In February 2010, the U.S. Food and Drug Administration (FDA, 2010) drafted guidance that discusses the statistical, clinical, and regulatory aspects of various adaptive designs for clinical trials. An important class of adaptive designs is adaptive randomization, which is considered very briefly in subsection VI.B of the guidance. The objective of this paper is to review several important new classes of adaptive randomization procedures and convey information on the recent developments in the literature on this topic. Much of this literature has been focused on the development of methodology to address past criticisms and concerns that have hindered the broader use of adaptive randomization. We conclude that adaptive randomization is a very broad area of experimental design that has important application in modern clinical trials.

Adaptive randomization for clinical trials.

Urn models have been widely studied and applied in both scientific and social science disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has been proved to be beneficial to both researchers, by providing more efficient clinical trials, and patients, by increasing the likelihood of receiving the better treatment. In this paper, we propose a new and general class of immigrated urn (IMU) models that incorporates the immigration mechanism into the urn process. Theoretical properties are developed and the advantages of the IMU models are discussed. In general, the IMU models have smaller variabilities than the classical urn models, yielding more powerful statistical inferences in applications. 
Illustrative examples are presented to demonstrate the wide applicability of the IMU models. The proposed IMU framework, including many popular classical urn models, not only offers a unify perspective for us to comprehend the urn process, but also enables us to generate several novel urn models with desirable properties.

Immigrated urn models - asymptotic properties and applications

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.

On Recent Advances in Optimal Allocation Designs in Clinical Trials

It is often important to incorporating covariate information in the design of clinical trials. In literature, there are many designs of using stratification and covariate-adaptive randomization to balance on certain known covariate. Recently Zhang, Hu, Cheung and Chan (2007) have proposed a family of covariate-adjusted response-adaptive (CARA) designs and studied their asymptotic properties. However, these CARA designs often have high variabilities. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs. We show that the new designs have smaller variabilities and therefore more efficient.

A New Family of Covariate-Adjusted Response Adaptive Designs and their Asymptotic Properties

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 feasible or ethically objectionable. In this paper we discuss and address a major criticism of RAR: the undesirable type I error inflation due to unknown time trends in the trial. Time trends can appear because of changes in the characteristics of recruited patients - so-called "patient drift". Patient drift is a realistic concern for clinical trials in rare diseases because these typically recruit patients over a very long period of time. We compute by simulations how large the type I error inflation is as a function of the time trend magnitude in order to determine in which contexts a potentially costly correction is actually necessary. We then assess the ability of different correction methods to preserve type I error in this context and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations of which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the two-armed and the multi-armed case. We further propose a RAR design for multi-armed clinical trials, which is computationally cheap and robust to several time trends considered.

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

A fundamental question in response–adaptive randomization is: What allocation proportion should we target to achieve required power while resulting in fewer treatment failures? For comparing two treatments, such optimal allocations are well studied in the literature. However, few authors address the question for multiple treatments and the generalization of optimal allocations is necessary in practice. We are interested in finding the optimal allocation proportion, which achieves a required power of a multivariate test of homogeneity in binary response experiments while minimizing expected treatment failures at the same time. We propose such an optimal allocation for three treatments by giving an analytical solution for the optimization problem. Numerical studies show that a response–adaptive randomization procedure that targets proposed optimal allocation is superior to complete randomization. We also discuss some future research topics and additional issues on optimal adaptive designs.

Youngsook Jeon

Papers

Optimal Adaptive Designs for Binary Response Trials With Three Treatments