Statistical Analysis On Exchangeable Binary Data

In many applications, it is reasonable to expect exchangeability to model the datafrom the same cluster. In fact, exchangeable binary data are commonly encounteredin cluster sample surveys, teratological experiments, ophthalmological and otolaryngologicstudies, and other clinical trials. This dissertation aims to propose some newstatistical methods for exchangeable binary data analysis.In order to solve the problem, we first present a general form of optimal unbiasedestimating equations and some results for the consistency and the asymptotic normalityof the solutions to general estimating equations. Then we present an iterative algorithmfor solving estimating equations in the presence of missing data. The algorithm iscalled the AU algorithm. It makes the computation very feasible and simple because ititerates between two steps: an A-step, in which the functions of the complete data arereplaced by the approximate values of their conditional expectations, and a U-step inwhich the parameters are updated using a closed-form expression. Theoretical resultsare obtained establishing convergence properties of the algorithm and the large sampleproperties of the estimators produced by the algorithm. Moreover, we give a generalform of the approximations of the conditional expectations in the A-step of the AUalgorithm.Based on the theories of estimating equations we have obtained, we use a pairwiselikelihood procedure to give a set of approximately optimal unbiased estimatingequations for estimating the mean and variance parameters for the exchangeable binarydata with random cluster sizes. An application to developmental toxicity data analysisis given. Simulation results show that our procedure performs better than the GEEprocedure for the exchangeable binary data.When the exchangeable binary data involve missing data, we combine the pairwiselikelihood procedure with the AU algorithm. An application is made to a data setfrom a reproductive toxicity study. Simulation results show that our method is valid and performs better than the complete-case analysis which ignores the subjects withmissing data.