Sada Allo, Maider
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Sada Allo
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Maider
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Estadística, Informática y Matemáticas
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Publication Open Access Influence of the slope in percentile estimation through binary regression for dose-finding experiments(Taylor & Francis, 2024-12-04) Flournoy, Nancy; Moler Cuiral, José Antonio; Sada Allo, Maider; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaDose-finding experiments aim to estimate the dose having a specified proportion of positive responses by collecting data in the vicinity of this unknown target dose. The importance of estimating the slope as well as a target dose has been recognized long ago in the literature. With large slopes at the target dose, a small error in the target dose estimate will be far from the target. Alternatively, with small slopes at the target, a large error conveys negligible changes on the associated response rate. Thus a reasonably reliable estimate of the slope of the response function at the target dose should accompany every reported target dose estimate. Assuming a monotone increasing dose-response relationship, we work with a sizable catalogue of binary location-scale regression models parameterized by the target dose and the slope at the target. A compound design is proposed for the joint estimation of both features.Publication Open Access The K-in-a-row design as a semi-Markov process(2025) Flournoy, Nancy; Oron, Assaf; Moler Cuiral, José Antonio; Sada Allo, Maider; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaEstimating the value of a stimulus variable that has a prespecified percentage of successes is common in many fields, and known generally as “dose-finding”. In most practical applications, only a few values of the stimuli can be applied to the statistical units that participate in the experiment. K-in-a-Row Up-and-Down is a popular experimental procedure that sequentially allocates statistical units to the permissible values of a stimulus variable, using simple invariant rules. Despite having been in use for 60 years, K-in-a-Row’s statistical properties are still not broadly understood. We show that it is naturally modeled by a semi-Markov process, and as far as we know it is the first stochastic design to appear as such. The stationary distribution is characterized assuming only that the success probability increases with the values of the stimuli. We prove the strong unimodality of the asymptotic distribution of the proportions of stimuli specific allocations. Thus the mode of the stimuli-specific allocation serves as a summary measure of location for these designs, and we explicitly identify it. We also show how design parameters can be chosen to locate the stationary distribution over the percentile of interest.