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Please note there will be a presentation regarding proposed CenSSOR PhD projects in Room 01.006 David Bates Building, Wednesday 22nd February, 4pm Subject to funding availability, the research projects for PhD students starting in September 2012 are as follows:   **1) The cost effectiveness of novel biomarkers for primary and secondary prevention of cardiovascular disease Dr K J Cairns, Prof F Kee Funding secured from the University’s Strategic Priority Studentships for a collaborative project with QUB School of Medicine, Dentistry and Biomedical Sciences (Centre for Public Health) 2) C-Ph distributions with multiple stochastic processes Prof A H Marshall, Dr K J Cairns 3) Discrete event simulation modelling for the C-Ph distribution Prof A H Marshall, Dr K J Cairns 4) Area-wide traffic control in road networks using macroscopic type-models of traffic flow Dr S Moutari, Prof A H Marshall 5) Road traffic incidents management in urban and and inter-urban road networks Dr S Moutari, Prof A H Marshall 6) Nonparametric estimation under shape constraints Dr M Pavlides, Prof A H Marshall 7) Advances in Perfect Simulation Dr M Pavlides, Prof A H Marshall 8) The impact of Krylov subspace methods in longitudinal data analysis Dr K J Cairns, Prof F Kee 9) Longitudinal data analysis: unstructured data Dr K J Cairns, Prof A H Marshall Applications are to be made online: http://go.qub.ac.uk/pgapply. Further details of how to apply (for both funding and admission) can be found here. The eligibility criteria for DEL Research Studentships Awards can be found here. Deadline for the project marked **: Friday 24th February 2012 Please contact the relevant supervisor for further information before applying.   Further information about PhD/MPhil research at CenSSOR can also be obtained by contacting a.h.marshall@qub.ac.uk. PhD Project Descriptions: PhD Title: The cost effectiveness of novel biomarkers for primary and secondary prevention of cardiovascular disease Supervisors: Dr K J Cairns and Prof F Kee The PhD Project: We have effective drugs for preventing heart disease and stroke for people at high risk. Many people at low risk prefer to judge for themselves the balance of risks, costs and benefits from taking a medication potentially for life. This research will help them by building a model of the decision which takes account explicitly of the assumptions that affect the final judgement of benefit, providing both the patient and the health service with an estimate of the cost effectiveness of a strategy that relies on the use of novel biomarkers to identify those most likely to benefit.   The student will incorporate information from prospective cohort studies across Europe and from clinical trials initially to assess the performance of a novel panel of biomarkers for predicting who might get a coronary event or stroke and who might benefit more or less from treatment. These risks, and the predictive performance metrics of the biomarkers, will be applied to Markov state transition models that incorporate weights for costs (of testing and treatment) and the quality of life associated with each event, in order to derive an incremental cost effectiveness ratio (ICER). Sensitivity analyses will permit the discovery of the key influences on these and where the greatest value for health services and for future research may lie. PhD Title: C-Ph distributions with multiple stochastic processes Supervisors: Prof A H Marshall and Dr K J Cairns The PhD Project: The primary focus of the PhD project is to elaborate on the theory of the C-Ph model to clearly define how the models can encompass more than one survival distribution and in effect deal with a mixture of Coxian phase-type distributions or stochastic processes. When modelling patient length of stay, it has become apparent that the patient stay in hospital is just one component of the system of care for which the patient experiences. Models are generally formed for this one component but it would be more beneficial to the hospital and healthcare service to be able to examine the length of time in hospital alongside the activity that happens in the community. Previous models use the number of readmissions to hospital as an indicator of activity in the community. Alternatively a more representative approach would be to model the actual length of time in community as well as hospital care and incorporate it into the BN component of the C-Ph model. This proposed research will provide the theoretical basis of the further development of the C-Ph model. The practical implications will be illustrated by applying the model to the length of stay distributions for both hospital and community thus demonstrating how the C-Ph model can be utilised in other healthcare scenarios and industrial domains. The stream of work for this PhD will provide the theoretical basis for the further development of a generalised phase-type distribution. PhD Title: Discrete event simulation modelling for the C-Ph distribution Supervisors: Prof A H Marshall and Dr K J Cairns The PhD Project: The aim of this PhD research is to make the C-Ph a practical tool for utilisation in hospital wards. There will be three stages to this development. The first will integrate the Coxian phase-type distribution into a discrete event simulation model of activity on the ward. Discrete event simulation will extend the modelling capabilities of the Coxian phase-type distribution by producing queuing performance measures, such as time in the system and time spent waiting in queues and capacity. The inherent flexibility of simulation modelling supports the user to perform management decisions such as changing capacity, implementing different access strategies, changing the rates or cease admissions and discharges for certain time periods. The stochastic nature of health systems and variability in the input and output parameters can also be easily accommodated. The second stage of the PhD will be the development of the theoretical model of the conditional phase-type distribution along with discrete event simulation. Its implementation will be the final stage of the PhD.   The application will focus on the length of stay of patients in NI hospitals with the further potential of, once achieving a successful result in Northern Ireland, applying the resulting system to patients in hospitals in rest of the UK. This has potential of further expansion to many other healthcare facilities and hospitals in similar healthcare countries. Further benefits could arise by facilitating benchmarking across the NHS thus having significant impact on healthcare developments. PhD Title: Area-wide traffic control in road networks using macroscopic type-models of traffic flow Supervisors: Dr S Moutari and Prof A H Marshall The PhD Project: Area-wide traffic control refers to sets actions, which aims to coordinate traffic flow information in road networks in order to address frequent occurrences of congestion. When properly implemented, area-wide traffic control schemes can have significant impacts on sustainable transportation in terms of safety, economic efficiency, air quality, etc.   Recent research works, based on microscopic traffic simulation, have shown that significant improvement over an optimized fixed time control. Although microscopic models can be regarded as an appropriate response in some specific situations, these models are impractical for crowded large road networks. Macroscopic traffic models, which provide a global view of the traffic in the area, could be an appropriate alternative to overcome the limitations of microscopic type models.   Assessments of large urban road networks are recently feasible due to the availability of comprehensive sets of area-wide traffic monitoring data. The aim of this proposal is to use such data to derive robust area-wide traffic control schemes within the macroscopic framework. PhD Title: Road traffic incidents management in urban and inter-urban road networks Supervisors: Dr S Moutari and Prof A H Marshall The PhD Project: The purpose of traffic incident management systems is to reduce the time to detect, verify an incident occurrence and implement the appropriate response, in order to increase the operating efficiency, safety, and mobility of transportation systems. To achieve these goals, the key inputs for traffic incidents management systems includes sufficient information about the current as well as the likely traffic dynamics on the road network.   Although it is impossible to forecast the future, efficient methods to assist in road traffic incident management should be able to provide scenarios of the future and estimate incident likelihood based on current circumstances and knowledge. Therefore, methods for identifying preconditions that are of importance for describing how a traffic situation may evolve into an incident need to be developed. The aims of this proposal is to develop an innovative framework for road traffic incidents management by combining traffic flow models, real-time and historical traffic as well as other key factors contributing to traffic incidents in road networks. PhD Title: Nonparametric estimation under shape constraints Supervisors: Dr Marios Pavlides and Professor Adele H Marshall The PhD Project: In a frequentist, non-parametric, density estimation setting we often encounter the problem of suitably estimating the continuous density or discrete probability mass function with a mere knowledge of a random sample of size n drawn from it. However, in real applications, we may have prior knowledge to assume that such a density satisfies certain shape constraints. For example, suppose we have a random sample (i.i.d. observations) from a continuous distribution on the positive real line that is assumed to be monotonically non-increasing. Various statistical estimators can be used at estimating the density itself, one of which is the Maximum Likelihood Estimator (MLE). Ulf Grenander first showed that the MLE in this simple setting does exist, is unique and converges to the truth (the true, unknown density) at a rate of n ^{1/3}, where n is the sample size.   Ever since, huge literature has appeared on large-sample asymptotics in different settings, where the different shape-constraints drive the rate of convergence of the MLE to the truth. Such shape constraints that have been studied include: log-concavity (for example, the normal distribution does satisfy this constraints), k-monotone densities, densities with convex contours, as well as monotone densities in higher-dimensions.   Only recently, however, have this field attracted enormous attention, and a vast number of publications continue to be made in this area.   The PhD project is suited at examining different estimators (such as the MLE, Least Squares or, even, Kernel density estimators) for shape-constraints that are appealing (applicable) to real-life settings (such as in survival analysis or econometrics, to mention a couple of fascinating fields.) Depending on the shape constraints to be studied, the enthusiastic applicant will aim at investigating the consistency of the proposed estimators, rates of convergence, model mis-sepcification issues (robustness) and ultimately construct large-sample confidence intervals of functionals of the densities under study, as well as develop large-sample hypotheses tests for testing various competing hypotheses.   The interested applicants are encouraged to contact us with specific questions, should they desire. PhD Title: Advances in Perfect Simulation Supervisors: Dr Marios Pavlides and Professor Adele H Marshall The PhD Project: Markov chain Monte Carlo (MCMC) has received enormous applicability as a computational tool for simulating approximate samples from the posterior distribution of the population parameters of interest, given the data, in Bayesian statistical methodology. However, MCMC samples are only exact, and the ergodic Markov chain, whose limiting distribution is the desired distribution from which we aim at drawing samples, often mixes poorly and various techniques, tailored to individual problems, have been suggested at determining the burn-in period before when the chain is assumed to have mixed adequately and which has converged to the limiting distribution, to a desired degree of tolerance.   In 1996, Prop and Wilson came to suggest a pioneering method, whose idea is simple to grasp and mathematically beautiful, that achieves simulating exact (i.e. perfect) samples from the equilibrium distribution of an ergofic Markov chain of a finite state space. They have called this method "Coupling From The Past" (CFTP) whose name is coined from the idea of the simple algorithm described in that paper. Since then, statisticians have embarked on rigorous research at extending Prop and Wilson's original algorithm to applications of Markov chains with continuous state spaces, developed modifications of the original algorithm that are more computationally tractable and have applied the methodology to a wide spectrum of real applications of interest of a wide spectrum of scientific fields.   This exciting PhD project is aimed at extending the state-of-the-art algorithms to new ones, either tailored-made for specific applications of interest to the PhD candidate and eventually applying these newly-developed techniques to real datasets, under the Bayesian framework.   For a quite exhaustive list of references of in this field, we direct the applicant to David Wilson's CFTP website at: http://dimacs.rutgers.edu/~dbwilson/exact/.   The interested applicants are encouraged to contact us with specific questions, should they desire. PhD Title: The impact of Krylov subspace methods in longitudinal data analysis Supervisors: Dr K J Cairns and Prof F Kee The PhD Project: Many issues in public health have resulted in multiple observations being recorded on individuals over time. Special methods of statistical analysis are needed for such longitudinal data, however implementing such methods can be cumbersome particularly when time-independent and time-dependent covariates need to be incorporated into any model, given the data typically exhibits missingness.   This research project will focus on developing the methodology and algorithms used in modelling longitudinal data, primarily through consideration of these issues within multi-state Markov models. For example, one aspect of the methodology of Markov models requires the evaluation of the exponential of a matrix. With this component of the method often taking the longest time computationally, this research project will consider exploiting alternative algorithms in its determination. One of the algorithms to be considered has already demonstrated its capability and efficiency in an alternative computationally-intensive application in theoretical physics.   The motivation in this research project is to develop the technqiues used to model longitudinal data and then to apply the new approaches to public health. One such data source would be the Tromsø Study which has been repeated at regular intervals and involves a large proportion of the municipality's population. This dataset has been developed with the aim to determine reasons for a wide range of diseases including cardiovascular disease, neurological and bowel-related diseases. This project should therefore contribute to research in statistics and public health potentially impacting on health policy and intervention.