Outlier effects on robust joint modelling of longitudinal and survival data

Robust joint modelling is an emerging field of research. Through the advancements in electronic patient healthcare records, the popularly of joint modelling approaches has grown rapidly in recent years providing simultaneous analysis of longitudinal and survival data. This research advances previous work through the development of a novel robust joint modelling methodology for one of the most common types of standard joint models, that which links a linear mixed model with a Cox proportional hazards model. Through t-distributional assumptions, longitudinal outliers are accommodated with their detrimental impact being down weighed and thus providing more efficient and reliable estimates. The robust joint modelling technique and its major benefits are showcased through the analysis of Northern Irish end stage renal disease patients. With an ageing population and growing prevalence of chronic kidney disease within the United Kingdom, there is a pressing demand to investigate the detrimental relationship between the changing haemoglobin levels of haemodialysis patients and their survival. As outliers within the NI renal data were found to have significantly worse survival, identification of outlying individuals through robust joint modelling may aid nephrologists to improve patient's survival. A simulation study was also undertaken to explore the difference between robust and standard joint models in the presence of increasing proportions and extremity of longitudinal outliers. More efficient and reliable estimates were obtained by robust joint models with increasing contrast between the robust and standard joint models when a greater proportion of more extreme outliers are present. Through illustration of the gains in efficiency and reliability of parameters when outliers exist, the potential of robust joint modelling is evident. The research presented in this thesis highlights the benefits and stresses the need to utilise a more robust approach to joint modelling in the presence of longitudinal outliers.

Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables

Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Dirichlet Process, which allows us to use the same prior model for all of them. Therefore, the tests are “consistent” among each other, in the sense that the probabilities that variables are dependent computed with these tests are commensurable across the different types of variables being tested. By means of simulations with artificial data, we show the effectiveness of the new tests.