Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

Critical appraisal of Bayesian dynamic borrowing from an imperfectly commensurate historical control

Bayesian dynamic borrowing designs facilitate borrowing information from historical studies. Historical data, when perfectly commensurate with current data, have been shown to reduce the trial duration and the sample size, while inflation in the type I error and reduction in the power have been reported, when imperfectly commensurate. These results, however, were obtained without considering that Bayesian designs are calibrated to meet regulatory requirements in practice and even no‐borrowing designs may use information from historical data in the calibration. The implicit borrowing of historical data suggests that imperfectly commensurate historical data may similarly impact no‐borrowing designs negatively. We will provide a fair appraiser of Bayesian dynamic borrowing and no‐borrowing designs. We used a published selective adaptive randomization design and real clinical trial setting and conducted simulation studies under varying degrees of imperfectly commensurate historical control scenarios. The type I error was inflated under the null scenario of no intervention effect, while larger inflation was noted with borrowing. The larger inflation in type I error under the null setting can be offset by the greater probability to stop early correctly under the alternative. Response rates were estimated more precisely and the average sample size was smaller with borrowing. The expected increase in bias with borrowing was noted, but was negligible. Using Bayesian dynamic borrowing designs may improve trial efficiency by stopping trials early correctly and reducing trial length at the small cost of inflated type I error.     

Blinded sample size re‐estimation in crossover bioequivalence trials

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re‐estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re‐estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre‐specified level. Furthermore, some refinements of the re‐estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive designs for single‐arm phase II trials in oncology

Clinical phase II trials in oncology are conducted to determine whether the activity of a new anticancer treatment is promising enough to merit further investigation. Two‐stage designs are commonly used for this situation to allow for early termination. Designs proposed in the literature so far have the common drawback that the sample sizes for the two stages have to be specified in the protocol and have to be adhered to strictly during the course of the trial. As a consequence, designs that allow a higher extent of flexibility are desirable. In this article, we propose a new adaptive method that allows an arbitrary modification of the sample size of the second stage using the results of the interim analysis or external information while controlling the type I error rate. If the sample size is not changed during the trial, the proposed design shows very similar characteristics to the optimal two‐stage design proposed by Chang et al. (Biometrics 1987; 43:865–874). However, the new design allows the use of mid‐course information for the planning of the second stage, thus meeting practical requirements when performing clinical phase II trials in oncology. Copyright © 2012 John Wiley & Sons, Ltd.     

Vaccine clinical trials with dynamic borrowing of historical controls: Two retrospective studies

Traditional vaccine efficacy trials usually use fixed designs with fairly large sample sizes. Recruiting a large number of subjects requires longer time and higher costs. Furthermore, vaccine developers are more than ever facing the need to accelerate vaccine development to fulfill the public's medical needs. A possible approach to accelerate development is to use the method of dynamic borrowing of historical controls in clinical trials. In this paper, we evaluate the feasibility and the performance of this approach in vaccine development by retrospectively analyzing two real vaccine studies: a relatively small immunological trial (typical early phase study) and a large vaccine efficacy trial (typical Phase 3 study) assessing prophylactic human papillomavirus vaccine. Results are promising, particularly for early development immunological studies, where the adaptive design is feasible, and control of type I error is less relevant.     

Group sequential designs using both type I and type II error probability spending functions

We propose flexible group sequential designs using type I and type II error probability spending functions. The proposed designs preserve the overall significance level and power and allow the repeated testing to be perloimed at a flexible schedule. Computational methods are described. An example on a mega clinical trial is provided.     

Curtailed two-stage designs with two dependent binary endpoints

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs.     

Adaptive graph‐based multiple testing procedures

Multiple testing procedures defined by directed, weighted graphs have recently been proposed as an intuitive visual tool for constructing multiple testing strategies that reflect the often complex contextual relations between hypotheses in clinical trials. Many well‐known sequentially rejective tests, such as (parallel) gatekeeping tests or hierarchical testing procedures are special cases of the graph based tests. We generalize these graph‐based multiple testing procedures to adaptive trial designs with an interim analysis. These designs permit mid‐trial design modifications based on unblinded interim data as well as external information, while providing strong family wise error rate control. To maintain the familywise error rate, it is not required to prespecify the adaption rule in detail. Because the adaptive test does not require knowledge of the multivariate distribution of test statistics, it is applicable in a wide range of scenarios including trials with multiple treatment comparisons, endpoints or subgroups, or combinations thereof. Examples of adaptations are dropping of treatment arms, selection of subpopulations, and sample size reassessment. If, in the interim analysis, it is decided to continue the trial as planned, the adaptive test reduces to the originally planned multiple testing procedure. Only if adaptations are actually implemented, an adjusted test needs to be applied. The procedure is illustrated with a case study and its operating characteristics are investigated by simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimizing trial design in pharmacogenetics research: comparing a fixed parallel group,group sequential,and adaptive selection design on sample size requirements

Two‐stage clinical trial designs may be efficient in pharmacogenetics research when there is some but inconclusive evidence of effect modification by a genomic marker. Two‐stage designs allow to stop early for efficacy or futility and can offer the additional opportunity to enrich the study population to a specific patient subgroup after an interim analysis. This study compared sample size requirements for fixed parallel group, group sequential, and adaptive selection designs with equal overall power and control of the family‐wise type I error rate. The designs were evaluated across scenarios that defined the effect sizes in the marker positive and marker negative subgroups and the prevalence of marker positive patients in the overall study population. Effect sizes were chosen to reflect realistic planning scenarios, where at least some effect is present in the marker negative subgroup. In addition, scenarios were considered in which the assumed ‘true’ subgroup effects (i.e., the postulated effects) differed from those hypothesized at the planning stage. As expected, both two‐stage designs generally required fewer patients than a fixed parallel group design, and the advantage increased as the difference between subgroups increased. The adaptive selection design added little further reduction in sample size, as compared with the group sequential design, when the postulated effect sizes were equal to those hypothesized at the planning stage. However, when the postulated effects deviated strongly in favor of enrichment, the comparative advantage of the adaptive selection design increased, which precisely reflects the adaptive nature of the design. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiplicity and flexibility in clinical trials

Flexible designs offer a large amount of flexibility in clinical trials with control of the type I error rate. This allows the combination of trials from different clinical phases of a drug development process. Such combinations require designs where hypotheses are selected and/or added at interim analysis without knowing the selection rule in advance so that both flexibility and multiplicity issues arise. The paper reviews the basic principles and some of the common methods for reaching flexibility while controlling the family-wise error rate in the strong sense. Flexible designs have been criticized because they may lead to different weights for the patients from the different stages when reassessing sample sizes. Analyzing the data in a conventional way avoids such unequal weighting but may inflate the multiple type I error rate. In cases where the conditional type I error rates of the new design (and conventional analysis) are below the conditional type I error rates of the initial design the conventional analysis may, however, be done without inflating the type I error rate. Focusing on a parallel group design with two treatments and a common control, we use this principle to investigate when we can select one treatment, reassess sample sizes and test the corresponding null hypotheses by the conventional level alpha z-test without compromising on the multiple type I error rate.     

On the practical application of mixed effects models for repeated measures to clinical trial data

The use of mixed effects models for repeated measures (MMRM) for clinical trial analyses has recently gained broad support as a primary analysis methodology. Some questions of practical implementation detail remain, however. For example, whether and how to incorporate clinical trial data that is collected at nonprotocol‐specified timepoints or clinic visits has not been systematically studied. In this paper, we compare different methods for applying MMRM to trials wherein data is available at protocol‐specified timepoints, as well as nonprotocol‐specified timepoints due to patient early discontinuation. The methods under consideration included observed case MMRM, per protocol visits MMRM, interval last observation carried forward (LOCF) MMRM, and a hybrid of the per protocol visits and interval LOCF MMRM approaches. Simulation results reveal that the method that best controls the type I error rate is the per protocol visits method. This method is also associated with the least precision among the competing methods. Thus, in confirmatory clinical trials wherein control of type I error rates is critical, per protocol visits MMRM is recommended. However, in exploratory trials where strict type I error control is not as critical, one may prefer interval LOCF MMRM due to its increased precision. Points to consider with respect to both study design (e.g., assigning schedule of events) and subsequent analysis are offered. Copyright © 2012 John Wiley & Sons, Ltd.     

Some practical issues of adaptive GPU design

We study some practical applications in clinical trial of the adaptive optimal generalized Pólya urn (GPU) design we recently proposed. We considered some common cases in clinical trial: delayed response, staggered/censored entry, heterogeneity and longitudinal/repeated observation. Asymptotic properties of these designs are studied.     

Multiple-objective response-adaptive repeated measurement designs for clinical trials

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achieve a specific goal. Response-adaptive designs for clinical trials are usually constructed to achieve a single objective. In this paper, we develop a new adaptive allocation rule to improve current strategies for building response-adaptive designs to construct multiple-objective repeated measurement designs. This new rule is designed to increase estimation precision and treatment benefit by assigning more patients to a better treatment sequence. We demonstrate that designs constructed under the new proposed allocation rule can be nearly as efficient as fixed optimal designs in terms of the mean squared error, while leading to improved patient care.     

Improving interim decisions in randomized trials by exploiting information on short‐term endpoints and prognostic baseline covariates

Conditional power calculations are frequently used to guide the decision whether or not to stop a trial for futility or to modify planned sample size. These ignore the information in short‐term endpoints and baseline covariates, and thereby do not make fully efficient use of the information in the data. We therefore propose an interim decision procedure based on the conditional power approach which exploits the information contained in baseline covariates and short‐term endpoints. We will realize this by considering the estimation of the treatment effect at the interim analysis as a missing data problem. This problem is addressed by employing specific prediction models for the long‐term endpoint which enable the incorporation of baseline covariates and multiple short‐term endpoints. We show that the proposed procedure leads to an efficiency gain and a reduced sample size, without compromising the Type I error rate of the procedure, even when the adopted prediction models are misspecified. In particular, implementing our proposal in the conditional power approach enables earlier decisions relative to standard approaches, whilst controlling the probability of an incorrect decision. This time gain results in a lower expected number of recruited patients in case of stopping for futility, such that fewer patients receive the futile regimen. We explain how these methods can be used in adaptive designs with unblinded sample size re‐assessment based on the inverse normal P‐value combination method to control Type I error. We support the proposal by Monte Carlo simulations based on data from a real clinical trial.     

An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

Bayesian hierarchical models for adaptive basket trial designs

Basket trials evaluate a single drug targeting a single genetic variant in multiple cancer cohorts. Empirical findings suggest that treatment efficacy across baskets may be heterogeneous. Most modern basket trial designs use Bayesian methods. These methods require the prior specification of at least one parameter that permits information sharing across baskets. In this study, we provide recommendations for selecting a prior for scale parameters for adaptive basket trials by using Bayesian hierarchical modeling. Heterogeneity among baskets attracts much attention in basket trial research, and substantial heterogeneity challenges the basic assumption of exchangeability of Bayesian hierarchical approach. Thus, we also allowed each stratum-specific parameter to be exchangeable or nonexchangeable with similar strata by using data observed in an interim analysis. Through a simulation study, we evaluated the overall performance of our design based on statistical power and type I error rates. Our research contributes to the understanding of the properties of Bayesian basket trial designs.     

Type I error rate control in adaptive designs for confirmatory clinical trials with treatment selection at interim

Interest in confirmatory adaptive combined phase II/III studies with treatment selection has increased in the past few years. These studies start comparing several treatments with a control. One (or more) treatment(s) is then selected after the first stage based on the available information at an interim analysis, including interim data from the ongoing trial, external information and expert knowledge. Recruitment continues, but now only for the selected treatment(s) and the control, possibly in combination with a sample size reassessment. The final analysis of the selected treatment(s) includes the patients from both stages and is performed such that the overall Type I error rate is strictly controlled, thus providing confirmatory evidence of efficacy at the final analysis. In this paper we describe two approaches to control the Type I error rate in adaptive designs with sample size reassessment and/or treatment selection. The first method adjusts the critical value using a simulation-based approach, which incorporates the number of patients at an interim analysis, the true response rates, the treatment selection rule, etc. We discuss the underlying assumptions of simulation-based procedures and give several examples where the Type I error rate is not controlled if some of the assumptions are violated. The second method is an adaptive Bonferroni-Holm test procedure based on conditional error rates of the individual treatment-control comparisons. We show that this procedure controls the Type I error rate, even if a deviation from a pre-planned adaptation rule or the time point of such a decision is necessary.     

An approach to use of an adaptive procedure to clinical trials for molecularly heterogenous subject selection at interim

Abstract

For clinical trials, molecular heterogeneity has played a more important role recently. Many novel clinical trial designs prospectively incorporate molecular information to evaluation of treatment effects. In this paper, an adaptive procedure incorporating a non-pre-specified genomic biomarker is employed in the interim of a conventional trial. A non-pre-specified binary genomic biomarker, which is predictive of treatment effect, is used to classify study patients into two mutually exclusive subgroups at the interim review. According to the observations at the interim stage, adaptations such as adjusting sample size or shifting eligibility of study patients are then made in case of different scenarios.     

Nested combination tests with a time‐to‐event endpoint using a short‐term endpoint for design adaptations

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family‐wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short‐term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short‐term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics.