Bayesian inference and model selection for partially observed stochastic epidemics.

Over the past decades, statistical models have been established as an important tool for understanding the transmission dynamics of infectious diseases. Inference in such models can be challenging due to the strong dependencies in the actual epidemic process, as well as the fact that observations often rely in diagnostic tests that have imperfect sensitivities. Moreover, samples are often taken with very low temporal resolution, which leads to the actual dynamics being only partially observed. Data augmentation techniques implemented within the framework of Markov chain Monte Carlo (MCMC) methods can tackle these problems by taking into account the unobserved dynamics of transmission and thus have been widely employed in practice. Despite the methodological advances in the context of partially observed epidemic models, there are still several open challenges that remain to be addressed. One of the key challenges is the establishment of model comparison techniques that can be efficiently applied in problems involving a large amount of missing information. In this thesis, we describe a framework based on importance sampling which provides estimates of the marginal likelihood and is well suited for applications in this complex setting. Until recently, the study of infectious diseases in large scale populations has been challenging due to the computationally intensive methods needed to these models. One further contribution of this thesis is the development of a data augmentation MCMC algorithm that can be used in both Markovian and non-Markovian epidemic models. Our algorithm achieves good computational efficiency and therefore can be viewed as an alternative to existing approaches, particularly for applications on big datasets. The last part of the thesis is concerned with epidemic data containing additional information regarding the strain of a pathogen with which individuals are infected. Quantifying the interactions between the different strains of pathogens is crucial in order to obtain a complete understanding of the disease but statistical methods for this type of problem are still in the early stages of development. Motivated by this demand, we construct a model that incorporates this additional information and propose a statistical algorithm for inference. The model improves upon existing methods in the sense that it allows for both imperfect diagnostic test sensitivities and strain misclassification. Finally, extensive simulation studies are conducted in order to assess the performance of our methods, while the utility of the developed methodologies is demonstrated on data obtained from two longitudinal studies of Escherichia coli in cattle

Statistical methods for linking geostatistical maps and transmission models: Application to lymphatic filariasis in East Africa.

Infectious diseases remain one of the major causes of human mortality and suffering. Mathematical models have been established as an important tool for capturing the features that drive the spread of the disease, predicting the progression of an epidemic and hence guiding the development of strategies to control it. Another important area of epidemiological interest is the development of geostatistical methods for the analysis of data from spatially referenced prevalence surveys. Maps of prevalence are useful, not only for enabling a more precise disease risk stratification, but also for guiding the planning of more reliable spatial control programmes by identifying affected areas. Despite the methodological advances that have been made in each area independently, efforts to link transmission models and geostatistical maps have been limited. Motivated by this fact, we developed a Bayesian approach that combines fine-scale geostatistical maps of disease prevalence with transmission models to provide quantitative, spatially-explicit projections of the current and future impact of control programs against a disease. These estimates can then be used at a local level to identify the effectiveness of suggested intervention schemes and allow investigation of alternative strategies. The methodology has been applied to lymphatic filariasis in East Africa to provide estimates of the impact of different intervention strategies against the disease.MBG

Efficient model comparison techniques for models requiring large scale data augmentation

Selecting between competing statistical models is a challenging problem especially when the competing models are non-nested. In this paper we offer a simple solution by devising an algorithm which combines MCMC and importance sampling to obtain computationally efficient estimates of the marginal likelihood which can then be used to compare the models. The algorithm is successfully applied to a longitudinal epidemic data set, where calculating the marginal likelihood is made more challenging by the presence of large amounts of missing data. In this context, our importance sampling approach is shown to outperform existing methods for computing the marginal likelihood

Model selection for time series of count data

Selecting between competing statistical models is a challenging problem especially when the competing models are non-nested. An effective algorithm is developed in a Bayesian framework for selecting between a parameter-driven autoregressive Poisson regression model and an observation-driven integer valued autoregressive model when modeling time series count data. In order to achieve this a particle MCMC algorithm for the autoregressive Poisson regression model is introduced. The particle filter underpinning the particle MCMC algorithm plays a key role in estimating the marginal likelihood of the autoregressive Poisson regression model via importance sampling and is also utilised to estimate the DIC. The performance of the model selection algorithms are assessed via a simulation study. Two real-life data sets, monthly US polio cases (1970-1983) and monthly benefit claims from the logging industry to the British Columbia Workers Compensation Board (1985-1994) are successfully analysed

On generalized competition index of a primitive tournament

AbstractFor positive integers k and m and a digraph D, the k-step m-competition graph Cmk(D) of D has the same set of vertices as D and an edge between vertices x and y if and only if there exist m distinct vertices v1,v2,…,vm in D such that there exist directed walks of length k from x to vi and from y to vi for 1≤i≤m. The m-competition index of a primitive digraph D is the smallest positive integer k such that Cmk(D) is a complete graph. In this paper, we study the m-competition indices of primitive tournaments and provide an upper bound for the m-competition index of a primitive tournament

Bayesian inference for multi-strain epidemics with application to Escherichia coli O157 : H7 in feedlot cattle

For most pathogens, testing procedures can be used to distinguish between different strains with which individuals are infected. Due to the growing availability of such data, multistrain models have increased in popularity over the past few years. Quantifying the interactions between different strains of a pathogen is crucial in order to obtain a more complete understanding of the transmission process, but statistical methods for this type of problem are still in the early stages of development. Motivated by this demand, we construct a stochastic epidemic model that incorporates additional strain information and propose a statistical algorithm for efficient inference. The model improves upon existing methods in the sense that it allows for both imperfect diagnostic test sensitivities and strain misclassification. Extensive simulation studies were conducted in order to assess the performance of our method, while the utility of the developed methodology is demonstrated on data obtained from a longitudinal study of Escherichia coli O157:H7 strains in feedlot cattle

Elimination or resurgence : modelling lymphatic filariasis after reaching the 1% microfilaremia prevalence threshold

The low prevalence levels associated with lymphatic filariasis elimination pose a challenge for effective disease surveillance. As more countries achieve the World Health Organization criteria for halting mass treatment and move on to surveillance, there is increasing reliance on the utility of transmission assessment surveys (TAS) to measure success. However, the long-term disease outcomes after passing TAS are largely untested. Using 3 well-established mathematical models, we show that low-level prevalence can be maintained for a long period after halting mass treatment and that true elimination (0% prevalence) is usually slow to achieve. The risk of resurgence after achieving current targets is low and is hard to predict using just current prevalence. Although resurgence is often quick (<5 years), it can still occur outside of the currently recommended postintervention surveillance period of 4–6 years. Our results highlight the need for ongoing and enhanced postintervention monitoring, beyond the scope of TAS, to ensure sustained success

Comparing antigenaemia- and microfilaraemia as criteria for stopping decisions in lymphatic filariasis elimination programmes in Africa

BACKGROUND: Mass drug administration (MDA) is the main strategy towards lymphatic filariasis (LF) elimination. Progress is monitored by assessing microfilaraemia (Mf) or circulating filarial antigenaemia (CFA) prevalence, the latter being more practical for field surveys. The current criterion for stopping MDA requires \u3c2% CFA prevalence in 6- to 7-year olds, but this criterion is not evidence-based. We used mathematical modelling to investigate the validity of different thresholds regarding testing method and age group for African MDA programmes using ivermectin plus albendazole. METHODOLGY/PRINCIPAL FINDINGS: We verified that our model captures observed patterns in Mf and CFA prevalence during annual MDA, assuming that CFA tests are positive if at least one adult worm is present. We then assessed how well elimination can be predicted from CFA prevalence in 6-7-year-old children or from Mf or CFA prevalence in the 5+ or 15+ population, and determined safe (\u3e95% positive predictive value) thresholds for stopping MDA. The model captured trends in Mf and CFA prevalences reasonably well. Elimination cannot be predicted with sufficient certainty from CFA prevalence in 6-7-year olds. Resurgence may still occur if all children are antigen-negative, irrespective of the number tested. Mf-based criteria also show unfavourable results (PPV \u3c95% or unpractically low threshold). CFA prevalences in the 5+ or 15+ population are the best predictors, and post-MDA threshold values for stopping MDA can be as high as 10% for 15+. These thresholds are robust for various alternative assumptions regarding baseline endemicity, biological parameters and sampling strategies. CONCLUSIONS/SIGNIFICANCE: For African areas with moderate to high pre-treatment Mf prevalence that have had 6 or more rounds of annual ivermectin/albendazole MDA with adequate coverage, we recommend to adopt a CFA threshold prevalence of 10% in adults (15+) for stopping MDA. This could be combined with Mf testing of CFA positives to ensure absence of a significant Mf reservoir for transmission