Sashegyi, Andreas Istvan2006-07-282006-07-2819981998http://hdl.handle.net/10012/272This thesis discusses several modelling approaches for the analysis of correlated binary data, as motivated by the results of a longitudinal school-based smoking prevention trial. In this study, WSPP3 - the third in a series called the Waterloo Smoking Prevention Projects, longitudinal observations were collected on a cohort of students, randomized to various study conditions in clusters defined by schools. An extension to the logistic-normal empirical Bayes random effects model is proposed, termed quasi empirical Bayes (QEB), which allows for the estimation of fixed effect model parameters, adjusting simultaneously for the effects of extraneous school-to-school variability as well as intra-individual correlation. A method of generating data with a composite correlation structure similar to that of the Smoking Prevention Projects data is developed; this is subsequently implemented in a simulation study to examine the properties of parameter estimates from the QEB model. We the n move into a discussion of the relationship between marginal or population-averaged models and cluster-specific models, and show that a straightforward modification of cluster-specific random effects models can be used to approximate a marginal correlation structure. With this approach one could for example determine easily whether or not the intra-school correlation in the WSPP3 data depends on school size. Our discussion focusses on the logistic-normal model in particular, with estimation in this case proceeding by maximum likelihood. Power considerations and the effects of model misspecification are addressed. Finally, we consider a general approach for testing the fit of models for correlated data. The emphasis here is on assessing how well a particular model captures the covariance structure of the data, assuming the mean is correctly specified. Some analytic results are given, as well as ones based on simulation,application/pdf8857548 bytesapplication/pdfenCopyright: 1998, Sashegyi, Andreas Istvan. All rights reserved.Harvested from Collections CanadaDoctoral Thesis