Nested sampling for Bayesian model comparison in the context of Salmonella disease dynamics.

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.RD was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I002189/1). TJM was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I012192/1). OR was funded by the Royal Society.This paper was originally published in PLOS ONE (Dybowski R, McKinley TJ, Mastroeni P, Restif O, PLoS ONE 2013, 8(12): e82317. doi:10.1371/journal.pone.0082317)

Simulation-based Bayesian inference for epidemic models

This is the author pre-print version. The final version is available from the publisher via the DOI in this record.A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods. © 2013 Elsevier B.V. All rights reserved.T. J. M. was in part supported by Department for the Environment, Food and Rural Affairs/Higher Education Funding Council of England, grant number VT0105 and BBSRC grant (BB/I012192/1). J. V. R was in part supported by Australian Research Council’s Discovery Projects funding scheme (project number DP110102893). R. D. was in part supported by Natural Sciences and Engineering Research Council (NSERC) of Canada’s Discovery Grants Program. A. R. C. was in part supported by National Medical Research Council (NMRC/HINIR/005/2009) and NUS Initiative to Improve Health in Asia. The authors would like to thank Andrew Conlan and Theo Kypraios for useful discussions

Nested sampling for Bayesian model comparison in the context of Salmonella disease dynamics.

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.RD was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I002189/1). TJM was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I012192/1). OR was funded by the Royal Society. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Efficient Bayesian model choice for partially observed processes: with application to an experimental transmission study of an infectious disease

Infectious diseases such as avian influenza pose a global threat to human health. Mathematical and statistical models can provide key insights into the mechanisms that underlie the spread and persistence of infectious diseases, though their utility is linked to the ability to adequately calibrate these models to observed data. Performing robust inference for these systems is challenging. The fact that the underlying models exhibit complex non-linear dynamics, coupled with practical constraints to observing key epidemiological events such as transmission, requires the use of inference techniques that are able to numerically integrate over multiple hidden states and/or infer missing information. Simulation-based inference techniques such as Approximate Bayesian Computation (ABC) have shown great promise in this area, since they rely on the development of suitable simulation models, which are often easier to code and generalise than routines that require evaluations of an intractable likelihood function. In this manuscript we make some contributions towards improving the efficiency of ABC-based particle Markov chain Monte Carlo methods, and show the utility of these approaches for performing both model inference and model comparison in a Bayesian framework. We illustrate these approaches on both simulated data, as well as real data from an experimental transmission study of highly pathogenic avian influenza in genetically modi fied chickens.This work was supported by the Biotechnology and Biological Sciences Research Council (grants BB/G00479X/1, BBS/B/00239, and BBS/B/00301) and by the Cambridge Infectious Diseases Consortium Department for Environment, Food and Rural Affairs-Higher Education Funding Council for England (grant VT0105). AJKC was supported by BBSRC grant BB/I024550/1

Quantification of the effects of antibodies on the extra- and intracellular dynamics of Salmonella enterica.

Antibodies are known to be essential in controlling Salmonella infection, but their exact role remains elusive. We recently developed an in vitro model to investigate the relative efficiency of four different human immunoglobulin G (IgG) subclasses in modulating the interaction of the bacteria with human phagocytes. Our results indicated that different IgG subclasses affect the efficacy of Salmonella uptake by human phagocytes. In this study, we aim to quantify the effects of IgG on intracellular dynamics of infection by combining distributions of bacterial numbers per phagocyte observed by fluorescence microscopy with a mathematical model that simulates the in vitro dynamics. We then use maximum likelihood to estimate the model parameters and compare them across IgG subclasses. The analysis reveals heterogeneity in the division rates of the bacteria, strongly suggesting that a subpopulation of intracellular Salmonella, while visible under the microscope, is not dividing. Clear differences in the observed distributions among the four IgG subclasses are best explained by variations in phagocytosis and intracellular dynamics. We propose and compare potential factors affecting the replication and death of bacteria within phagocytes, and we discuss these results in the light of recent findings on dormancy of Salmonella.This work was funded by grants from the Wellcome Trust and from the Medical Research Council to PM. O.R. is supported by the Royal Society through a University Research Fellowship. M.P. is supported by a studentship from the Wellcome Trust

Risk factors and variations in detection of new bovine tuberculosis breakdowns via slaughterhouse surveillance in Great Britain.

Slaughterhouse surveillance through post-mortem meat inspection provides an important mechanism for detecting bovine tuberculosis (bTB) infections in cattle herds in Great Britain (GB), complementary to the live animal skin test based programme. We explore patterns in the numbers of herd breakdowns detected through slaughterhouse surveillance and develop a Bayesian hierarchical regression model to assess the associations of animal-level factors with the odds of an infected animal being detected in the slaughterhouse, allowing us to highlight slaughterhouses that show atypical patterns of detection. The analyses demonstrate that the numbers and proportions of breakdowns detected in slaughterhouses increased in GB over the period of study (1998-2013). The odds of an animal being a slaughterhouse case was strongly associated with the region of the country that the animal spent most of its life, with animals living in high-frequency testing areas of England having on average 21 times the odds of detection compared to animals living in Scotland. There was also a strong effect of age, with animals slaughtered at > 60 months of age having 5.3 times the odds of detection compared to animals slaughtered between 0-18 months of age. Smaller effects were observed for cattle having spent time on farms with a history of bTB, quarter of the year that the animal was slaughtered, movement and test history. Over-and-above these risks, the odds of detection increased by a factor of 1.1 for each year of the study. After adjustment for these variables, there were additional variations in risk between slaughterhouses and breed. Our framework has been adopted into the routine annual surveillance reporting carried out by the Animal Plant Health Agency and may be used to target more detailed investigation of meat inspection practices.Defra Project SE3133. (Department of Environment and Rural Affairs, UK Government

The demography of free-roaming dog populations and applications to disease and population control

Understanding the demography of domestic dog populations is essential for effective disease control, particularly of canine-mediated rabies. Demographic data are also needed to plan effective population management. However, no study has comprehensively evaluated the contribution of demographic processes (i.e. births, deaths and movement) to variations in dog population size or density, or determined the factors that regulate these processes, including human factors. We report the results of a 3-year cohort study of domestic dogs, which is the first to generate detailed data on the temporal variation of these demographic characteristics. The study was undertaken in two communities in each of Bali, Indonesia and Johannesburg, South Africa, in rabies-endemic areas and where the majority of dogs were free-roaming. None of the four communities had been engaged in any dog population management interventions by local authorities or animal welfare organizations. All identified dogs in the four communities were monitored individually throughout the study. We observed either no population growth or a progressive decline in population size during the study period. There was no clear evidence that population size was regulated through environmental resource constraints. Rather, almost all of the identified dogs were owned and fed regularly by their owners, consistent with population size regulated by human demand. Finally, a substantial fraction of the dogs originated from outside the population, entirely through the translocation of dogs by people, rather than from local births. These findings demonstrate that previously reported growth of dog populations is not a general phenomenon and challenge the widely held view that free-roaming dogs are unowned and form closed populations. Synthesis and applications. These observations have broad implications for disease and population control. The accessibility of dogs for vaccination and evaluation through owners and the movement of dogs (some of them infected) by people will determine the viable options for disease control strategies. The impact of human factors on population dynamics will also influence the feasibility of annual vaccination campaigns to control rabies and population control through culling or sterilization. The complex relationship between dogs and people is critically important in the transmission and control of canine-mediated rabies. For effective management, human factors must be considered in the development of disease and population control programmes

Emulation and History Matching using the hmer Package

Modelling complex real-world situations such as infectious diseases, geological phenomena, and biological processes can present a dilemma: the computer model (referred to as a simulator) needs to be complex enough to capture the dynamics of the system, but each increase in complexity increases the evaluation time of such a simulation, making it difficult to obtain an informative description of parameter choices that would be consistent with observed reality. While methods for identifying acceptable matches to real-world observations exist, for example optimisation or Markov chain Monte Carlo methods, they may result in non-robust inferences or may be infeasible for computationally intensive simulators. The techniques of emulation and history matching can make such determinations feasible, efficiently identifying regions of parameter space that produce acceptable matches to data while also providing valuable information about the simulator's structure, but the mathematical considerations required to perform emulation can present a barrier for makers and users of such simulators compared to other methods. The hmer package provides an accessible framework for using history matching and emulation on simulator data, leveraging the computational efficiency of the approach while enabling users to easily match to, visualise, and robustly predict from their complex simulators.Comment: 40 pages, 11 figures; submitted to Journal of Statistical Software: author order correcte

Age-dependent patterns of bovine tuberculosis in cattle.

Bovine tuberculosis (BTB) is an important livestock disease, seriously impacting cattle industries in both industrialised and pre-industrialised countries. Like TB in other mammals, infection is life long and, if undiagnosed, may progress to disease years after exposure. The risk of disease in humans is highly age-dependent, however in cattle, age-dependent risks have yet to be quantified, largely due to insufficient data and limited diagnostics. Here, we estimate age-specific reactor rates in Great Britain by combining herd-level testing data with spatial movement data from the Cattle Tracing System (CTS). Using a catalytic model, we find strong age dependencies in infection risk and that the probability of detecting infection increases with age. Between 2004 and 2009, infection incidence in cattle fluctuated around 1%. Age-specific incidence increased monotonically until 24-36 months, with cattle aged between 12 and 36 months experiencing the highest rates of infection. Beef and dairy cattle under 24 months experienced similar infection risks, however major differences occurred in older ages. The average reproductive number in cattle was greater than 1 for the years 2004-2009. These methods reveal a consistent pattern of BTB rates with age, across different population structures and testing patterns. The results provide practical insights into BTB epidemiology and control, suggesting that targeting a mass control programme at cattle between 12 and 36 months could be beneficial.EBP is funded by an Engineering and Physical Sciences Research Council (EPSRC) fellowship. JLNW is supported by the Alborada Trust and the RAPIDD program of the Science & Technology Directorate, U.S. Department of Homeland Security, and the Fogarty International Center, U.S. National Institutes of Health. AJKC is supported by Defra grant no. SE-3127. TJM is supported by the BBSRC. We thank Steve Holdship and Rose Nicholson at Defra the AHVLA team for providing access to the CTS and VetNet