Sequential monitoring of response-adaptive randomized clinical trials

Clinical trials are complex and usually involve multiple objectives such as controlling type I error rate, increasing power to detect treatment difference, assigning more patients to better treatment, and more. In literature, both response-adaptive randomization (RAR) procedures (by changing randomization procedure sequentially) and sequential monitoring (by changing analysis procedure sequentially) have been proposed to achieve these objectives to some degree. In this paper, we propose to sequentially monitor response-adaptive randomized clinical trial and study it's properties. We prove that the sequential test statistics of the new procedure converge to a Brownian motion in distribution. Further, we show that the sequential test statistics asymptotically satisfy the canonical joint distribution defined in Jennison and Turnbull (\citeyearJT00). Therefore, type I error and other objectives can be achieved theoretically by selecting appropriate boundaries. These results open a door to sequentially monitor response-adaptive randomized clinical trials in practice. We can also observe from the simulation studies that, the proposed procedure brings together the advantages of both techniques, in dealing with power, total sample size and total failure numbers, while keeps the type I error. In addition, we illustrate the characteristics of the proposed procedure by redesigning a well-known clinical trial of maternal-infant HIV transmission.Comment: Published in at http://dx.doi.org/10.1214/10-AOS796 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotics in randomized urn models

This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2,...,n-1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition and the patient allocation under general assumptions on random generating matrices which determine how balls are added to the urn. Also we obtain explicit forms of the asymptotic variance-covariance matrices of both the urn composition and the patient allocation. The conditions on the nonhomogeneity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed.Comment: Published at http://dx.doi.org/10.1214/105051604000000774 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient randomized-adaptive designs

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on Taylor expansions of the allocation probability functions, which do not apply to nondifferentiable cases. In the present paper, we study stopping times of stochastic processes to establish the asymptotic efficiency results. Furthermore, we demonstrate our proposal through examples, simulations and a discussion on the relationship with earlier works, including Efron's biased coin design.Comment: Published in at http://dx.doi.org/10.1214/08-AOS655 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic theorems of sequential estimation-adjusted urn models

The Generalized P\'{o}lya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum of applications. Because the proposed urn model depends on sequential estimations of unknown parameters, the derivation of asymptotic properties is mathematically intricate and the corresponding results are unavailable in the literature. We overcome these hurdles and establish the strong consistency and asymptotic normality for both the patient allocation and the estimators of unknown parameters, under some widely satisfied conditions. These properties are important for statistical inferences and they are also useful for the understanding of the urn limiting process. A superior feature of our proposed model is its capability to yield limiting treatment proportions according to any desired allocation target. The applicability of our model is illustrated with a number of examples.Comment: Published at http://dx.doi.org/10.1214/105051605000000746 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

carat: An R Package for Covariate-Adaptive Randomization in Clinical Trials

Covariate-adaptive randomization is gaining popularity in clinical trials because they enable the generation of balanced allocations with respect to covariates. Over the past decade, substantial progress has been made in both new innovative randomization procedures and the theoretical properties of associated inferences. However, these results are scattered across the literature, and a single tool kit does not exist for use by clinical trial practitioners and researchers to conduct and evaluate these methods. The R package carat is proposed to address this need. It facilitates a broad range of covariate-adaptive randomization and testing procedures, such as the most common and classical methods, and also reflects recent developments in the field. The package contains comprehensive evaluation and comparison tools for use in both randomization procedures and tests. This enables power analysis to be conducted to assist the planning of a covariate-adaptive clinical trial. The package also implements a command-line interface to allow for an interactive allocation procedure, which is typically the case in real-world applications. In this paper, the features and functionalities of carat are presented