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Generalized Pólya urn Designs with Null Balance

  • Alessandro Baldi Antognini (a1) and Simone Giannerini (a1)

Abstract

In this paper we propose a class of sequential urn designs based on generalized Pólya 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 with the corresponding Markov process.

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Copyright

Corresponding author

Postal address: Dipartimento di Scienze Statistiche, Via delle Belle Arti 41, Bologna 40126, Italy.
∗∗ Email address: giannerini@stat.unibo.it

References

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