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Abstract:
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Dependent or correlated binary data occur in experimental studies such as teratological risk assessment. Groups of correlated responses are often called clusters, and the response of interest is the number of affected units in a cluster. The simplest statistical model for binary outcomes is binomial distribution, which assumes individuals to be iid. However, assumptions of the binomial distribution are often violated. Both parametric (such as beta-binomial, q-power) and non-parametric (exchangeable binary) models have been proposed to model distribution of the number of affected individuals over several treatment groups. We propose a semi-parametric model that combines a non-parametric baseline describing the within-cluster dependence structure with a parametric between-group effect. The proposed model avoids making parametric assumptions about higher-order dependence, but is more parsimonious than non-parametric models. We fit the semi-parametric model with an Expectation Minimization Minorize-Maximize algorithm to some real datasets, and compare the semi-parametric estimates of joint probabilities from different dose levels with corresponding GEE and non-parametric estimates.
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