Joint modelling of complex longitudinal and survival data, with applications to HIV studies

In HIV vaccine studies, a major research objective is to identify immune response biomarkers measured longitudinally that may be associated with risk of HIV infection. This objective can be assessed via joint modelling of longitudinal and survival data. Joint models for HIV vaccine data are complicated by the following issues: (i) left censoring of some longitudinal data due to lower limits of quantification; (ii) mixed types of longitudinal variables; (iii) measurement errors, missing values, and outliers in longitudinal data; and (iv) computational challenges associated with likelihood inference. In this thesis, we propose innovative joint models and methods for complex longitudinal and survival data to address the foregoing issues simultaneously. Specifically, we consider two approaches to handle left censored data and a robust method to address b-outliers and e-outliers in longitudinal data. For parameter estimation, we propose approximate likelihood estimation methods based on so-called h-likelihood, which are computationally much more efficient than “exact” or Monte Carlo methods such as Monte Carlo EM algorithms. We evaluate the performances of the models and methods via comprehensive simulation studies. Real data analyses are carried out in depth for a HIV vaccine study.Science, Faculty ofStatistics, Department ofGraduat