title: A unified approach for analyzing exchangeable binary data with applications to developmental toxicity studies.
abstract: In this article, we present a general procedure to analyze exchangeable binary data that may also be viewed as realizations of binomial mixtures. Our approach unifies existing models and is practical and computationally easy. Resulting from completely monotonic functions, we introduce a rich family of parametric parsimonious binomial mixtures, including the incomplete Beta-, Gamma-, Normal-, and Poisson-binomial, generalizing the Beta-binomial. We show that the family is closed under convex linear combinations, products, and composites. We also give the moments and the Markov property of the family. With such distributions, we can perform statistical inference on correlated binary data and, in particular, overdispersed data. We propose a regression procedure that generalizes logistic regression. We provide a forward model selection procedure. We run a small simulation to validate the inclusion of the binomial distribution. Finally, we apply the proposed procedure to analyze the 2, 4, 5-Trichlorophenoxyacetic acid and E2 data and compare the results with existing procedures.
authors: Department of Mathematics, University of Mississippi, MS 38677, USA.
authors: Xin
authors: X
authors: Dang
authors: Stephine Lena
authors: SL
authors: Keeton
authors: Hanxiang
authors: H
authors: Peng
mesh_terms: D015085:2,4,5-Trichlorophenoxyacetic Acid / Q000009:adverse effects; D000014:Abnormalities, Drug-Induced; D000465:Algorithms; D000818:Animals; D016010:Binomial Distribution; D003198:Computer Simulation; D064420:Drug-Related Side Effects and Adverse Reactions / Q000196:embryology*; D005313:Fetal Death; D016013:Likelihood Functions; D008390:Markov Chains; D051379:Mice; D015233:Models, Statistical; D012044:Regression Analysis
chemical_list: D015085:2,4,5-Trichlorophenoxyacetic Acid