6,811 research outputs found
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
Forward simulation MCMC with applications to stochastic epidemic models
For many stochastic models, it is difficult to make inference about the model parameters because it is impossible to write down a tractable likelihood given the observed data. A common solution is data augmentation in a Markov chain Monte Carlo (MCMC) framework. However, there are statistical problems where this approach has proved infeasible but where simulation from the model is straightforward leading to the popularity of the approximate Bayesian computation algorithm. We introduce a forward simulation MCMC (fsMCMC) algorithm, which is primarily based upon simulation from the model. The fsMCMC algorithm formulates the simulation of the process explicitly as a data augmentation problem. By exploiting non-centred parameterizations, an efficient MCMC updating schema for the parameters and augmented data is introduced, whilst maintaining straightforward simulation from the model. The fsMCMC algorithm is successfully applied to two distinct epidemic models including a birth–death–mutation model that has only previously been analysed using approximate Bayesian computation methods
Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model
The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus
occurs so rapidly that the viruses' genomes contain information on past
ecological dynamics. Hence, we develop a phylodynamic method that enables the
joint estimation of epidemiological parameters and phylogenetic history. Based
on a compartmental susceptible-infected-removed (SIR) model, this method
provides separate information on incidence and prevalence of infections.
Detailed information on the interaction of host population dynamics and
evolutionary history can inform decisions on how to contain or entirely avoid
disease outbreaks.
We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First,
five human immunodeficiency virus type 1 clusters sampled in the United Kingdom
between 1999 and 2003 are analyzed. The estimated basic reproduction ratios
range from 1.9 to 3.2 among the clusters. All clusters show a decline in the
growth rate of the local epidemic in the middle or end of the 90's.
The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the
local epidemic in the C\'ordoban city Cruz del Eje originated around 1906
(median), coinciding with an immigration wave from Europe to central Argentina
that dates from 1880--1920. The estimated time of epidemic peak is around 1970.Comment: Journal link:
http://rsif.royalsocietypublishing.org/content/11/94/20131106.ful
Efficient data augmentation for fitting stochastic epidemic models to prevalence data
Stochastic epidemic models describe the dynamics of an epidemic as a disease
spreads through a population. Typically, only a fraction of cases are observed
at a set of discrete times. The absence of complete information about the time
evolution of an epidemic gives rise to a complicated latent variable problem in
which the state space size of the epidemic grows large as the population size
increases. This makes analytically integrating over the missing data infeasible
for populations of even moderate size. We present a data augmentation Markov
chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic
epidemic model parameters, in which measurements are augmented with
subject-level disease histories. In our MCMC algorithm, we propose each new
subject-level path, conditional on the data, using a time-inhomogeneous
continuous-time Markov process with rates determined by the infection histories
of other individuals. The method is general, and may be applied, with minimal
modifications, to a broad class of stochastic epidemic models. We present our
algorithm in the context of multiple stochastic epidemic models in which the
data are binomially sampled prevalence counts, and apply our method to data
from an outbreak of influenza in a British boarding school
Fitting stochastic epidemic models to gene genealogies using linear noise approximation
Phylodynamics is a set of population genetics tools that aim at
reconstructing demographic history of a population based on molecular sequences
of individuals sampled from the population of interest. One important task in
phylodynamics is to estimate changes in (effective) population size. When
applied to infectious disease sequences such estimation of population size
trajectories can provide information about changes in the number of infections.
To model changes in the number of infected individuals, current phylodynamic
methods use non-parametric approaches, parametric approaches, and stochastic
modeling in conjunction with likelihood-free Bayesian methods. The first class
of methods yields results that are hard-to-interpret epidemiologically. The
second class of methods provides estimates of important epidemiological
parameters, such as infection and removal/recovery rates, but ignores variation
in the dynamics of infectious disease spread. The third class of methods is the
most advantageous statistically, but relies on computationally intensive
particle filtering techniques that limits its applications. We propose a
Bayesian model that combines phylodynamic inference and stochastic epidemic
models, and achieves computational tractability by using a linear noise
approximation (LNA) --- a technique that allows us to approximate probability
densities of stochastic epidemic model trajectories. LNA opens the door for
using modern Markov chain Monte Carlo tools to approximate the joint posterior
distribution of the disease transmission parameters and of high dimensional
vectors describing unobserved changes in the stochastic epidemic model
compartment sizes (e.g., numbers of infectious and susceptible individuals). We
apply our estimation technique to Ebola genealogies estimated using viral
genetic data from the 2014 epidemic in Sierra Leone and Liberia.Comment: 43 pages, 6 figures in the main tex
Enhancing Bayesian risk prediction for epidemics using contact tracing
Contact tracing data collected from disease outbreaks has received relatively
little attention in the epidemic modelling literature because it is thought to
be unreliable: infection sources might be wrongly attributed, or data might be
missing due to resource contraints in the questionnaire exercise. Nevertheless,
these data might provide a rich source of information on disease transmission
rate. This paper presents novel methodology for combining contact tracing data
with rate-based contact network data to improve posterior precision, and
therefore predictive accuracy. We present an advancement in Bayesian inference
for epidemics that assimilates these data, and is robust to partial contact
tracing. Using a simulation study based on the British poultry industry, we
show how the presence of contact tracing data improves posterior predictive
accuracy, and can directly inform a more effective control strategy.Comment: 40 pages, 9 figures. Submitted to Biostatistic
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