Xinlei Wang, Min Chen
This dissertation contains two topics: (1) A Comparative Study of Statistical Methods for Quantifying and Testing Between-study Heterogeneity in Meta-analysis with Focus on Rare Binary Events; (2) Estimation of Variances in Cluster Randomized Designs Using Ranked Set Sampling.
Meta-analysis, the statistical procedure for combining results from multiple studies, has been widely used in medical research to evaluate intervention efficacy and safety. In many practical situations, the variation of treatment effects among the collected studies, often measured by the heterogeneity parameter, may exist and can greatly affect the inference about effect sizes. Comparative studies have been done for only one or two of the heterogeneity-related topics including statistical models used, descriptive measures, estimation, hypothesis testing, and confidence intervals. Also, none of the studies is focused on rare binary events that require special attention. Our goal is to provide a comprehensive review of all the topics and to evaluate the performance of existing methods involved and make recommendations based on simulation studies that examine various realistic scenarios for rare binary events. We summarize 13 models, 11 descriptive measures, 23 estimators, 33 tests, and 16 confidence intervals in total. We not only provide synthesized information but also categorize the methods based on their key features. We find that there is no uniformly “best” estimator or inference method. However, methods with consistently better performance do exist.
We consider the estimation of variance components in cluster randomized designs (CRDs) using ranked set sampling (RSS). Under the hierarchical linear model (HLM), we propose nonparametric estimators for the between and within cluster variances and explore the impact of design parameters on their performance. Simulation studies show that these RSS-based variance estimators are more efficient than the SRS-based estimator even when the ranking is imperfect. We also illustrate our proposed methods with a real data example.
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Zhang, Chiyu, "Inference of Heterogeneity in Meta-analysis of Rare Binary Events and RSS-structured Cluster Randomized Studies" (2019). Statistical Science Theses and Dissertations. 11.