George Streftaris

Bayesian analysis of experimental epidemics of foot-and-mouth disease.

We investigate the transmission dynamics of a certain type of foot–and–mouth disease (FMD) virus under experimental conditions. Previous analyses of experimental data from FMD outbreaks in non–homogeneously mixing populations of sheep have suggested a decline in viraemic level through serial passage of the virus, but these do not take into account possible variation in the length of the chain of viral transmission for each animal, which is implicit in the non–observed transmission process. We consider a susceptible–exposed–infectious–removed non–Markovian compartmental model for partially observed epidemic processes, and we employ powerful methodology (Markov chain Monte Carlo) for statistical inference, to address epidemiological issues under a Bayesian framework that accounts for all available information and associated uncertainty in a coherent approach. The analysis allows us to investigate the posterior distribution of the hidden transmission history of the epidemic, and thus to determine the effect of the length of the infection chain on the recorded viraemic levels, based on the posterior distribution of a p–value. Parameter estimates of the epidemiological characteristics of the disease are also obtained. The results reveal a possible decline in viraemia in one of the two experimental outbreaks. Our model also suggests that individual infectivity is related to the level of viraemia.

Bayesian inference for stochastic epidemics in closed populations

We consider continuous-time stochastic compartmental models that can be applied in veterinary epidemiology to model the within-herd dynamics of infectious diseases. We focus on an extension of Markovian epidemic models, allowing the infectious period of an individual to follow a Weibull distribution, resulting in a more flexible model for many diseases. Following a Bayesian approach we show how approximation methods can be applied to design efficient MCMC algorithms with favourable mixing properties for fitting non-Markovian models to partial observations of epidemic processes. The methodology is used to analyse real data concerning a smallpox outbreak in a human population, and a simulation study is conducted to assess the effects of the frequency and accuracy of diagnostic tests on the information yielded on the epidemic process.

A Systematic Bayesian Integration of Epidemiological and Genetic Data

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process.

Non-exponential tolerance to infection in epidemic systems—modeling, inference, and assessment

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.

Modeling the consistency of hypoglycemic symptoms: high variability in diabetes.

BACKGROUND The aim of the present study was to examine symptoms of hypoglycemia, to develop a method to quantify individual differences in the consistency of symptom reporting, and to investigate which factors affect these differences. METHODS Participants recorded their symptoms with every episode of hypoglycemia over a 9-12-month period. A novel logistic-type latent variable model was developed to quantify the consistency of each individuals symptom complex and was used to analyze data from 59 subjects (median age, 57.5 years [range, 22-74 years], 65% male, 77% type 1 diabetes) who had experienced 19 or more hypoglycemic episodes. The association between the calculated consistency parameter and age, sex, type and duration of diabetes, and C-peptide and serum angiotensin converting enzyme concentration was examined using a generalized linear model. Analyses were performed under a Bayesian framework, using Markov chain Monte-Carlo methodology. RESULTS Individuals exhibited substantial differences in between-episode consistency of their symptom reports, with only a small number of individuals exhibiting high levels of consistency. Men were more consistent than women. No other factors affected consistency in patients with normal hypoglycemia awareness. CONCLUSIONS By using a novel stochastic model as a quantitative tool to compare the consistency of hypoglycemic symptom reporting, much greater intra-individual variability in symptom reporting was identified than has been recognized previously. This is relevant when instructing patients on identification of hypoglycemic symptoms and in interpreting symptomatic responses during experimentally induced hypoglycemia.

New model diagnostics for spatio-temporal systems in epidemiology and ecology.

A cardinal challenge in epidemiological and ecological modelling is to develop effective and easily deployed tools for model assessment. The availability of such methods would greatly improve understanding, prediction and management of disease and ecosystems. Conventional Bayesian model assessment tools such as Bayes factors and the deviance information criterion (DIC) are natural candidates but suffer from important limitations because of their sensitivity and complexity. Posterior predictive checks, which use summary statistics of the observed process simulated from competing models, can provide a measure of model fit but appropriate statistics can be difficult to identify. Here, we develop a novel approach for diagnosing mis-specifications of a general spatio-temporal transmission model by embedding classical ideas within a Bayesian analysis. Specifically, by proposing suitably designed non-centred parametrization schemes, we construct latent residuals whose sampling properties are known given the model specification and which can be used to measure overall fit and to elicit evidence of the nature of mis-specifications of spatial and temporal processes included in the model. This model assessment approach can readily be implemented as an addendum to standard estimation algorithms for sampling from the posterior distributions, for example Markov chain Monte Carlo. The proposed methodology is first tested using simulated data and subsequently applied to data describing the spread of Heracleum mantegazzianum (giant hogweed) across Great Britain over a 30-year period. The proposed methods are compared with alternative techniques including posterior predictive checking and the DIC. Results show that the proposed diagnostic tools are effective in assessing competing stochastic spatio-temporal transmission models and may offer improvements in power to detect model mis-specifications. Moreover, the latent-residual framework introduced here extends readily to a broad range of ecological and epidemiological models.

Modelling under-reporting in epidemics

Under-reporting of infected cases is crucial for many diseases because of the bias it can introduce when making inference for the model parameters. The objective of this paper is to study the effect of under-reporting in epidemics by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. In particular, we first investigate the effect on the estimation process of ignoring under-reporting when it is present in an epidemic outbreak. We show that such an approach leads to under-estimation of the infection rate and the reproduction number. Secondly, by allowing for the fact that under-reporting is occurring, we develop suitable models for estimation of the epidemic parameters and explore how well the reporting rate and other model parameters can be estimated. We consider the case of a constant reporting probability and also more realistic assumptions which involve the reporting probability depending on time or the source of infection for each infected individual. Due to the incomplete nature of the data and reporting process, the Bayesian approach provides a natural modelling framework and we perform inference using data augmentation and reversible jump Markov chain Monte Carlo techniques.

Modelling critical illness claim diagnosis rates I: methodology

In a series of two papers, this paper and the one by Ozkok et al. (Modelling critical illness claim diagnosis rates II: results), we develop statistical models to be used as a framework for estimating, and graduating, Critical Illness (CI) insurance diagnosis rates. We use UK data for 1999–2005 supplied by the Continuous Mortality Investigation (CMI) to illustrate their use. In this paper, we set out the basic methodology. In particular, we set out some models, we describe the data available to us and we discuss the statistical distribution of estimators proposed for CI diagnosis inception rates. A feature of CI insurance is the delay, on average about 6 months but in some cases much longer, between the diagnosis of an illness and the settlement of the subsequent claim. Modelling this delay, the so-called Claim Delay Distribution, is a necessary first step in the estimation of the claim diagnosis rates and this is discussed in the present paper. In the subsequent paper, we derive and discuss diagnosis rates for CI claims from ‘all causes’ and also from specific causes.

Modeling Probability of Blockage at Culvert Trash Screens Using Bayesian Approach

Trash screens are commonly installed at culvert entrances to prevent the ingress of debris that might otherwise become lodged within the structure. However, these can be a hazard in themselves if not cleared at an appropriate interval. There are currently no tools available to support making decisions regarding screen inspection requirements based upon potential site-by-site blockage risks. The analysis reported here was performed to address this issue. The parameter considered as key in the decision-making process was the probability of screen blockage. To determine this for any screen under consideration, a stochastic predictive model was developed using inspection records, obtained from 140 screens in Belfast, Northern Ireland, to relate blockage probabilities to seven potential drivers extracted from channel, land-use, meteorological, temporal, and social deprivation factors, employing a logistic regression approach. To allow for randomness in the data set, a Bayesian framework was adopted through which the uncertainty associated with any prediction could be reported using appropriate credible intervals. The predictive accuracy of the model was also assessed using appropriate measures and, despite documented uncertainties, was shown to be well within acceptable limits.

The effect of model uncertainty on the pricing of critical illness insurance

Abstract In this paper we calculate and compare diagnosis and net premium rates for critical illness insurance using different models for the claim delay distribution (CDD). The choice of CDD affects the diagnosis rates and hence the net premium rates in two ways: through the estimation of missing dates of diagnosis and through the adjustment of the exposure to allow for claims diagnosed but not settled in the observation period. We consider two CDDs: a three-parameter Burr distribution and a lognormal distribution. Our conclusion, based on a single, but extensive, data set, is that net premium rates are not significantly affected by the choice of CDD.