Bayesian nonparametric methods for individual-level stochastic epidemic models

Simulating from and making inference for stochastic epidemic models are key strategies for understanding and controlling the spread of infectious diseases. Current methods for modelling infection rate functions are exclusively parametric. This often involves making strict assumptions about the way the disease spreads and choices which may lack any biological or epidemiological justification. To remove the need for making such assumptions, we develop a Bayesian nonparametric framework which allows us to learn how the disease spreads directly from the data. In this thesis, we consider individual-level models where the infection rate between each pair of individuals depends on characteristics of their relationship. We begin by considering infectious diseases where the infection rate between any two individuals can be modelled by a function of a single characteristic, for example, the distance between them. We model this function nonparametrically by assigning a Gaussian Process prior distribution to it and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to infer this function, alongside the prior distribution hyperparameters and the times individuals were infected. We develop this methodology further, first for multi-type outbreaks and then for outbreaks where the infection rate function depends on more than one characteristic. For multi-type outbreaks, where the infection rate between two individuals not only depends on the characteristics, but also the type of individual being infected, we develop a Multi-Output Gaussian Process method. This method allows us to compare how susceptible each type of individual is to infection. We extend our Gaussian Process method into several dimensions for modelling outbreaks where the infection rate between individuals can be modelled as a function of multiple continuous variables. Finally, we demonstrate our results on two data sets, giving new insights and analysis. The first is an outbreak of Avian Influenza in the Netherlands in 2003, where over 30 million birds were culled. Using the posterior predictive distribution of our nonparametric model, we simulate outbreaks of Avian Influenza to assess various control measures. Alongside our nonparametric analysis, we are able to investigate which of the pre-emptively culled farms were infected. The second is an outbreak of Foot and Mouth Disease in Cumbria, UK. We are able to analyse the relationship between the infection rate of farms with different kind of livestock, showing that farms with both cattle and sheep were much more susceptible to the virus than farms with a single type of livestock

Multi-Level Spatial Comparative Judgement Models To Map Deprivation

While current comparative judgement models provide strong algorithmic efficiency, they remain data inefficient, often requiring days or weeks of extensive data collection to provide sufficient pair- wise comparisons for stable and accurate parameter estimation. This disparity between data and algorithm efficiency is preventing widespread adoption, especially so in challenging data-collection environments such as mapping human rights abuses. We address the data inefficiency challenge by introducing the finite element Gaussian process Bradley–Terry mixture model, an approach that significantly reduces the number of pairwise comparisons required by comparative judgement mod- els. This is achieved via integration of prior spatial assumptions, encoded as a mixture of functions, each function introducing a spatial smoothness constraint at a specific resolution. These functions are modelled nonparametrically, through Gaussian process prior distributions. We use our method to map deprivation in the city of Dar es Salaam, Tanzania and locate slums in the city where poverty reduction measures can be carried out

Bayesian nonparametric methods for individual-level stochastic epidemic models

Simulating from and making inference for stochastic epidemic models are key strategies for understanding and controlling the spread of infectious diseases. Current methods for modelling infection rate functions are exclusively parametric. This often involves making strict assumptions about the way the disease spreads and choices which may lack any biological or epidemiological justification. To remove the need for making such assumptions, we develop a Bayesian nonparametric framework which allows us to learn how the disease spreads directly from the data. In this thesis, we consider individual-level models where the infection rate between each pair of individuals depends on characteristics of their relationship. We begin by considering infectious diseases where the infection rate between any two individuals can be modelled by a function of a single characteristic, for example, the distance between them. We model this function nonparametrically by assigning a Gaussian Process prior distribution to it and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to infer this function, alongside the prior distribution hyperparameters and the times individuals were infected. We develop this methodology further, first for multi-type outbreaks and then for outbreaks where the infection rate function depends on more than one characteristic. For multi-type outbreaks, where the infection rate between two individuals not only depends on the characteristics, but also the type of individual being infected, we develop a Multi-Output Gaussian Process method. This method allows us to compare how susceptible each type of individual is to infection. We extend our Gaussian Process method into several dimensions for modelling outbreaks where the infection rate between individuals can be modelled as a function of multiple continuous variables. Finally, we demonstrate our results on two data sets, giving new insights and analysis. The first is an outbreak of Avian Influenza in the Netherlands in 2003, where over 30 million birds were culled. Using the posterior predictive distribution of our nonparametric model, we simulate outbreaks of Avian Influenza to assess various control measures. Alongside our nonparametric analysis, we are able to investigate which of the pre-emptively culled farms were infected. The second is an outbreak of Foot and Mouth Disease in Cumbria, UK. We are able to analyse the relationship between the infection rate of farms with different kind of livestock, showing that farms with both cattle and sheep were much more susceptible to the virus than farms with a single type of livestock

Bayesian nonparametric inference for heterogeneously mixing infectious disease models

Infectious disease transmissionmodels require assumptions about how the pathogen spreads between individuals. These assumptions may be somewhat arbitrary, particularly when it comes to describing how transmission varies between individuals of different types or in different locations, and may in turn lead to incorrect conclusions or policy decisions. We develop a general Bayesian nonparametric framework for transmission modeling that removes the need to make such specific assumptions with regard to the infection process. We use multioutput Gaussian process prior distributions to model different infection rates in populations containing multiple types of individuals. Further challenges arise because the transmission process itself is unobserved, and large outbreaks can be computationally demanding to analyze. We address these issues by data augmentation and a suitable efficient approximationmethod. Simulation studies using synthetic data demonstrate that our framework gives accurate results. We analyze an outbreak of foot and mouth disease in the United Kingdom, quantifying the spatial transmission mechanism between farms with different combinations of livestock

A Bayesian nonparametric analysis of the 2003 outbreak of highly pathogenic avian influenza in the Netherlands

Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form. Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved. We adopt a fully Bayesian approach by assigning a transformed Gaussian process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference. We use the posterior predictive distribution to simulate the effect of different disease control methods and their economic impact. We analyse a large outbreak of avian influenza in the Netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled. We use our results to analyse ring-culling strategies, and conclude that although effective, ring-culling has limited impact in high-density areas

The Bayesian Spatial Bradley–Terry model: Urban deprivation modelling in Tanzania

Identifying the most deprived regions of any country or city is key if policy makers are to design successful interventions. However, locating areas with the greatest need is often surprisingly challenging in developing countries. Due to the logistical challenges of traditional household surveying, official statistics can be slow to be updated; estimates that exist can be coarse, a consequence of prohibitive costs and poor infrastructures; and mass urbanization can render manually surveyed figures rapidly out-of-date. Comparative judgement models, such as the Bradley–Terry model, offer a promising solution. Leveraging local knowledge, elicited via comparisons of different areas' affluence, such models can both simplify logistics and circumvent biases inherent to household surveys. Yet widespread adoption remains limited, due to the large amount of data existing approaches still require. We address this via development of a novel Bayesian Spatial Bradley–Terry model, which substantially decreases the number of comparisons required for effective inference. This model integrates a network representation of the city or country, along with assumptions of spatial smoothness that allow deprivation in one area to be informed by neighbouring areas. We demonstrate the practical effectiveness of this method, through a novel comparative judgement data set collected in Dar es Salaam, Tanzania

Association between rheumatoid arthritis disease activity, progression of functional limitation and long-term risk of orthopaedic surgery : Combined analysis of two prospective cohorts supports EULAR treat to target DAS thresholds

Objectives: To examine the association between disease activity in early rheumatoid arthritis (RA), functional limitation and long-term orthopaedic episodes. Methods: Health Assessment Questionnaire (HAQ) disability scores were collected from two longitudinal early RA inception cohorts in routine care; Early Rheumatoid Arthritis Study and Early Rheumatoid Arthritis Network from 1986 to 2012. The incidence of major and intermediate orthopaedic surgical episodes over 25 years was collected from national data sets. Disease activity was categorised by mean disease activity score (DAS28) annually between years 1 and 5; remission (RDAS≤2.6), low (LDAS>2.6-3.2), low-moderate (LMDAS≥3.2-4.19), high-moderate (HMDAS 4.2-5.1) and high (HDAS>5.1). Results: Data from 2045 patients were analysed. Patients in RDAS showed no HAQ progression over 5 years, whereas there was a significant relationship between rising DAS28 category and HAQ at 1 year, and the rate of HAQ progression between years 1 and 5. During 27 986 person-years follow-up, 392 intermediate and 591 major surgeries were observed. Compared with the RDAS category, there was a significantly increased cumulative incidence of intermediate surgery in HDAS (OR 2.59 CI 1.49 to 4.52) and HMDAS (OR 1.8 CI 1.05 to 3.11) categories, and for major surgery in HDAS (OR 2.48 CI 1.5 to 4.11), HMDAS (OR 2.16 CI 1.32 to 3.52) and LMDAS (OR 2.07 CI 1.28 to 3.33) categories. There was no significant difference in HAQ progression or orthopaedic episodes between RDAS and LDAS categories. Conclusions: There is an association between disease activity and both poor function and long-term orthopaedic episodes. This illustrates the far from benign consequences of persistent moderate disease activity, and supports European League Against Rheumatism treat to target recommendations to secure low disease activity or remission in all patients.Peer reviewedFinal Published versio

The implied audience of communications policy making: regulating media in the interests of citizens and consumers

This handbook offers a comprehensive overview of the complexity and diversity of audience studies in the advent of digital media