In this paper we propose a class of sequential urn designs based on Generalized Pòlya Urn (GPU) models for balancing the allocations of two treatments in sequential clinical trials. In particular, we consider a GPU model characterized by a 2 x 2 random addition matrix with null balance (i.e. null row sums) and replacement rule depending upon the urn composition. Under this scheme, the urn process has a Markovian structure and can be regarded as a random extension of the classical Ehrenfest model. We establish almost sure convergence and asymptotic normality for the frequency of treatment allocations and show that in some peculiar cases the asymptotic variance of the design admits a natural representation based on the set of orthogonal polynomials associated to the corresponding Markov process.
Generalized Pòlya Urn designs with null balance
GIANNERINI, SIMONE
2007-01-01
Abstract
In this paper we propose a class of sequential urn designs based on Generalized Pòlya Urn (GPU) models for balancing the allocations of two treatments in sequential clinical trials. In particular, we consider a GPU model characterized by a 2 x 2 random addition matrix with null balance (i.e. null row sums) and replacement rule depending upon the urn composition. Under this scheme, the urn process has a Markovian structure and can be regarded as a random extension of the classical Ehrenfest model. We establish almost sure convergence and asymptotic normality for the frequency of treatment allocations and show that in some peculiar cases the asymptotic variance of the design admits a natural representation based on the set of orthogonal polynomials associated to the corresponding Markov process.File | Dimensione | Formato | |
---|---|---|---|
JAP12193.pdf
non disponibili
Licenza:
Non pubblico
Dimensione
139.43 kB
Formato
Adobe PDF
|
139.43 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.