Statistical Methods for the Analysis of Observational Data With Multiple Correlated Outcomes

Abstract

In 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.