Confidence Interval Construction for the Difference of Proportions Based on Correlated Bilateral Data
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It is common that in medical group comparison studies (e.g. ophthalmological, orthopaedic and otolaryngologic studies), information of paired organs from each subject is collected and contributed to the analysis. Binary responses of treatment or control can be summarized in a contingency table. Previous studies have shown that ignoring the dependence nature of correlated bilateral data could yield biased inference. Hypothesis testing methods for correlated bilateral data have received a lot of attention in recent years. Since confidence interval (CI) is more informative than significance test, we focus on confidence interval construction for the difference of proportions. In this dissertation, we study various asymptotic CI estimators under large sample, taking the intra-class correlation into account. First, for comparison between one treatment group and one control, we propose Wald CI based on maximum likelihood estimate, and profile likelihood CI based on the model suggested in Rosner . Then, for many-to-one comparisons of treatment group with control, simultaneous confidence intervals are constructed with multiplicity adjustment. Finally we construct CIs under the `ρ model' suggested in Donner  considering the intra-class correlation and multiplicity. The performance of the resulting CIs are investigated in Monte Carlo simulation studies with respect to coverage probabilities and interval widths.