Cai, TianxiDominici, FrancescaCai, Tianyi2019-05-172017-112017-09-112017http://nrs.harvard.edu/urn-3:HUL.InstRepos:39987982In this work, we consider three problems in applied statistics motivated by complex datasets, with approaches from both Frequentist and Bayesian paradigms. Chapter 2 is motivated by case-control data collected for the Army Study to Assess Risk and Resilience in Servicemembers. We derive estimation and testing methods for data sampled by a composite indicator matched on covariates, with an added complexity of misclassified outcomes. Chapter 3 is motivated by multilevel data collected from the Consumer Assessment of Healthcare Providers and Systems surveys. We develop a spatial-temporal Bayesian random effects model with a flexible parameterization, and formulate a Bayesian hat matrix to transparently assess how information is being used in construction of the model estimates. Finally, a cross-validation approach is implemented to evaluate models. Chapter 4 is motivated by observational data from a large administrative database of Medicare beneficiaries, containing patients clustered by hospital providers. We propose a Bayesian hierarchical model to assess associations at the hospital level of the model. A case-mix adjustment is provided at the patient level, with adjustment for hospital-level confounders at the second level. A skew-$t$ distribution is used for the random effects to allow greater flexibility and to compare model adequacy.application/pdfenBiology, BiostatisticsStatisticsThesis or Dissertation2019-05-17