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Abstract:
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Urn models are useful when randomization is important. Treatments assignments correspond to the color of a drawn ball. If balls are added or taken away depending on outcomes, the urn is said to be response-driven. Much work has focused on replacement procedures that increase the chances of allocating better treatments. The Randomized Reinforcement Urn (RRU) is optimal in the sense that it assigns patients to the best treatment with probability converging to one. No other urn model in the literature has this property. For binary random variables, this urn was studied by Durham, Flournoy and Li (1998). However, the allocation proportions degenerate to 0 or 1 (or to a random variable if treatments are equal ) and theory that permits testing for treatment differences has only just been obtained (May and Flournoy, manuscript 2006). I will describe the general RRU and its application.
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