Robust Joint Modelling: Extensions in Time-Varying Outlier Impacts
Applications are now CLOSED
The interaction between repeated measurements over time and the time until an event of interest is prevalent in a wide range of applications. The simultaneous exploration of these two processes is one of the main driving factors for the rapid development of joint modelling [1, 2]. Despite consistent advancements in joint modelling over the last decade, the majority of models maintain the assumption of normality for the random terms. Such assumptions are greatly and negatively impacted by the presence of outliers - individuals who are not typical of the population (b-outlier) or observations that outlie from an individual’s usual trend line over time (e-outlier). This research will advance robust joint modelling methodology - the use of t-distributional assumptions for the random terms to accommodate and down weigh the bias and inefficiency caused by longitudinal outliers [3, 4]. Whilst such models can be utilised in a variety of applications, they are commonly applied in a medical context with clinicians interested in the factors that influence patients’ changing biomarkers and how this impacts their survival. However, patients typically take time to stabilise and adjust to new treatments. This period of adjustment means they are more prone to outlying responses early in their treatment regime, with that changing as time progresses. In medicine, this is known as the “heterogeneity of treatment effects” and is an important concept in clinical practice that should therefore be reflected in statistical literature .
Recent work has focused on this, developing methods to better represent time-varying outlier impacts . In doing so, this work has highlighted the detrimental impact of incorrectly modelling such scenarios on our ability to fully understand how factors impact the survival of individuals. This PhD will advance that work further, refining what has been investigated to date and exploring other avenues to advance robust joint modelling to better represent how parameters are likely to vary as time progresses. Each avenue has the great potential to
significantly impact this field of research and the analysis of this type of real world data.
For further details about the project, please contact the primary supervisor.
 Elashoff R.M. (2017). Joint modeling of longitudinal and time-to-event data. CRC Press.
 Asar O., Ritchie J., Kalra P. A. and Diggle P. J. (2015). Joint modelling of repeated measurement and ¨
time-to-event data: an introductory tutorial. International Journal of Epidemiology 44(1), 334-344.
 Pinheiro J. C., Liu C., and Wu Y. N. (2001). Efficient algorithms for robust estimation in linear mixedeffects models using the multivariate t distribution. Journal of Computational and Graphical Statistics 10,
 Asar O., Fournier M.-C. and Dantan E. (2020). Dyanmic predictions of kidney graft survival in the presence ¨
of longitudinal outliers. Statistical Methods in Medical Research.
 Kravitz, R.L., Duan, N. and Braslow, J. (2004). Evidence-based medicine, heterogeneity of treatment
effects, and the trouble with averages. The Milbank Quarterly 82(4), 661–687.
 McFetridge L., Asar O. and Wallin J. (2020). Robust joint modelling of longitudinal and ¨
survival data with a time-varying degrees-of-freedom parameter Under review. Available at
The Mathematical Research Centre conducts world-class research in the following areas: Algebra, Analysis, Operator Algebras, Algebraic Topology, Topological Data Analysis, PDEs, Survival Analysis, Bayesian Networks, Data Analytics and Operational Research. It maintains vibrant international links with a large number of researchers around the globe and regularly hosts international conferences and research visitors.
List of researchers, their interests and upcoming PhD projects can be found at:
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Information on the research interests and activities of academics in the Mathematical Science Research Centre can be found at https://web.am.qub.ac.uk/wp/msrc/. These interests fit into the themes: Algebra, Analysis, Data Science, Optimization and Operational Research, Partial Differential Equations, Statistics, Topology and Geometry.
Mathematical and statistical skills are in great demand in the economy, particularly the advanced skills developed at the PhD level.
Employment after the Course
As well as continuing in research careers, our PhD graduates have also gone on to work in finance, computing, data analysis, management and teaching. Our advisors will be happy to provide further information on the career prospects arising from your chosen research area. Further information on careers can be obtained from the School and the Faculty.
People teaching you
Dr David Barnes
Postgraduate Advisor - Mathematical Sciences Research Centre
Dr Salissou Moutari
Director of Research - Mathematical Sciences Research Centre
Assessment processes for the Research Degree differ from taught degrees. Students will be expected to present drafts of their work at regular intervals to their supervisor who will provide written and oral feedback; a formal assessment process takes place annually.
This Annual Progress Review requires students to present their work in writing and orally to a panel of academics from within the School. Successful completion of this process will allow students to register for the next academic year.
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|Northern Ireland (NI) 1||£4,500|
|Republic of Ireland (ROI) 2||£4,500|
|England, Scotland or Wales (GB) 1||£4,500|
|EU Other 3||£17,460|
1 EU citizens in the EU Settlement Scheme, with settled or pre-settled status, are expected to be charged the NI or GB tuition fee based on where they are ordinarily resident, however this is provisional and subject to the publication of the Northern Ireland Assembly Student Fees Regulations. Students who are ROI nationals resident in GB are expected to be charged the GB fee, however this is provisional and subject to the publication of the Northern Ireland Assembly student fees Regulations.
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There are no specific additional course costs associated with this programme.
Additional course costs
Depending on the programme of study, there may also be other extra costs which are not covered by tuition fees, which students will need to consider when planning their studies . Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £100 per year for photocopying, memory sticks and printing charges. Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen. There are also additional charges for graduation ceremonies, and library fines. In undertaking a research project students may incur costs associated with transport and/or materials, and there will also be additional costs for printing and binding the thesis. There may also be individually tailored research project expenses and students should consult directly with the School for further information.
How do I fund my study?1.PhD Opportunities
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