MODELING AND ANALYZING MULTIVARIATE LONGITUDINAL LEFT-CENSORED BIOMARKER DATA

Many medical studies collect biomarker data to gain insight into the biological mechanisms underlying both acute and chronic diseases. These markers may be obtained at a single point in time to aid in the diagnosis of an illness or may be collected longitudinally to provide information on the relationship between changes in a given biomarker as it relates to the course of the illness. While there are many different biomarkers presented in the medical literature there are very few studies that examine the relationship between multiple biomarkers, measured longitudinally, and predictors of interest.The first part of this dissertation addresses the analysis of multiple biomarkers subject to left-censoring over time. Imputation methods and methods that account for censoring are extended to handle multiple outcomes and are compared and evaluated for both accuracy and efficiency through a simulation study. Estimation is based on a parametric multivariate linear mixed model for longitudinally measured biomarkers. For left censored biomarkers an extension of this method based on MLE is used.The linear mixed effects model based on a full likelihood is one of the few methods available to model longitudinal data subject to left-censoring. However, a full likelihood approach is complicated algebraically due to the large dimension of the numeric computations, and maximum likelihood estimation can be computationally prohibitive when the data are heavily censored. Moreover, the complexity of the computation increases as the dimension of the random effects in the model increases. The second part of the dissertation focuses on developing a method that addresses these problems. We propose a method based on a pseudo likelihood function that simplifies the computational complexities, allows all possible multivariate models, and that can be used for any data structure including settings where the level of censoring is high. A robust variance-covariance estimator is used to adjust and correct the variance-covariance estimate. A simulation study is conducted to evaluate and compare the performance of the proposed method for efficiency, simplicity and convergence with existing methods. The proposed methodology is illustrated in the analysis of Genetic and Inflammatory Markers for Sepsis study conducted at the University of Pittsburgh.