Immigrated urn models—theoretical properties and applications

Abstract

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.1 imsart-aos ver.

RARtool: AMATLABSoftware Package for Designing Response-Adaptive Randomized Clinical Trials with Time-to-Event Outcomes

“…There are two types of optimal RAR procedures with established statistical properties that can be used for this purpose: the doubly-adaptive biased coin design (DBCD; Hu and Zhang 2004) and optimal RAR designs based on urn models (Zhang, Hu, Cheung, and Chan 2011). In our software development we implement the former approach.…”

Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design

“…The drop-the-loser allocation-rule, introduced in Ivanova (2003), is outstanding among them; see Atkinson and Biswas (2014). Asymptotic results for this rule under a population model are obtained in Zhang et al (2011), but in the context of randomization-based inference (RBI), where responses are considered fixed, this procedure becomes quite difficult to handle; see Flournoy, Galbete et al (2013). In Galbete et al (2014) the Klein allocation-rule, that is, the Klein urn design-was introduced and its properties were thoroughly studied under the assumption of a population model; it was also proved that the drop-the-loser rule and the Klein allocation rule behave asymptotically in the same way and share the same performance characteristics.…”

“…Several asymptotical tools have been developed to make statistical inference when patients are allocated with adaptive rules; see, for instance, Rosenberger et al (1997), Bélisle and Melfi (2007), Hu and Zhang (2004), and Zhang et al (2011). These tools rely heavily on the hypothesis that a population model is valid; that is, they assume that the whole target population is available for the experiment, that patients' responses to treatments follow a probability distribution with some unknown parameter, and that patients are randomly chosen to participate in the experiment.…”

Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns

“…In the long history of the development of adaptive designs, urn models have remained an influential and popular family of response adaptive-randomization procedures ever since Wei and Durham [33] proposed the randomized play-the-winner rule. Recently, Zhang et al [35] unified the most classical urn models into a general family of urn models (the immigrated urn (IMU) models) 586 L.-X. ZHANG ET AL.…”