In some medical comparative studies， outcomes are bilateral and dichotomous. Inference can be made by either treating subject as the fundamental unit or treating the paired outcomes as independent and ignoring the intra-class correlation information. The latter strategy is usually easier but may lead to inappropriate or wrong conclusions when correlation really exists. Taking the correlation into account can reduce variability and make comparison more precise. In this book， we base our statistical inference assuming that there is correlation in the bilateral binary data. In Chapter 2， we consider testing equality of the correlations of two paired binary responses from two treatment groups. Several statistics for testing the equality of correlations and sample size formulae for a two-arm randomized clinical trial are developed. Simulations are performed to evaluate the behaviors of various tests and the accuracy of different sample size formulae in terms of actual size and power. In Chapter 3， we construct and evaluate different confidence interval estimators for correlated proportion differences from bilateral binary data in two-arm randomized clinical trials under the dependence model with equal correlation coefficients between groups. We evaluate the performance of various confidence interval estimators with respect to exact coverage probabilities， exact confidence widths and non-coverage probabilities. In Chapter 4， we focus on model selection issues. We compare the performance of several goodness-of-fit tests for several dependence models used for bilateral binary data in the literature and demonstrate how one may choose an appropriate model in practice. In Chapter 5， we test the equality of the response rates between two treatments using combined unilateral and bilateral data. In particular， we propose several test statistics and investigate their performance. In chapter 6， we develop five test statistics for testing the homogeneity of proportion ratios for stratified correlated bilateral binary data based on an equal correlation model assumption and we derive approximate sample size formulas based on the recommended test procedures. We also apply our proposed methods in each chapter to a real problem using real data sets. Chapter 7 contains conclusions and possible future work in this field.
Chapter 1 Introduction Chapter 2 Testing Equality of Correlations of Two Paired Binary Responses from Two Treated Groups 2.1 Introduction 2.2 Testing Problem 2.2.1 Test Statistics 2.2,2 Simulation Study 2.3 Sample Size Determination for Power Achievement 2.3.1 Approximate Sample Size Formulae 2.3.2 Simulation Study 2.4 The Bovine Collagen Clinical Trial 2.5 Conclusion Chapter 3 Confidence Intervals for Correlated Proportion Differences from Paired Correlated Data 3.1 Introduction 3.2 Statistical Model 3.3 Confidence Interval Estimators 3.4 Simulation Study 3.5 Application to Reanalyze a Scleroderma ClinicarIYial 3.6 Conclusion Chapter 4 Goodness-of-fit Tests for Correlated Paired Binary Data 4.1 Introduction 4.2 Alternative Models for Paired Correlated Data 4.2.1 Saturated Model 4.2.2 Rosner's Moclel 4.2.3 Dallal7s Model 4.2.4 Equal Correlation Coefficients Model 4.2.5 Independence Model 4.3 Methods for Goodness-of-fit Test 4.4 Simulation Study 4.5 Real Data Analysis and Model Selection 4.6 Conclusion Chapter 5 Testing the Equality of Two Proportions forCombined Unilateral and Bilateral Data 5.1 Introduction 5.2 Data Structure and Dependence Model …… Chapter 6 Testing homogeneity of proportion ratios for stratified correlated bilateral data Chapter 7 Conclusion and Future Work
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