Estimation of multiple transmission rates for epidemics in heterogeneous populations

Cook, Alex R.; Otten, Wilfred; Marion, Glenn; Gibson, Gavin J.; Gilligan, Christopher A.

doi:10.1073/pnas.0706461104

Cited by 57 publications

(66 citation statements)

References 41 publications

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“…Also, in contrast to other approaches, for example posterior predictive checks, our method uses the full posterior distribution of unobserved data and model parameters, and may offer a higher sensitivity to model mis-specifications. As it is common practice to conduct Bayesian analyses of partially observed epidemics using data augmentation supported by computational techniques, for example MCMC methods [5,20,27,28], the framework represents a potentially valuable addendum to the model-testing toolkit used in epidemiological and ecological studies.…”

Section: Discussionmentioning

confidence: 99%

“…A further approach to model checking is to compare the posterior predictive distribution of summary statistics with their observed values [20,28]. In the electronic supplementary material, Section 6, we consider posterior predictive checks based on common spatial autocorrelation measures including Moran's I and Geary's c indices [33], where application to simulated data shows that these measures are insensitive to the choice of model.…”

Section: Comparison With Common Bayesian Model Checking Techniquesmentioning

confidence: 99%

“…It is now standard practice to conduct Bayesian analyses of partially observed epidemics using the process of data augmentation supported by computational techniques such as Markov chain Monte Carlo (MCMC) methods [5,20,27,28]. Given partial data y, these approaches involve simulating from the joint posterior distribution pðu, zjyÞ, where z represents the complete epidemic data as above.…”

Section: Bayesian Inference and Model Assessmentmentioning

confidence: 99%

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

Lau

Marion

Streftaris³

et al. 2014

J. R. Soc. Interface.

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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 misspecifications 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.

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Section: Discussionmentioning

confidence: 99%

Section: Comparison With Common Bayesian Model Checking Techniquesmentioning

confidence: 99%

Section: Bayesian Inference and Model Assessmentmentioning

confidence: 99%

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

Lau

Marion

Streftaris³

et al. 2014

J. R. Soc. Interface.

Self Cite

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“…Rhizoctonia has a latent period, LP, of 2.5 days (Gibson et al 2004) and an infectious period, IP, of about 15 days (Cook et al 2007). The virulence can thus be approximated by 1.…”

Section: Severity 4mentioning

confidence: 99%

Periodic host absence can select for higher or lower parasite transmission rates

et al. 2010

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1This paper explores the effect of discontinuous periodic host absence on the evolution of 2 pathogen transmission rates by using R 0 maximisation techniques. The physiological 3 consequence of an increased transmission rate can be either an increased virulence, i.e. there 4 is a transmission-virulence trade-off or ii) a reduced between season survival, i.e. there is a 5 transmission-survival trade-off. The results reveal that the type of trade-off determines the 6 direction of selection, with relatively longer periods of host absence selecting for higher 7 transmission rates in the presence of a trade-off between transmission and virulence but lower 8 transmission rates in the presence of a trade-off between transmission and between season 9 survival. The fact that for the transmission-virulence trade-off both trade-off parameters 10 operate during host presence whereas for the transmission-survival trade-off one operates 11 during host presence (transmission) and the other (survival) during the period of host absence 12 is the main cause for this difference in selection direction. Moreover, the period of host 13 absence seems to be the key determinant of the pathogen's transmission rate. Comparing plant 14 patho-systems with contrasting biological features suggests that airborne plant pathogens 15 respond differently to longer periods of host absence than soil-borne plant pathogens. 16 17 3

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“…Bayesian percolation models have proven popular for modeling spatio-temporal dynamical processes (e.g., Catterall et al, 2012;Gibson et al, 2006) and have been applied to epidemics (e.g., Cook et al, 2007), but they ignore the true process hidden behind the noisy data. More recent Bayesian hierarchical models, which are widely used for mapping non-infectious diseases, aim to capture the true spatial process (e.g., Besag et al, 1991;Carlin and Banerjee, 2002), but their process models and parameter models are not appropriate for epidemics.…”

Section: S(t) + I(t) + R(t) = Nmentioning

confidence: 99%

Bayesian hierarchical statistical SIRS models

Zhuang

Cressie

2014

Stat Methods Appl

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The classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are "mass balanced. " Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynam-ical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS (CSIRS) model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic. AbstractThe classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are "mass balanced." Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynamical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS (CSIRS) model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic.

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Estimation of multiple transmission rates for epidemics in heterogeneous populations

Cited by 57 publications

References 41 publications

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

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

Periodic host absence can select for higher or lower parasite transmission rates

Bayesian hierarchical statistical SIRS models

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