Joint modeling of longitudinal and time-to-event data with the application to kidney transplant data

The main thesis develops the novel and powerful statistical methodology to solve the problems in kidney transplant. Firstly, we use functional principal component analysis (FPCA) through conditional expectation to explore major sources of variations of GFR curves. The estimated FPC scores can be used to cluster GFR curves. Ordering FPC scores can detect abnormal GFR curves. FPCA can effectively estimate missing GFR values and predict GFR values. Secondly, we propose new joint models with mixed-effect and Accelerated Failure Time (AFT) submodels, where the piecewise linear function is used to calculate the non-proportional dynamic hazard ratio curve of a time-dependent side event. The finite sample performance of the proposed method is investigated in simulation studies. Our method is demonstrated by fitting the joint model for some clinical kidney data. Thirdly, we develop a joint model with FPCA and multi-state model to fit the longitudinal and multiple time-to event outcomes together. FPCA is efficient in reducing the dimensions of the longitudinal trajectories. Multistate submodel can be used to describe the dynamic process of multiple time-to-event outcomes. The relationships between the longitudinal and time-to-event outcomes can be assessed based on the shared latent feathers. The latent variables FPC scores are significantly related to time-to-event outcomes in the application example, and Cox model may cause bias for multiple time-to event outcomes compared with multi-state model. Fourthly, we develop a flexible class joint model of generalized linear latent variables for multivariate responses, which has an underlying Gaussian latent processes. The model accommodates any mixture of outcomes from the exponential family. Monte Carlo EM is proposed for parameter estimation and the variance components of the latent processes. We demonstrate this methodology by kidney transplant studies. Finally, in many social and health studies, measurement of some covariates are only available from units of subjects, rather than from individual. Such kind of measures are referred as to aggregate average exposures. The current method fails to evaluate high-order or nonlinear effect of aggregated exposures. Therefore, we develop a nonparametric method based on local linear fitting to overcome the difficulty. We demonstrate this methodology by kidney transplant studies.