In population based genetic association studies, confounding due to population stratification (PS) arises when differences in both allele and disease frequencies exist in a population of mixed racial/ethnic subpopulations. Propensity scores are often used to address confounding in observational...

Two-stage predictor substitution (2SPS) and the two-stage residual inclusion (2SRI) are two approaches to instrumental variable (IV) analysis. While 2SPS and 2SRI with linear models are well-studied methods of causal inference, the properties of 2SPS and 2SRI for logistic binary outcomes have...

In causal inference for longitudinal data, standard methods usually assume that the underlying processes are discrete time processes, and that the observational time points are the time points when the processes change values. The identification of these standard models often relies on the...

This research is concerned with estimating the relationship between the occurrence of metastases and the size of primary cancers. We are interested in finding the distribution functions of tumor sizes at the points of nodal metastatic and distant metastatic transitions. Understanding the...

A commonly used method for confounder selection is to determine the percent difference between the crude and adjusted odds ratio of the covariate of interest, and to include the adjusting variable if the difference is greater than 10-15%. However, in logistic regression the crude and adjusted...

The random field model has been applied to model spatial heterogeneity for spatial data in many applications. The purpose of this dissertation is to explore statistical properties of noisy spatial data through estimation of the Gaussian random field. Large sample properties of the Maximum...

The automatic collection and increasing availability of health data provides a new opportunity for techniques to monitor this information. By monitoring pre-diagnostic data sources, such as over-the-counter cough medicine sales or emergency room chief complaints of cough, there exists the...

In public health studies, it is common for exposure status to be misclassified. In this dissertation, statistical models to adjust for misclassification will be proposed to address four related questions of interest.The first question focuses on exploring the association between a disease and...

We propose two tests to identify a time dependent covariate effect in the partly parametric linear risk model, and derive asymptotic distributions of the test statistics under the assumption that the covariate effect of interest is constant. One of the asymptotic distributions depends on unknown...