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A unified approach for analyzing exchangeable binary data with applications to developmental toxicity studies
Author(s) -
Dang Xin,
Keeton Stephine Lena,
Peng Hanxiang
Publication year - 2009
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3638
Subject(s) - binary data , computer science , developmental toxicity , binary number , statistics , mathematics , biology , arithmetic , genetics , pregnancy , gestation
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. Copyright © 2009 John Wiley & Sons, Ltd.