The Chain Event Graph (CEG) is a new class of graphical model, first introduced in Smith and Anderson [2008], which is derived from a probability tree by merging vertices whose associated conditional probabilities are the same. It is proving to be a useful framework for modelling asymmetric problems and further generalises the Bayesian Network (BN), by allowing for context-specific dependence structures between the variables of the problem. This thesis provides a first demonstration of the value of using the CEG in real-world applications and the new techniques developed here are motivated by problems that arise from two health studies; the Christchurch Health and Development Study (CHDS) and the UK Cerebral Palsy (UKCP) Cohort Study. A direct comparison of the BN and CEG on the CHDS demonstrates that the CEG can lead to significantly higher scoring models than the BN and further that it enables additional conclusions to be drawn on the health study directly from the topology of its graph. An extension of the CEG, the Ordinal CEG, is developed in this thesis, which further enhances the graphical representation of the CEGs for studies with a binary outcome. Motivated by the UKCP this thesis further investigates how missing data structures can be explicitly represented by a CEG and how its graph can consequently provide a precise understanding of the influence of missingness. Finally, a dynamic version of the CEG is developed and it is demonstrated how this new class of models generalises the Dynamic BN and is further closely linked to (semi-) Markov processes. The expressiveness of this model is illustrated through a fictional example.

Emergency Medical Services (EMS) play a pivotal role in any healthcare organisation. Response and turnaround time targets are always of great concern for the Welsh Ambulance NHS Trust (WAST). In particular, the more rural areas in South East Wales consistently perform poorly with respect to Government set response standards, whilst delayed transfer of care to Emergency Departments (EDs) is a problem publicised extensively in recent years. Many Trusts, including WAST, are additionally moving towards clinical outcome based performance measures, allowing an alternative system-evaluation approach to the traditional response threshold led strategies, resulting in a more patient centred system. Three main investigative parts form this thesis, culminating in a suite of operational and strategic decision support tools to aid EMS managers. Firstly, four novel allocation model methods are developed to provide vehicle allocations to existing stations whilst maximising patient survival. A detailed simulation model then evaluates clinical outcomes given a survival based (compared to response target based) allocation, determining also the impact of the fleet, its location and a variety of system changes of interest to WAST (through ‘what-if?’ style experimentation) on entire system performance. Additionally, a developed travel time matrix generator tool, enabling the calculation and/or prediction of journey times between all pairs of locations from route distances is utilised within the aforementioned models. The conclusions of the experimentation and investigative processes suggest system improvements can in fact come from better allocating vehicles across the region, by reducing turnaround times at hospital facilities and, in application to South East Wales, through alternative operational policies without the need to increase resources. As an example, a comparable degree of improvement in patient survival is witnessed for a simulation scenario where the fleet capacity is increased by 10% in contrast to a scenario in which ideal turnaround times (within the target) occur.

It is now widely acknowledged that spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In this work I investigate an ensemble of techniques for understanding the stochastic dynamics of spatial and discrete epidemic processes, with especial consideration given to SIR disease dynamics for the Levins-type metapopulation. I present a toolbox of techniques for the modeller of spatial epidemics. The highlight results are a novel form of moment closure derived directly from a stochastic differential representation of the epidemic, a stochastic simulation algorithm that asymptotically in system size greatly out-performs existing simulation methods for the spatial epidemic and finally a method for tackling optimal vaccination scheduling problems for controlling the spread of an invasive pathogen.

This thesis discusses issues arising in the analysis of repeated measurement studies with missing data. The first part of the thesis is motivated by a study where continuous and bounded longitudinal data form the outcome of interest. The aim of this study is to investigate the change over time in the outcome variable and factors that influence this change. The analysis is complicated because some patients withdraw from the study, leading to an incomplete data set. We propose a non-linear mixed model that specifies the rate of change and the bounds of the outcome as a function of covariates. This mixed model has advantages over transforming the data and is easy to interpret. We discuss different models for the covariance structure of bounded continuous longitudinal data. To explore the impact of missingness, we perform several sensitivity analyses. Further, we propose a model for informative missingness, taking into account the number and nature of reminders made to contact initial non-responders, and evaluate the impact of missingness on estimates of change. We contrast this model with the traditional selection model, where the missingness process is modelled. Our investigations suggest that using the richer information of the reminder process enables a more accurate choice of covariates which induce missingness, than modelling the missingness process. Regarding the reminder process, we observe that phone calls are most effective. The second part of this thesis is motivated by dose-finding studies, where the number of events per subject within a specified study period form the primary outcome. These studies aim to identify a target dose for which the new drug can be shown to be as effective as a competitor medication. Given a pain-related outcome, we expect many patients to drop out before the end of the study. The impact of missingness on the analysis and models for the missingness process must be carefully considered. The recurrent events are modelled as over-dispersed Poisson process data, with dose as regressor. Additional covariates may be included. Constant and time-varying rate functions are examined. Based on a range of such models, the impact of missingness on the precision of the target dose estimation is evaluated by simulations. Five different analysis methods are assessed: a complete case analysis; two analyses using different single imputation techniques; a direct likelihood analysis; and an analysis using pattern-mixture models. The target dose estimation is robust if the same missingness process holds for the target dose group and the active control group. This robustness is lost as soon as the missingness mechanisms for the active control and the target dose differ. Of the methods explored, the direct-likelihood approach performs best, even when a missing not at random mechanism holds.

Health care is a complex system and it is therefore expected to behave in a non-linear manner. It is important for the delivery of health interventions to patients that the best possible analysis of available data is undertaken. Many of the conventional models used for health care data are linear. This research compares the performance of linear models with non-linear models for two health care data sets of complex interventions. Logistic regression, latent class analysis and a classification artificial neural network were each used to model outcomes for patients using data from a randomised controlled trial of a cognitive behavioural complex intervention for non-specific low back pain. A Cox proportional hazards model and an artificial neural network were used to model survival and the hazards for different sub-groups of patients using an observational study of a cardiovascular rehabilitation complex intervention. The artificial neural network and an ordinary logistic regression were more accurate in classifying patient recovery from back pain than a logistic regression on latent class membership. The most sensitive models were the artificial neural network and the latent class logistic regression. The best overall performance was the artificial neural network, providing both sensitivity and accuracy. Survival was modelled equally well by the Cox model and the artificial neural network, when compared to the empirical Kaplan-Meier survival curve. Long term survival for the cardiovascular patients was strongly associated with secondary prevention medications, and fitness was also important. Moreover, improvement in fitness during the rehabilitation period to a fairly modest 'high fitness' category was as advantageous for long-term survival as having achieved that same level of fitness by the beginning of the rehabilitation period. Having adjusted for fitness, BMI was not a predictor of long term survival after a cardiac event or procedure. The Cox proportional hazards model was constrained by its assumptions to produce hazard trajectories proportional to the baseline hazard. The artificial neural network model produced hazard trajectories that vary, giving rise to hypotheses about how the predictors of survival interact in their influence on the hazard. The artificial neural network, an exemplar non-linear model, has been shown to match or exceed the capability of conventional models in the analysis of complex health care data sets.

This thesis is focused on the topic of competing risks survival analysis. The first chapter provides an introduction and motivation with a brief literature review. Chapter 2 considers the fundamental functional of all competing risks data: the crude incidence function. This function is considered in the light of the counting process framework which provides powerful mathematics to calculate confidence bands in an analytical form, rather than bootstrapping or simulation. Chapter 3 takes the Peterson bounds and considers what happens in the event of covariate information. Fortunately, these bounds do become tighter in some cases. Chapter 4 considers what can be inferred about the effect of covariates in the case of competing risks. The conclusion is that there exist bounds on any covariate-time transformation. These two preceding chapters are illustrated with a data set in chapter 5. Chapter 6 considers the result of Heckman and Honore (1989) and investigates the question of their generalisation. It reaches the conclusion that the simple assumption of a univariate covariate-time transformation is not enough to provide identifiability. More practical questions of modeling dependent competing risks data through the use of frailty models to induce dependence is considered in chapter 7. A practical and implementable model is illustrated. A diversion is taken into more abstract probability theory in chapter 8 which considers the Bayesian non-parametric tool: P61ya trees. The novel framework of this tool is explained and some results are obtained concerning the limiting random density function and the issues which arise when trying to integrate with a realised P61ya distribution as the integrating measure. Chapter 9 applies the theory of chapters 7 and 8 to a competing risks data set of a prostate cancer clinical trial. This has several continuous baseline covariates and gives the opportunity to use a frailty model discussed in chapter 7 where the unknown frailty distribution is modeled using a P61ya tree which is considered in chapter 8. An overview of the thesis is provided in chapter 10 and directions for future research are considered here.

This research consists of a collaborative study of internal communication in a National Health Service Trust. Information was obtained by means of interviews, discussions and surveys of staff. A small comparative study was carried out with senior officers from a Borough Council. Strengths and weaknesses in organisational communications have been identified. The most important of these strengths was recognition in the Trust that communication is everybody's responsibility. Weaknesses were apparent in interdepartmental communication, visibility and approachability of management and lack of information and briefing on general matters and changes. The study has demonstrated the successful use of mechanisms for identifying both weak areas and groups. A new scale has been utilised and indices have been developed and evaluated to measure specific aspects of communication. These include: (i) Overall communication satisfaction and level. (ii) Frequency of communication. (iii) Information overload. (iv) Non-occurrence or breakdown of communication. These measures have facilitated the identification of categories of staff in the Trust that are either communication advantaged or disadvantaged. As a further contribution, the measures can be used to examine certain hypotheses such as those relating communication to involvement with the organisation. The thesis also describes key areas that need to be addressed in the future. The NHS Trust has accepted and utilised the findings of this study and is implementing improvements. The mechanisms and management of the improvement processes are detailed.

Background: Cardiac Magnetic Resonance (CMR) has utility in the risk stratification of patients post ST elevation myocardial infarction (STEMI). Myocardial strain is theoretically more linked to left ventricular pump function than left ventricular ejection fraction (LVEF). There are a number of CMR strain techniques including bespoke methods such as displacement encoding with stimulated echoes (DENSE) and cine derived methods such as feature-tracking. Whilst cine-derived strain is more appealing for imaging in real-world practice, there are concerns on accuracy, especially on a myocardial segmental level. Deformation-tracking is a new technique based on tissue-tracking from cine imaging which has been developed in our group and is theoretically more accurate at identifying myocardial displacement and shortening than other commercial cine-strain techniques. Hypothesis: Compared with standard methods for imaging heart function, novel strain methods have superior diagnostic and prognostic performance. Objectives: (1) I aimed to compare circumferential strain derived from DENSE, deformation-tracking and feature-tracking in a group of 81 healthy volunteers, and in a group of STEMI patients. I investigated the relationship between strain age and sex in the healthy volunteers. (2) I also investigated the comparative performance of the three strain techniques and LV surrogate outcomes (LVEF, LV end diastolic volume indexed to body surface area, infarct size) as well as composite health outcomes (major adverse cardiac events) at 4 years in the STEMI patients. (3) I investigated the incremental predictive utility of segmental circumferential strain over infarct size to predict segmental functional improvement by wall-motion scoring at 6 months in patients with STEMI, and the influence of infarct characteristics (microvascular obstruction, intra-myocardial haemorrhage) on segmental circumferential strain at 6 months. (4) I investigated the utility of feature-tracking derived global longitudinal strain in this STEMI group. (5) Finally, I performed a de-novo study implementing a new DENSE technique in a group of STEMI patients and compared deformation-tracking and feature-tracking against this new technique. Methods: 1. Healthy Volunteers Study: 81 participants underwent multi-parametric CMR at 1.5T. 2. STEMI population 1: 324 patients underwent a similar multi-parametric CMR at 3 days and 295 at 6 months post STEMI. Composite health outcomes that are pathophysiologically linked to STEMI were collected by an independent team. 3. STEMI population 2: 50 patients underwent a multi-parametric CMR at 1 day and 6 months post STEMI. This protocol included the new 2D-Spiral DENSE sequence. The imaging analyses were performed using standardised methods. Health outcomes were analysed and adjudicated by an independent team blinded to the rest of the study. Statistical analyses were carried out under the supervision of a biostatistician. Results: The main findings of this thesis are: 1. Deformation-tracking performed well when compared with a reference method (DENSE) in a large group of healthy volunteers. The advantage of utilising a cine-strain derived method is that this would obviate the need for bespoke strain sequences being acquired, limiting the total duration of an CMR scan, and making strain more accessible in the clinical setting. 2. Global circumferential strain with DENSE provides incremental prognostic value over infarct size and pathologies revealed by contrast-enhanced CMR for LV surrogate outcomes. Strain imaging with DENSE has emerging potential as a new reference test for prognostication in patients after an acute STEMI. 3. Global circumferential strain with DENSE provides incremental prognostic value over infarct size and pathologies revealed by contrast-enhanced CMR for MACE. Conclusions: The data presented in this thesis indicate that CMR strain imaging may be clinically useful in the assessment of patients following an acute STEMI. This indicates that strain should be more widely used in clinical studies as both global and segmental strain provide incremental utility over more commonly used markers of prognosis for global and regional LV function, as well as major adverse cardiac events. 2D-Spiral DENSE is a new technique, which I have demonstrated, to be feasible to acquire in STEMI patients and has the potential to investigate LV pump function in more detail than conventional methods.

A review on nosocomial infection has shown that there are various compelling evidence to suggest that the role of the airborne route to infection in a multi-bed environment cannot be ignored. Expiratory activities such as coughing, sneezes, talking and patient-centric activities such as bed-making has been shown in literature to generate significant quantity of infectious quanta that may become airborne and pose an infection threat to vulnerable patients. In this study, an airborne infection route of MRSA in the health care environment has been investigated using both the large-eddy simulation (LES) technique and an infection modeling. From analyzing flow field regimes in both a single room (typically found in isolation wards) and multi-bed ward environments, it was observed that the supply air delivered into the ventilated space produces pockets of recirculation areas near the walls and midway of the room in the wake of the advancing ventilation outlet bound flows, after impinging on internal surfaces such as beds. These recirculation areas have been identified as hot spots for possible airborne infection. Furthermore, the results suggests that the further the outlet vent is away from the inlet vent, the more likely will be the generation of recirculation regions, which directly translate to poor ventilation spots and that the use of curtains within the vicinity of the aerosol generating activities increases the number of recirculation areas. The overall airflow analysis suggest that any engineering solution designed to limit or remove the recirculation regions from the flow regime will be an effective way of fighting cross infections within the hospital ward environment, and as such ventilation schemes that are optimally designed to achieve this should be encouraged and investigated. This study has also predicted the possibility of a secondary infection in a multiward environment using various modeling approaches. The results obtained indicated that the posture of an infected person involved in the release of pathogens in relation to cohorts can have a profound effect on infection rates within the ward environment. The study of the coughing episode with the patient lying on the side generated a unit secondary infection, whilst the same simulated episode with an adjacent curtain in position failed to generate a secondary infection within the exposure period. The activity of bed making was also found to generate a secondary infection over the duration of the simulation, suggesting that bed-making can be a potential source of infection. The particle concentration decay curves examined in this work equally suggest that patients are at their most vulnerable state at the initial stages of coughing/sneezes, and talking episodes where the infecting patient assumes a directly facing posture to the susceptible.