Joint modelling of longitudinal and survival data on breast cancer

Tese de Doutoramento em Ciências (Especialidade em Matemática)

Joint modelling of obstacle induced and mesoscale changes: current limits and challenges

Obstacles considerably influence boundary layer processes. Their influences have been included in mesoscale models (MeM) for a long time. Methods used to parameterise obstacle effects in a MeM are summarised in this paper using results of the mesoscale model METRAS as examples. Besides the parameterisation of obstacle influences it is also possible to use a joint modelling approach to describe obstacle induced and mesoscale changes. Three different methods may be used for joint modelling approaches: The first method is a time-slice approach, where steady basic state profiles are used in an obstacle resolving microscale model (MiM, example model MITRAS) and diurnal cycles are derived by joining steady-state MITRAS results. The second joint modelling approach is one-way nesting, where the MeM results are used to initialise the MiM and to drive the boundary values of the MiM dependent on time. The third joint modelling approach is to apply multi-scale models or two-way nesting approaches, which include feedbacks from the MiM to the MeM. The advantages and disadvantages of the different approaches and remaining problems with joint Reynolds-averaged Navier–Stokes modelling approaches are summarised in the paper.

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.