Generalized additive model (GAM) with natural cubic splines (NS) has been commonly used as a standard analytical tool in time series studies of health effects of air pollution. Standard model selection procedures used in GAM ignore the uncertainty in model fitting. This may lead to biased...

Tree-structured survival analysis (TSSA) is used to recursively detect covariate values that best divide the sample into subsequent subsets with respect to a time to event outcome. The result is a set of empirical classification groups, each of which identifies individuals with more homogeneous...

Adaptive treatment regime is a set of rules that governs the assignment of time-varying treatment based on observed covariates and intermediate response. Treatment choices are made sequentially as patients make transition from one health state to another. Specifically, in two stage randomization...

Many research areas require multiple outcomes. For example, neuropsychological hypotheses may not be testable using a single measure. Similarly, genetic researchers frequently examine multiple markers across the genome. Examining multiple hypotheses requires the use of multiple testing...

Mediational analysis is used to explain how a predictor affects the outcome through an intervening variable called a mediator. In a cross-sectional study, the predictor, the mediator, and the outcome are measured at single time points and these time points need to be chronologically in the same...

One of the most popular uses for tree-based methods is in survival analysis for censored time data where the goal is to identify factors that are predictive of survival. Tree-based methods, due to their ability to identify subgroups in a hierarchical manner, can sometimes provide a useful...

When an outcome is rated by several raters, ensuring consistency across raters increases the reliability of the measurement. Tanner and Young (1985) proposed a general class of log-linear models to assess agreement among K raters and a rating scale with C nominal categories. Their methodology...

Missing problem is very common in today's public health studies because of responses measured longitudinally. In this dissertation we proposed two latent variable models for longitudinal data with informative missingness. In the first approach, a latent variable model is developed for the...

The proliferation of many clinical studies obtaining multiple biophysical signals from several individuals repeatedly in time is increasingly recognized, a recognition generating growth in statistical models that analyze cross-sectional time series data. In general, these statistical models try...

Estimated associations between an outcome variable and misclassified covariates tend to be biased when the methods of estimation that ignore the classification error are applied. Available methods to account for misclassification often require the use of a validation sample (i.e, a gold...