Outside the domain of traditional physics, statistical mechanics provides a framework to describe the behaviour of systems from a diverse range of disciplines. In this thesis, we investigate several problems in medical statistics. In particular, we focus on the topics of network metaanalysis (NMA) and dynamic prediction. NMA is a technique for combining data from multiple medical trials that compare different combinations of treatment options. Dynamic prediction on the other hand, is a topic in survival analysis. Specifically, it refers to the process of making survival predictions based on the history of timevarying covariate measurements and updating prognosis as more observations are made. In the first part of the thesis we present a statistical physics perspective on network metaanalysis. As well as introducing the technical details of the methodology for a physics audience, we compile existing analogies between the two fields, and discuss ideas for how statistical mechanics may be useful for NMA in the future. A particular source of interest for statistical physicists lies in the representation of the treatments and trials as a network graph. In Chapters 3 and 4 we present two research projects on NMA that each stem from considerations of this graph. First, we investigate the effect of network topology on NMA outcomes via a simulation study. The results of this study indicate that irregularity in the number of trials each treatment is involved in is negatively associated with the accuracy and precision of parameter estimates. Second, we use the graph representation of NMA to introduce an analogy between NMA and random walks. The analogy provides insight into NMA methodology and leads to an analytical derivation of the socalled 'proportion contribution matrix' that overcomes limitations of previous algorithms used to construct this quantity. In the next part of the thesis, we introduce the topic of survival analysis. Then, in Chapter 6 we develop an approach to dynamic prediction that, in comparison to standard methods, makes full use of the available data while remaining relatively parsimonious. In applications to clinical data sets, we find that our model performs similarly to standard approaches in terms of predictive accuracy. The work in this thesis explores an interdisciplinary connection between statistical mechanics and medical statistics. I hope that this work is interesting for physicists and statisticians alike, and that it demonstrates that statistical physics ideas can make useful contributions to medical statistics.
Date of Award  1 Aug 2022 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Tobias Galla (Supervisor) & Ahsan Nazir (Supervisor) 

Statistical mechanics approaches to network metaanalysis and dynamic prediction with timevarying covariates
Davies, A. (Author). 1 Aug 2022
Student thesis: Phd