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Nonparametric bayes testing of changes in a response distribution with an ordinal predictor.

Pennell ML, Dunson DB

Division of Biostatistics, College of Public Health, The Ohio State University, B-115 Starling-Loving Hall, 320 West 10th Avenue, Columbus, Ohio 43210, USA. mpennell@cph.osu.edu

In certain biomedical studies, one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor. For instance, in toxicology studies, skewness and modality might change as dose increases. To address this issue, we propose a Bayesian nonparametric method for testing for distribution changes across an ordinal predictor. Using a dynamic mixture of Dirichlet processes, we allow the response distribution to change flexibly at each level of the predictor. In addition, by assigning mixture priors to the hyperparameters, we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution. The method also provides a natural framework for performing tests across multiple outcomes. We apply our method to data from a genotoxicity experiment.

Published 16 May 2008 in Biometrics, 64(2): 413-23.
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