Longitudinal censoring is a common artifact when evaluating biomarkers and an obstacle to overcome when jointly investigating the longitudinal nature of the data and the impact on the survival prognoses of a study population. To fully appreciate the complexity of this scenario one has to devise a modeling strategy that can simultaneously account for (i) longitudinal censoring, (ii) outcome dependent dropout, and potentially (iii) correlated biomarkers. In this thesis we propose a novel joint modeling approach to account for the aforementioned issues by linkingtogether a univariate or multivariate Tobit mixed effects model to a suitable parametric event time distribution. This method is significant to public health research since it enables researchers to evaluate the evolution of the disease process in the presence of complex biomarker data where there may be censoring, correlation, and outcome dependent dropout. This approach allows for the analysis of data in a single unified framework. The performance of the proposed Joint Tobit model will be compared to the commonly used "fill-in" methods for censored longitudinal data in a joint modeling framework. Furthermore, we will show that the implementation of our proposed model is fairly straightforward in commercially available software, thus avoiding the complexity and problem specific nature of the expectation maximization (EM) algorithm.
