One difficulty in regression analysis for longitudinal data is that the outcomes are oftenmissing in a non-ignorable way (Little & Rubin, 1987). Likelihood based approaches todeal with non-ignorable missing outcomes can be divided into selection models and patternmixture models based on the way...

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...

Statistical approaches used for gene mapping can be divided into two types: linkage and association analysis. This dissertation work addresses statistical methods in both areas.In the area of linkage analysis, I consider the problem of QTL (Quantitative Trait Locus) linkage analysis. Linkage...

Gray's extension of Cox's proportional hazards (PH) model for right-censored survival data allows for a departure from the PH assumption via introduction of time-varying regression coefficients (TVC) using penalized splines. Gray's work focused on estimation, inference and residual analyses, but...

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...

Medication non-adherence impacts public health by impeding the evaluation of medication efficacy, decreasing improvement and/or increasing morbidity in patients, while increasing health care costs. As a result, intervention studies are designed to improve adherence rates. Medication adherence is...

In a longitudinal study of biomarker data collected during a hospital stay, observations may be missing due to administrative reasons, the death of the subject or the subject's discharge from the hospital, resulting in non-ignorable missing data. Standard likelihood-based methods for the...

Survival analysis has been used to estimate underlying survival or failure probabilities and to estimate the effects of covariates on survival times. The Cox proportional hazards regression model is the most commonly used approach. However, in practical situations, the assumption of proportional...

The selection of variables used to predict a time to event outcome is a common and important issue when analyzing survival data. This is an essential step in accurately assessing risk factors in medical and public health studies. Ignoring an important variable in a regression model may result in...