Bayesian inference for correlated binary data with an application to diabetes complication progression.

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dc.contributor.advisor Seaman, John Weldon, 1956- Carlin, Patricia M.
dc.contributor.other Baylor University. Dept. of Statistical Sciences. en 2006-08
dc.description.abstract Correlated binary measurements can occur in a variety of practical contexts and afford interesting statistical modeling challenges. In order to model the separate probabilities for each measurement we must somehow account for the relationship between them. We choose to focus our applications to the progression of the complications of diabetic retinopathy and diabetic nephropathy. We first consider probabilistic models which employ Bayes' theorem for predicting the probability of onset of diabetic nephropathy given that a patient has developed diabetic retinopathy, modifying the work of Ballone, Colagrande, Di Nicola, Di Mascio, Di Mascio, and Capani (2003). We consider beta-binomial models using the Sarmanov (1966) framework which allows us to specify the marginal distributions for a given bivariate likelihood. We present both maximum likelihood and Bayesian methods based on this approach. Our Bayesian methods include a fully identified model based on proportional probabilities of disease incidence. Finally, we consider Bayesian models for three different prior structures using likelihoods representing the data in the form of a 2-by-2 table. To do so, we consider the data as counts resulting from two correlated binary measurements: the onset of diabetic retinopathy and the onset of diabetic nephropathy. We compare resulting posterior distributions from a Jeffreys' prior, independent beta priors, and conditional beta priors, based on a structural zero likelihood model and the bivariate binomial model. en
dc.rights Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact for inquiries about permission. en
dc.subject Bayesian statistical decision theory. en
dc.subject Diabetic nephropathies. en
dc.subject Diabetic retinopathy. en
dc.title Bayesian inference for correlated binary data with an application to diabetes complication progression. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Baylor University access only en
dc.contributor.department Statistical Sciences. en

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