Response-adaptive Randomization Procedures Research Articles

Group Response-Adaptive Randomization With Delayed and Missing Responses.

Response-adaptive randomization (RAR) procedures have been extensively studied in the literature, but most of the procedures rely on updating therandomization after each response, which is impractical in many clinical trials. In this article, we propose a new family of RAR procedures that dynamically update based on the responses of a group of individuals, either when available or at fixed time intervals (weekly or biweekly). We show that the proposed design retains the essential theoretical properties of Hu and Zhang's doubly adaptive biased coin designs (DBCD), and performs well in scenarios involving delayed and randomly missing responses. Numerical studies have been conducted to demonstrate that the new proposed group doubly adaptive biased coin design has similar properties to the Hu and Zhang's DBCDs in different situations. We also apply the new design to a real clinical trial, highlighting its advantages and practicality. Our findings open the door to studying the properties of other group response adaptive designs, such as urn models, and facilitate the application of response-adaptive randomized clinical trials in practice.

An alternative metric for evaluating the potential patient benefit of response-adaptive randomization procedures.

When planning a two-arm group sequential clinical trial with a binary primary outcome that has severe implications for quality of life (e.g., mortality), investigators may strive to find the design that maximizes in-trial patient benefit. In such cases, Bayesian response-adaptive randomization (BRAR) is often considered because it can alter the allocation ratio throughout the trial in favor of the treatment that is currently performing better. Although previous studies have recommended using fixed randomization over BRAR based on patient benefit metrics calculated from the realized trial sample size, these previous comparisons have been limited by failures to hold type I and II error rates constant across designs or consider the impacts on all individuals directly affected by the design choice. In this paper, we propose a metric for comparing designs with the same type I and II error rates that reflects expected outcomes among individuals who would participate in the trial if enrollment is open when they become eligible. We demonstrate how to use the proposed metric to guide the choice of design in the context of two recent trials in persons suffering out of hospital cardiac arrest. Using computer simulation, we demonstrate that various implementations of group sequential BRAR offer modest improvements with respect to the proposed metric relative to conventional group sequential monitoringalone.

Response‐adaptive treatment allocation for clinical studies with recurrent event and terminal event data

In long-term clinical studies, recurrent event data are frequently collected to contrast the efficacy of two different treatments. However, the recurrent event process can be stopped by a terminal event, such as death. For analyzing recurrent event and terminal event data, joint frailty modeling has recently received considerable attention because it makes it possible to study the joint evolution over time of both recurrent and terminal event processes and gives consistent and efficient parameters. For a two-arm clinical trial design based on these data sets, there has been limited research on investigating the balanced design, let alone adaptive treatment allocation. Although equal sample size allocation obtained for both treatments is intuitively first adopted in a trial design, if one treatment is expected to be superior, it may be desirable to allocate more subjects to the effective treatment. In this article, we calculate the required sample size based on restricted randomization and then propose a target response-adaptive randomization procedure for recurrent and terminal event outcomes based on the joint frailty model. A randomization procedure, the doubly adaptive biased coin design that targets some optimal allocations, is implemented. The proposed adaptive treatment allocation schemes have been shown to be capable of reducing the number of trial participants who receive inferior treatment while simultaneously reaching an optimal target, as well as retaining a comparable test power as compared to a restricted randomization design. Finally, two clinical studies, the COAPT trial and the A-HeFT trial, are used to illustrate the advantages of adopting the proposed procedure.

Compound optimal allocations for survival clinical trials.

The aim of the present paper is to provide optimal allocations for comparative clinical trials with survival outcomes. The suggested targets are derived adopting a compound optimization strategy based on a subjective weighting of the relative importance of inferential demands and ethical concerns. The ensuing compound optimal targets are continuous functions of the treatment effects, so we provide the conditions under which they can be approached by standard response-adaptive randomization procedures, also guaranteeing the applicability of the classical asymptotic inference. The operating characteristics of the suggested methodology are verified both theoretically and by simulation, including the robustness to model misspecification. With respect to the other available proposals, our strategy always assigns more patients to the best treatment without compromising inference, taking into account estimation efficiency and power as well. We illustrate our procedure by redesigning two real oncologicaltrials.

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes.

We propose a novel response‐adaptive randomization procedure for multi‐armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non‐myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response‐adaptive algorithm based on the Gittins index for the multi‐armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969‐978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi‐armed setting, there are efficiency and patient benefit gains of using a response‐adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response‐adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi‐armed trial context.

Response adaptive randomization procedures in seamless phase II/III clinical trials

ABSTRACTIt is desirable to work efficiently and cost effectively to evaluate new therapies in a time-sensitive and ethical manner without compromising the integrity and validity of the development process. The seamless phase II/III clinical trial has been proposed to meet this need, and its efficient, ethical and economic advantages can be strengthened by its combination with innovative response adaptive randomization (RAR) procedures. In particular, well-designed frequentist RAR procedures can target theoretically optimal allocation proportions, and there are explicit asymptotic results. However, there has been little research into seamless phase II/III clinical trials with frequentist RAR because of the difficulty in performing valid statistical inference and controlling the type I error rate. In this paper, we propose the framework for a family of frequentist RAR designs for seamless phase II/III trials, derive the asymptotic distribution of the parameter estimators using martingale processes and offer solutions to control the type I error rate. The numerical studies demonstrate our theoretical findings and the advantages of the proposed methods.

Optimal designs for testing hypothesis in multiarm clinical trials.

The present paper deals with the problem of designing randomized multiarm clinical trials for treatment comparisons in order to achieve a suitable trade-off among inferential precision and ethical concerns. Although the large majority of the literature is focused on the estimation of the treatment effects, in particular for the case of two treatments with binary outcomes, the present paper takes into account the inferential goal of maximizing the power of statistical tests to detect correct conclusions about the treatment effects for normally response trials. After discussing the allocation optimizing the power of the classical multivariate test of homogeneity, we suggest a multipurpose design methodology, based on constrained optimization, which maximizes the power of the test under a suitable ethical constraint reflecting the effectiveness of the treatments. The ensuing optimal allocation depends in general on the unknown model parameters but, contrary to the unconstrained optimal solution or to some targets proposed in the literature, it is a non-degenerate continuous function of the treatment contrasts, and therefore it can be approached by standard response-adaptive randomization procedures. The properties of this constrained optimal allocation are described both theoretically and through suitable examples, showing good performances both in terms of ethical gain and statistical efficiency, taking into account estimation precision as well.

Nonparametric response-adaptive randomization for continuous responses.

Many response-adaptive randomization procedures have been proposed and studied over the past few decades. However, most of these procedures are based on parametric structure and do not directly apply to nonparametric models. In this paper, we propose a response-adaptive randomization procedure based on Mann-Whitney U test statistic. Under widely satisfied conditions, we derive asymptotic properties of the randomization procedure and further obtain power functions in form under Mann-Whitney U test. Simulations show the proposed procedure is more robust and more ethical than classical response-adaptive randomization procedures in some circumstances. Advantages of the procedure are also illustrated in a redesigned real clinical trial.

A class of Covariate-Adjusted Response-Adaptive Allocation Designs for Multitreatment Binary Response Trials

ABSTRACTA class of covariate-adjusted response-adaptive randomization procedures is developed for binary treatment outcomes in a phase III clinical trial set up involving multiple treatments. The target allocation is developed by combining the ethical aspects with statistical precision under the existence of treatment covariate interaction. Relevant measures of the performance for the proposed allocation designs are studied and compared.

Statistical inference for response adaptive randomization procedures with adjusted optimal allocation proportions

ABSTRACTSeamless phase II/III clinical trials have attracted increasing attention recently. They mainly use Bayesian response adaptive randomization (RAR) designs. There has been little research into seamless clinical trials using frequentist RAR designs because of the difficulty in performing valid statistical inference following this procedure. The well-designed frequentist RAR designs can target theoretically optimal allocation proportions, and they have explicit asymptotic results. In this paper, we study the asymptotic properties of frequentist RAR designs with adjusted target allocation proportions, and investigate statistical inference for this procedure. The properties of the proposed design provide an important theoretical foundation for advanced seamless clinical trials. Our numerical studies demonstrate that the design is ethical and efficient.

Implementing optimal allocation in clinical trials with multiple endpoints

Modern clinical trials are often complex, with multiple competing objectives and multiple endpoints. Such trials should be both ethical and efficient. In this paper, we overcome the obstacles introduced by the large number of unknown parameters and the possible correlations between the multiple endpoints. We obtain the optimal allocation proportions for the following two optimization problems: (1) maximizing the power of the test of homogeneity with a fixed sample size, and (2) minimizing the expected weighted number of failures with a fixed power. Further, we implement these optimal allocations through response-adaptive randomization procedures. Our theoretical results provide the foundation for the implementation and further investigation of the procedure, and our numerical studies demonstrate its ability to achieve diverse objectives.

A Bayesian response-adaptive trial in tuberculosis: The endTB trial.

To evaluate the use of Bayesian adaptive randomization for clinical trials of new treatments for multidrug-resistant tuberculosis. We built a response-adaptive randomization procedure, adapting on two preliminary outcomes for tuberculosis patients in a trial with five experimental regimens and a control arm. The primary study outcome is treatment success after 73 weeks from randomization; preliminary responses are culture conversion at 8 weeks and treatment success at 39 weeks. We compared the adaptive randomization design with balanced randomization using hypothetical scenarios. When we compare the statistical power under adaptive randomization and non-adaptive designs, under several hypothetical scenarios we observe that adaptive randomization requires fewer patients than non-adaptive designs. Moreover, adaptive randomization consistently allocates more participants to effective arm(s). We also show that these advantages are limited to scenarios consistent with the assumptions used to develop the adaptive randomization algorithm. Given the objective of evaluating several new therapeutic regimens in a timely fashion, Bayesian response-adaptive designs are attractive for tuberculosis trials. This approach tends to increase allocation to the effective regimens.

Randomization tests in recursive response-adaptive randomization procedures

In a randomized clinical trial, response-adaptive randomization procedures use the information gathered, including the previous patients' responses, to allocate the next patient. In this setting, we consider randomization-based inference. We provide an algorithm to obtain exact p-values for statistical tests that compare two treatments with dichotomous responses. This algorithm can be applied to a family of response adaptive randomization procedures which share the following property: the distribution of the allocation rule depends only on the imbalance between treatments and on the imbalance between successes for treatments 1 and 2 in the previous step. This family includes some outstanding response adaptive randomization procedures. We study a randomization test to contrast the null hypothesis of equivalence of treatments and we show that this test has a similar performance to that of its parametric counterpart. Besides, we study the effect of a covariate in the inferential process. First, we obtain a parametric test, constructed assuming a logit model which relates responses to treatments and covariate levels, and we give conditions that guarantee its asymptotic normality. Finally, we show that the randomization test, which is free of model specification, performs as well as the parametric test that takes the covariate into account.

Start-up designs for response-adaptive randomization procedures with sequential estimation.

Response-adaptive randomization procedures are appropriate for clinical trials in which two or more treatments are to be compared, patients arrive sequentially and the response of each patient is recorded before the next patient arrives. However, for those procedures that involve sequential estimation of model parameters, start-up designs are commonly required in order to provide initial estimates of the parameters. In this paper, a suite of such start-up designs for two treatments and binary patient responses are considered and compared in terms of the numbers of patients required in order to give meaningful parameters estimates, the number of patients allocated to the better treatment, and the bias in the parameter estimates. It is shown that permuted block designs with blocks of size 4 are to be preferred over a wide range of parameter values. For the case of two treatments, normal responses and selected start-up procedures, a design incorporating complete randomization followed appropriately by repeats of one of the treatments yields the minimum expected number of patients and is to be preferred.

RARtool: A MATLAB Software Package for Designing Response-Adaptive Randomized Clinical Trials with Time-to-Event Outcomes.

Response-adaptive randomization designs are becoming increasingly popular in clinical trial practice. In this paper, we present RARtool, a user interface software developed in MATLAB for designing response-adaptive randomized comparative clinical trials with censored time-to-event outcomes. The RARtool software can compute different types of optimal treatment allocation designs, and it can simulate response-adaptive randomization procedures targeting selected optimal allocations. Through simulations, an investigator can assess design characteristics under a variety of experimental scenarios and select the best procedure for practical implementation. We illustrate the utility of our RARtool software by redesigning a survival trial from the literature.

Multi-treatment covariate-adjusted adaptive design under informative censoring

In the present work, we find a set of reliability functionals to fix up an allocation strategy among K(≥2) treatments when the response distributions, conditionally dependent on some continuous prognostic variable, are exponential with unknown linear regression functions as the means of the respective conditional distributions. Targeting such reliability functionals, we propose a covariate-adjusted response-adaptive randomization procedure for the multi-treatment single-period clinical trial under the Koziol–Green model for informative censoring. We compare the proposed procedure with its competitive covariate-eliminated procedure.

On Recent Advances in Optimal Allocation Designs in Clinical Trials

One of the fundamental questions in the design of clinical trials is how to optimally allocate treatments to study subjects to achieve selected experimental objectives. In this article we review major recent methodological advances in optimal allocation for clinical trials. A literature review shows that starting from the 2000s many new allocation methods have been proposed to enhance the design of multiobjective and multiarm clinical trials. These allocation designs can provide improvements over traditional balanced allocation designs both in terms of statistical efficiency and ethical criteria. We also discuss state-of-the art response-adaptive randomization procedures for implementing optimal allocation designs in practice.

Response Adaptive Designs with Misclassified Responses

We consider response adaptive designs when the binary response may be misclassified and extend relevant results in the literature. We derive the optimal allocations under various objectives and examine the relationship between the power of statistical test and the variability of treatment allocation. Asymptotically best response adaptive randomization procedures and effects of misclassification on the optimal allocations are investigated. A real-life clinical trial is also discussed to illustrate our proposed approach.

Longitudinal covariate-adjusted response-adaptive randomized designs

Clinical trials often involve longitudinal data set which has two important characteristics: repeated and correlated measurements and time-varying covariates. In this paper, we propose a general framework of longitudinal covariate-adjusted response-adaptive (LCARA) randomization procedures. We study their properties under widely satisfied conditions. This design skews the allocation probabilities which depend on both patients' first observed covariates and sequentially estimated parameters based on the accrued longitudinal responses and covariates. The asymptotic properties of estimators for the unknown parameters and allocation proportions are established. The special case of binary treatment and continuous responses is studied in detail. Simulation studies and an analysis of the National Cooperative Gallstone Study (NCGS) data are carried out to illustrate the advantages of the proposed LCARA randomization procedure.

A Graphical Comparison of Response-Adaptive Randomization Procedures

Response-adaptive randomization procedures have a dual goal of estimating the treatment effect and randomizing patients with a higher probability of receiving the superior treatment. These are competing objectives, and no procedure in the literature is “perfect” with respect to both objectives. For clinical trials of two treatments, we discuss metrics for comparing response-adaptive randomization procedures that can be represented graphically to compare designs. These metrics involve the simulated distribution of the set of jointly sufficient statistics for estimating functions of the unknown parameters. We explore the binary response and normal cases, and compare numerous procedures found in the literature. We distinguish between metrics of efficiency and metrics that measure ethical cost. Each of these is a function of the joint sufficient statistics. When graphed against each other, we can gauge competing designs in obtaining these competing objectives. We find that, contrary to asymptotic results, tuning parameters that affect the variability of the procedure do not have much impact in the finite case. In the binary response case, we find that procedures that target an optimal allocation based on ethical and efficiency considerations generally provide a better compromise design than procedures that do not. In the normal response case, a randomly reinforced urn tends to provide a good compromise procedure.