In this thesis, we propose to analyze panel count data using a spline-basedsieve generalized estimating equation method with a semiparametric proportional mean model E(N(t)|Z) = Λ0(t) eβT0Z. The natural log of the baseline mean function, logΛ0(t), is approximated by a monotone cubic B-spline...

An important challenge in statistical modeling involves determining an appropriate structural form for a model to be used in making inferences and predictions. Missing data is a very common occurrence in most research settings and can easily complicate the model selection problem. Many useful...

One of the most frequently used regression models for survival data was proposed by Sir David Cox in 1972, the proportional hazards (PH) model. Even though numerous goodness-of-fit tests have been proposed for the PH model, model assumptions are checked infrequently by researchers utilizing it...

A one factor experimental design is developed based on the potential observable outcome framework, sampling from finite population of units and random allocation of treatments. No assumptions are made about the distribution of units and distribution of treatments. We introduce sampling and...

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...

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...

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...

Curve Registration is a technique for aligning a set of curves whose time scale is observed subject to random error. In this dissertation, a general approach to Curve Registration for longitudinal and functional data, in the possible presence of informative dropout and time-varying treatments,...

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...