Mixed types of multivariate outcomes are common in clinical investigations. Survival time is one of the primary goals in practice. In addition, hospitalization attracts increasing attention as it is a main contributor to the total cost of care, and the identification of related risk factors is of interest in many health economics studies. Meanwhile, we are also interested in the longitudinal path of important clinical measurements along the progress of disease. Joint modeling is often required as both hospitalization frequencies or longitudinal measurements can be informatively censored due to death. In this dissertation, we will propose three research projects which jointly model multiple aspects of the outcomes.

The first research project models survival time and hospitalization together through a latent subject-specific random frailty. B-spline bases are introduced for flexible forms of baseline hazard and the offset function. Computational methods to solve for the MLE and to select knots are developed. The proposed methods are applied to study the risk factors of hospitalization and survival time among end-stage-renal-disease (ESRD) patients.

The second part proposes a joint model of hospitalization and readmission. Number of hospitalizations is modeled as a Poisson random variable and number of readmissions is treated as a Binomial random variable with number of hospitalizations being the total number of trials. The proposed joint modeling framework is applied to evaluate the performance of an intervention program from Fresenius Medical Care in reducing number of hospitalizations and readmissions.

The third research project jointly models survival time and multiple longitudinal observations. A penalized likelihood approach is described for variable selection. We design a Coordinate Descent Algorithm to solve for the penalized MLE and a two-stage estimation method to reduce the bias resulting from penalization. Simulation results demonstrate good selection and estimation property. We illustrate the practical usage of proposed method through an application to ESRD patients.