Statistical Inference For Correlated Binary Data From Bilateral Studies

In some medical comparative studies, outcomes are bilateral and dichoto-mous. Inference can be made by either treating subject as the fundamental unitor treating the paired outcomes as independent and ignoring the intra-class corre-lation information. The latter strategy is usually easier but may lead to inappro-priate or wrong conclusions when correlation really exists. Taking the correlationinto account can reduce variability and make comparison more precise. In mythesis, we base our statistical inference assuming that there is correlation in thebilateral binary data. In Chapter 2, we consider testing equality of the correla-tions of two paired binary responses from two treatment groups. Several statisticsfor testing the equality of correlations and sample size formulae for a two-armrandomized clinical trial are developed. Simulations are performed to evaluatethe behaviors of various tests and the accuracy of di?erent sample size formu-lae in terms of actual size and power. In Chapter 3, we construct and evaluatedi?erent con?dence interval estimators for correlated proportion di?erences frombilateral binary data in two-arm randomized clinical trials under the dependencemodel with equal correlation coe?cients between groups. We evaluate the per-formance of various con?dence interval estimators with respect to exact coverageprobabilities, exact con?dence widths and non-coverage probabilities. In Chapter4, we focus on model selection issues. We compare the performance of severalgoodness-of-?t tests for several dependence models used for bilateral binary datain the literature and demonstrate how one may choose an appropriate model inpractice. In Chapter 5, we test the equality of the response rates between twotreatments using combined unilateral and bilateral data. In particular, we pro-pose several test statistics and investigate their performance. We also apply ourproposed methods in each chapter to a real problem using real data sets. Chapter6 contains conclusions and possible future work in this ?eld.