In the design of experiments, urn models have been widely used as randomization devices to allocate subjects to treatments and incorporate ethical constraints. We propose a new adaptive randomly reinforced urn design, in a clinical trial context. The design consists of a randomly reinforced urn wherein a sequential allocation of patients to treatments is performed and the associated responses are collected. The model is based on two stochastic sequences representing random and time-dependent thresholds for the urn proportion process. These thresholds are defined as functions of the estimators of unknown parameters modeling the response distributions, so that they change any time a new response is collected. First and second-order asymptotic results under different conditions have been investigated. Specifically, we present the limit, the rate of convergence and the asymptotic distribution of the proportion of subjects assigned to the treatments.

Ghiglietti, A. (2016). Asymptotic Properties of an Adaptive Randomly Reinforced Urn model. In mODa 11 - Advances in Model-Oriented Design and Analysis - Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016 (pp.113-121). DEU : Springer International Publishing Switzerland [10.1007/978-3-319-31266-8_14].

Asymptotic Properties of an Adaptive Randomly Reinforced Urn Model

Ghiglietti, A
2016

Abstract

In the design of experiments, urn models have been widely used as randomization devices to allocate subjects to treatments and incorporate ethical constraints. We propose a new adaptive randomly reinforced urn design, in a clinical trial context. The design consists of a randomly reinforced urn wherein a sequential allocation of patients to treatments is performed and the associated responses are collected. The model is based on two stochastic sequences representing random and time-dependent thresholds for the urn proportion process. These thresholds are defined as functions of the estimators of unknown parameters modeling the response distributions, so that they change any time a new response is collected. First and second-order asymptotic results under different conditions have been investigated. Specifically, we present the limit, the rate of convergence and the asymptotic distribution of the proportion of subjects assigned to the treatments.
No
paper
Scientifica
2-COLOR; DESIGNS; ALLOCATIONS
English
11th International Workshop on Model-Oriented Design and Analysis - JUN 12-17, 2016
978-3-319-31264-4
http://www.springer.com/us/book/9783319312644
Ghiglietti, A. (2016). Asymptotic Properties of an Adaptive Randomly Reinforced Urn model. In mODa 11 - Advances in Model-Oriented Design and Analysis - Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016 (pp.113-121). DEU : Springer International Publishing Switzerland [10.1007/978-3-319-31266-8_14].
Ghiglietti, A
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/391735
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
Social impact