Statistical inference for joint modelling of longitudinal and survival data

In longitudinal studies, data collected within a subject or cluster are somewhat correlated by their very nature and special cares are needed to account for such correlation in the analysis of data. Under the framework of longitudinal studies, three topics are being discussed in this thesis.In chapter 2, the joint modelling of multivariate longitudinal process consisting of different types of outcomes are discussed. In the large cohort study of UK north Stafforshire osteoarthritis project, longitudinal trivariate outcomes of continuous, binary and ordinary data are observed at baseline, year 3 and year 6. Instead of analysing each process separately, joint modelling is proposed for the trivariate outcomes to account for the inherent association by introducing random effects and the covariance matrix G. The influence of covariance matrix G on statistical inference of fixed-effects parameters has been investigated within the Bayesian framework. The study shows that by joint modelling the multivariate longitudinal process, it can reduce the bias and provide with more reliable results than it does by modelling each process separately.Together with the longitudinal measurements taken intermittently, a counting process of events in time is often being observed as well during a longitudinal study. It is of interest to investigate the relationship between time to event and longitudinal process, on the other hand, measurements taken for the longitudinal process may be potentially truncated by the terminated events, such as death. Thus, it may be crucial to jointly model the survival and longitudinal data. It is popular to propose linear mixed-effects models for the longitudinal process of continuous outcomes and Cox regression model for survival data to characterize the relationship between time to event and longitudinal process, and some standard assumptions have been made. In chapter 3, we try to investigate the influence on statistical inference for survival data when the assumption of mutual independence on random error of linear mixed-effects models of longitudinal process has been violated. And the study is conducted by utilising conditional score estimation approach, which provides with robust estimators and shares computational advantage. Generalised sufficient statistic of random effects is proposed to account for the correlation remaining among the random error, which is characterized by the data-driven method of modified Cholesky decomposition. The simulation study shows that, by doing so, it can provide with nearly unbiased estimation and efficient statistical inference as well.In chapter 4, it is trying to account for both the current and past information of longitudinal process into the survival models of joint modelling. In the last 15 to 20 years, it has been popular or even standard to assume that longitudinal process affects the counting process of events in time only through the current value, which, however, is not necessary to be true all the time, as recognised by the investigators in more recent studies. An integral over the trajectory of longitudinal process, along with a weighted curve, is proposed to account for both the current and past information to improve inference and reduce the under estimation of effects of longitudinal process on the risk hazards. A plausible approach of statistical inference for the proposed models has been proposed in the chapter, along with real data analysis and simulation study.