Recent Developments in Statistical Methods of Partially Paired Data
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Paired data are ubiquitous in practice, such as in pre-post treatment studies, or in genomic experiments to find differentially expressed genes between two conditions. However, missing values often occur in practice. The incompleteness can be from either one arm or both arms, yielding "partially paired data with incompleteness in one arm", or "partially paired data with incompleteness in both arms." Traditional approaches to deal with such data are either performing a paired test for the portion of data with complete pairs and discard the portion of data with missing values (named "naive paired tests"); or performing a two-sample test using all available data but ignore the correlation between paired portion of data. The former approach is legitimate but may lack of power since it only uses partial information; the latter approach is not legitimate and thus may lead to biased results.While there exist many literatures on partially paired data, most of them only focus on the scenarios with incompleteness in both arms. So far, only a handful literatures studied paired data with incompleteness in one arm, mainly targeting hypothesis testing. This dissertation contains several topics with regards to partially paired data for both missing types: 1) to propose several new methods for hypothesis testing for partially paired data with incompleteness in one arm; 2) to study confidence interval estimation of the mean difference for partially paired data with incompleteness in one arm; 3) to propose several new approaches for conducting hypothesis testing and confidence interval estimation for partially paired data with incompleteness in both arms; 4) to compare powers between naive paired tests and p-value combination methods analytically under normality and to present our counterintuitive findings that using more data does not necessarily yield higher power, for both missing types.