation. We propose to use a quadratic approximation to the log‐likelihood for each historical trial based on 2 independent terms for the log mean rate and the log of the dispersion parameter. A Bayesian hierarchical meta‐analysis model then provides the posterior predictive distribution for these parameters. Simulations show this approach with back‐calculated parameter estimates results in very similar inference as using parameter estimates from individual patient data as an input. We illustrate how to design and analyze a new randomized placebo‐controlled exacerbation trial in severe eosinophilic asthma using data from 11 historical trials.     

Standard versus adaptive monitoring procedures: A commentary

In the standard approach to designing definitive clinical trials, the primary endpoint and test statistic to be used for the primary analysis are specified before trial initiation. The false positive error rate for the null hypothesis and statistical power to detect the targeted size of treatment effect are also specified. Standard monitoring procedures, such as the group sequential guidelines, enable interim monitoring while maintaining the integrity of this approach. In contrast, adaptive monitoring procedures seek to provide flexibility to modify these pre-specified design features during the course of the trial. However, these procedures have several undesirable properties, including lesser statistical efficiency, reduced interpretability of primary outcome results, basing design changes on unreliable interim estimates of efficacy, risks to the integrity and credibility of the trial, loss of flexibility to use emerging results from external sources to alter key design features, and overemphasis of the importance of statistical significance relative to clinical significance.     

Evaluating futility of a binary clinical endpoint using early read-outs

Interim analyses are routinely used to monitor accumulating data in clinical trials. When the objective of the interim analysis is to stop the trial if the trial is deemed futile, it must ideally be conducted as early as possible. In trials where the clinical endpoint of interest is only observed after a long follow-up, many enrolled patients may therefore have no information on the primary endpoint available at the time of the interim analysis. To facilitate earlier decision-making, one may incorporate early response data that are predictive for the primary endpoint (eg, an assessment of the primary endpoint at an earlier time) in the interim analysis. Most attention so far has been given to the development of interim test statistics that include such short-term endpoints, but not to decision procedures. Existing tests moreover perform poorly when the information is scarce, eg, due to rare events, when the cohort of patients with observed primary endpoint data is small, or when the short-term endpoint is a strong but imperfect predictor. In view of this, we develop an interim decision procedure based on the conditional power approach that utilizes the short-term and long-term binary endpoints in a framework that is expected to provide reliable inferences, even when the primary endpoint is only available for a few patients, and has the added advantage that it allows the use of historical information. The operational characteristics of the proposed procedure are evaluated for the phase III clinical trial that motivated this approach, using simulation studies.     

Frequentist operating characteristics of Bayesian optimal designs via simulation

Bayesian adaptive designs have become popular because of the possibility of increasing the number of patients treated with more beneficial treatments, while still providing sufficient evidence for treatment efficacy comparisons. It can be essential, for regulatory and other purposes, to conduct frequentist analyses both before and after a Bayesian adaptive trial, and these remain challenging. In this paper, we propose a general simulation-based approach to compare frequentist designs with Bayesian adaptive designs based on frequentist criteria such as power and to compute valid frequentist p-values. We illustrate our approach by comparing the power of an equal randomization (ER) design with that of an optimal Bayesian adaptive (OBA) design. The Bayesian design considered here is the dynamic programming solution of the optimization of a specific utility function defined by the number of successes in a patient horizon, including patients whose treatment will be affected by the trial's results after the end of the trial. While the power of an ER design depends on treatment efficacy and the sample size, the power of the OBA design also depends on the patient horizon size. Our results quantify the trade-off between power and the optimal assignment of patients to treatments within the trial. We show that, for large patient horizons, the two criteria are in agreement, while for small horizons, differences can be substantial. This has implications for precision medicine, where patient horizons are decreasing as a result of increasing stratification of patients into subpopulations defined by molecular markers.     

Stopping rules and estimation problems in clinical trials

Stopping rules in clinical trials can lead to bias in point estimation of the magnitude of treatment difference. A simulation exercise, based on estimation of the risk ratio in a typical post-myocardial infarction trial, examines the nature of this exaggeration of treatment effect under various group sequential plans and also under continuous naive monitoring for statistical significance. For a fixed treatment effect the median bias in group sequential design is small, but it is greatest for effects that the trial has reasonable power to detect. Bias is evidently greater in trials that stop early and is dramatic under naive monitoring for significance. Group sequential plans lead to a multimodal sampling distribution of treatment effect, which poses problems for incorporating their estimates into meta-analyses. By simulating a population of trials with treatment effects modelled by an underlying distribution of true risk ratios, a Bayesian method is proposed for assessing the plausible range of true treatment effect for any trial based on interim results. This approach is particularly useful for producing shrinkage of the unexpectedly large and imprecise observed treatment effects that arise in clinical trials that stop early. Its implications for trial design are discussed.     

Bayesian predictive power for interim adaptation in seamless phase II/III trials where the endpoint is survival up to some specified timepoint

Integration of a phase II and a phase III clinical trial into a single confirmatory study aims to shorten the development time without compromising the chance of success for a development program. These seamless phase II/III trials involve complex adaptations at the interim analysis, such as treatment selection, sample size reassessment, and stopping for futility. Bayesian methods can support these interim adaptations, and make this decision process more transparent. Use of a frequentist combination test for the final evaluation ensures that the type I error is controlled regardless of the adaptation rule employed at the interim analysis. In this paper, an adaptive seamless phase II/III trial design is proposed for studies where the endpoint is survival up to some specified timepoint and where Bayesian predictive power (PP) guides interim adaptations. For the evaluation of PP at the interim analysis, the event time is modelled as a piecewise exponential distribution, with informative priors for the hazard rates. As an illustrative example, regimen selection at interim in a four-arm trial with an active control is considered, where both non-inferiority and superiority to the control arm are tested. Frequentist properties of the adaptation criterion based on Bayesian PP are assessed by simulations.     

A sequential procedure for monitoring clinical trials against historical controls

In this paper, we develop a sequential procedure to monitor clinical trials against historical controls. When there is a strong ethical concern about randomizing patients to existing treatment because biological and medical evidence suggests that the new treatment is potentially superior to the existing one, or when the enrollment is too limited for randomization of subjects into experimental and control groups, one can monitor the trial sequentially against historical controls if the historical data with required quality and sample size are available to form a valid reference for the trial. This design of trial is sometimes the only alternative to a randomized phase III trial design that is intended but not feasible in situations such as above. Monitoring this type of clinical trial leads to a statistical problem of comparing two population means in a situation in which data from one population are sequentially collected and compared with all data from the other population at each interim look. The proposed sequential procedures is based on the sequential conditional probability ratio test (SCPRT) by which the conclusion of the sequential test would be virtually the same as that arrived at by a non-sequential test based on all data at the planned end of the trial. We develop the sequential procedure by proposing a Brownian motion that emulates the test statistic, and then proposing an SCPRT that is adapted to the special properties of the trial.     

Performance of adaptive sample size adjustment with respect to stopping criteria and time of interim analysis

The benefit of adjusting the sample size in clinical trials on the basis of treatment effects observed in interim analysis has been the subject of several recent papers. Different conclusions were drawn about the usefulness of this approach for gaining power or saving sample size, because of differences in trial design and setting. We examined the benefit of sample size adjustment in relation to trial design parameters such as 'time of interim analysis' and 'choice of stopping criteria'. We compared the adaptive weighted inverse normal method with classical group sequential methods for the most common and for optimal stopping criteria in early, half-time and late interim analyses. We found that reacting to interim data might significantly reduce average sample size in some situations, while classical approaches can out-perform the adaptive designs under other circumstances. We characterized these situations with respect to time of interim analysis and choice of stopping criteria.     

A Bayesian design for phase II clinical trials with delayed responses based on multiple imputation

Interim monitoring is routinely conducted in phase II clinical trials to terminate the trial early if the experimental treatment is futile. Interim monitoring requires that patients’ responses be ascertained shortly after the initiation of treatment so that the outcomes are known by the time the interim decision must be made. However, in some cases, response outcomes require a long time to be assessed, which causes difficulties for interim monitoring. To address this issue, we propose a Bayesian trial design to allow for continuously monitoring phase II clinical trials in the presence of delayed responses. We treat the delayed responses as missing data and handle them using a multiple imputation approach. Extensive simulations show that the proposed design yields desirable operating characteristics under various settings and dramatically reduces the trial duration. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayesian adaptive dose selection procedure with an overdispersed count endpoint

Adaptive trial designs can considerably improve upon traditional designs, by modifying design aspects of the ongoing trial, like early stopping, adding, or dropping doses, or changing the sample size. In the present work, we propose a two‐stage Bayesian adaptive design for a Phase IIb study aimed at selecting the lowest effective dose for Phase III. In this setting, efficacy has been proved for a high dose in a Phase IIa proof‐of‐concept study, but the existence of a lower but still effective dose is investigated before the scheduled Phase III starts. In the first stage, we randomize patients to placebo, maximal tolerated dose, and one or more additional doses within the dose range. Based on an interim analysis, we either stop the study for futility or success or continue the study to the second stage, where newly recruited patients are allocated to placebo, some fairly high dose, and one additional dose chosen based on interim data. At the interim analysis, we use the criteria based on the predictive probability of success to decide on whether to stop or to continue the trial and, in the latter case, which dose to select for the second stage. Finally, we will select a dose as lowest effective dose for Phase III either at the end of the first stage or at the end of the second stage. We evaluate the operating characteristics of the procedure via simulations and present the results for several scenarios, comparing the performance of the proposed procedure to those of the non‐adaptive design. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian leveraging of historical control data for a clinical trial with time-to-event endpoint

The recent 21st Century Cures Act propagates innovations to accelerate the discovery, development, and delivery of 21st century cures. It includes the broader application of Bayesian statistics and the use of evidence from clinical expertise. An example of the latter is the use of trial-external (or historical) data, which promises more efficient or ethical trial designs. We propose a Bayesian meta-analytic approach to leverage historical data for time-to-event endpoints, which are common in oncology and cardiovascular diseases. The approach is based on a robust hierarchical model for piecewise exponential data. It allows for various degrees of between trial-heterogeneity and for leveraging individual as well as aggregate data. An ovarian carcinoma trial and a non-small cell cancer trial illustrate methodological and practical aspects of leveraging historical data for the analysis and design of time-to-event trials.     

A two-stage Bayesian design for co-development of new drugs and companion diagnostics

Most new drug development in oncology is based on targeting specific molecules. Genomic profiles and deregulated drug targets vary from patient to patient making new treatments likely to benefit only a subset of patients traditionally grouped in the same clinical trials. Predictive biomarkers are being developed to identify patients who are most likely to benefit from a particular treatment; however, their biological basis is not always conclusive. The inclusion of marker-negative patients in a trial is therefore sometimes necessary for a more informative evaluation of the therapy. In this paper, we present a two-stage Bayesian design that includes both marker-positive and marker-negative patients in a clinical trial. We formulate a family of prior distributions that represent the degree of a priori confidence in the predictive biomarker. To avoid exposing patients to a treatment to which they may not be expected to benefit, we perform an interim analysis that may stop accrual of marker-negative patients or accrual of all patients. We demonstrate with simulations that the design and priors used control type I errors, give adequate power, and enable the early futility analysis of test-negative patients to be based on prior specification on the strength of evidence in the biomarker.     

Exploring the benefits of adaptive sequential designs in time-to-event endpoint settings

Sequential analysis is frequently employed to address ethical and financial issues in clinical trials. Sequential analysis may be performed using standard group sequential designs, or, more recently, with adaptive designs that use estimates of treatment effect to modify the maximal statistical information to be collected. In the general setting in which statistical information and clinical trial costs are functions of the number of subjects used, it has yet to be established whether there is any major efficiency advantage to adaptive designs over traditional group sequential designs. In survival analysis, however, statistical information (and hence efficiency) is most closely related to the observed number of events, while trial costs still depend on the number of patients accrued. As the number of subjects may dominate the cost of a trial, an adaptive design that specifies a reduced maximal possible sample size when an extreme treatment effect has been observed may allow early termination of accrual and therefore a more cost-efficient trial. We investigate and compare the tradeoffs between efficiency (as measured by average number of observed events required), power, and cost (a function of the number of subjects accrued and length of observation) for standard group sequential methods and an adaptive design that allows for early termination of accrual. We find that when certain trial design parameters are constrained, an adaptive approach to terminating subject accrual may improve upon the cost efficiency of a group sequential clinical trial investigating time-to-event endpoints. However, when the spectrum of group sequential designs considered is broadened, the advantage of the adaptive designs is less clear.     

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.     

Bayesian sequential meta‐analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program

Recently, the Center for Drug Evaluation and Research at the Food and Drug Administration released a guidance that makes recommendations about how to demonstrate that a new antidiabetic therapy to treat type 2 diabetes is not associated with an unacceptable increase in cardiovascular risk. One of the recommendations from the guidance is that phases II and III trials should be appropriately designed and conducted so that a meta‐analysis can be performed. In addition, the guidance implies that a sequential meta‐analysis strategy could be adopted. That is, the initial meta‐analysis could aim at demonstrating the upper bound of a 95% confidence interval (CI) for the estimated hazard ratio to be < 1.8 for the purpose of enabling a new drug application or a biologics license application. Subsequently after the marketing authorization, a final meta‐analysis would need to show the upper bound to be < 1.3. In this context, we develop a new Bayesian sequential meta‐analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for sequential meta‐analysis clinical trial design with a focus on controlling the familywise type I error rate and power. We use the partial borrowing power prior to incorporate the historical survival meta‐data into the Bayesian design. We examine various properties of the proposed methodology, and simulation‐based computational algorithms are developed to generate predictive data at various interim analyses, sample from the posterior distributions, and compute various quantities such as the power and the type I error in the Bayesian sequential meta‐analysis trial design. We apply the proposed methodology to the design of a hypothetical antidiabetic drug development program for evaluating cardiovascular risk. Copyright © 2013 John Wiley & Sons, Ltd.     

ComPAS: A Bayesian drug combination platform trial design with adaptive shrinkage

Combining different treatment regimens provides an effective approach to induce a synergistic treatment effect and overcome resistance to monotherapy. The challenge is that, given the large number of existing monotherapies, the number of possible combinations is huge and new potentially more efficacious compounds may become available any time during drug development. To address this challenge, we propose a flexible Bayesian drug combination platform design with adaptive shrinkage (ComPAS), which allows for dropping futile combinations, graduating effective combinations, and adding new combinations during the course of the trial. A new adaptive shrinkage method is developed to adaptively borrow information across combinations and efficiently identify the efficacious combinations based on Bayesian model selection and hierarchical models. Simulation studies show that ComPAS identifies the effective combinations with higher probability than some existing designs. ComPAS provides an efficient and flexible platform to accelerate drug development in a seamless and timely fashion.     

Bayesian adaptive model selection for optimizing group sequential clinical trials

This article presents a new approach to the problem of deriving an optimal design for a randomized group sequential clinical trial based on right-censored event times. We are motivated by the fact that, if the proportional hazards assumption is not met, then a conventional design's actual power can differ substantially from its nominal value. We combine Bayesian decision theory, Bayesian model selection and forward simulation (FS) to obtain a group sequential procedure that maintains targeted false-positive rate and power, under a wide range of true event time distributions. At each interim analysis, the method adaptively chooses the most likely model and then applies the decision bounds that are optimal under the chosen model. A simulation study comparing this design with three conventional designs shows that, over a wide range of distributions, our proposed method performs at least as well as each conventional design, and in many cases it provides a much smaller trial.     

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 general statistical principle for changing a design any time during the course of a trial

A general method is presented that allows the researcher to change statistical design elements such as the residual sample size during the course of an experiment, to include an interim analysis for early stopping when no formal rule for early stopping was foreseen, to increase or reduce the number of planned interim analyses, to change time points and the type I error spending function for the further design of interim analyses, or to change the test statistic, the outcome measure, etc. At the time of a pre-planned interim analysis for early stopping or at any time of an interim look without spending part of the type I error level the method offers the option to completely redesign the remaining part of the trial, without affecting the type I error level. The method is described in the usual Brownian motion model and extended to the general context of statistical decision functions. It is based on the conditional rejection probability of a decision variable.