Efficient real-time monitoring of an emerging influenza epidemic: how feasible?

A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased, and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter non-identifiability.

[1]  Paul J. Birrell,et al.  Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in The Netherlands , 2015, Journal of The Royal Society Interface.

[2]  L. Bettencourt,et al.  Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases , 2008, PloS one.

[3]  W. Gilks,et al.  Following a moving target—Monte Carlo inference for dynamic Bayesian models , 2001 .

[4]  J. Wallinga,et al.  Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures , 2004, American journal of epidemiology.

[5]  S. Cauchemez,et al.  Estimating in real time the efficacy of measures to control emerging communicable diseases. , 2006, American journal of epidemiology.

[6]  Claudia Czado,et al.  Predictive Model Assessment for Count Data , 2009, Biometrics.

[7]  T. Hamill,et al.  Variogram-Based Proper Scoring Rules for Probabilistic Forecasts of Multivariate Quantities* , 2015 .

[8]  Leonhard Held,et al.  Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture , 2017, Statistics in medicine.

[9]  Artem Lebedev,et al.  Revealing the True Incidence of Pandemic A(H1N1)pdm09 Influenza in Finland during the First Two Seasons — An Analysis Based on a Dynamic Transmission Model , 2016, PLoS Comput. Biol..

[10]  Branko Ristic,et al.  Monitoring and prediction of an epidemic outbreak using syndromic observations. , 2011, Mathematical biosciences.

[11]  Sadanori Konishi,et al.  Inferences on Multivariate Measures of Interclass and Intraclass Correlations in Familial Data , 1991 .

[12]  Nicholas G. Polson,et al.  Tracking Epidemics With Google Flu Trends Data and a State-Space SEIR Model , 2012, Journal of the American Statistical Association.

[13]  Jakub Szymanik,et al.  Methods Results & Discussion , 2007 .

[14]  A. Dawid,et al.  On Testing the Validity of Sequential Probability Forecasts , 1993 .

[15]  Alexandros Beskos,et al.  Sequential Monte Carlo Methods for High-Dimensional Inverse Problems: A Case Study for the Navier-Stokes Equations , 2013, SIAM/ASA J. Uncertain. Quantification.

[16]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[17]  J. Rosenthal,et al.  Optimal scaling for various Metropolis-Hastings algorithms , 2001 .

[18]  Paul J. Birrell,et al.  Bayesian modeling to unmask and predict influenza A/H1N1pdm dynamics in London , 2011, Proceedings of the National Academy of Sciences.

[19]  Jun S. Liu,et al.  Blind Deconvolution via Sequential Imputations , 1995 .

[20]  Frank Ball,et al.  A threshold theorem for the Reed-Frost chain-binomial epidemic , 1983, Journal of Applied Probability.

[21]  A Donner,et al.  The estimation of intraclass correlation in the analysis of family data. , 1980, Biometrics.

[22]  Paul Fearnhead,et al.  An Adaptive Sequential Monte Carlo Sampler , 2010, 1005.1193.

[23]  N. Chopin.  A sequential particle filter method for static models , 2002 .

[24]  Simon J. Godsill,et al.  Monte Carlo Filtering of Piecewise Deterministic Processes , 2011 .

[25]  Leonhard Held,et al.  Probabilistic forecasting in infectious disease epidemiology: The thirteenth Armitage lecture , 2017, bioRxiv.

[26]  M. Girolami,et al.  Riemann manifold Langevin and Hamiltonian Monte Carlo methods , 2011, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[27]  P. Fearnhead,et al.  The Random Walk Metropolis: Linking Theory and Practice Through a Case Study , 2010, 1011.6217.

[28]  R. Eggo,et al.  Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model , 2016, Epidemics.

[29]  Simon J. Godsill,et al.  An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo , 2007, Proceedings of the IEEE.

[30]  W. Wong,et al.  Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models , 2001 .

[31]  David M. Blei,et al.  Variational Inference: A Review for Statisticians , 2016, ArXiv.

[32]  P. Fearnhead.  MCMC, sufficient statistics and particle filters. , 2002 .

[33]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[34]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[35]  H. Ahrens,et al.  Multivariate variance‐covariance components (MVCC) and generalized intraclass correlation coefficient (GICC) , 1976 .

[36]  C. Geyer.  Markov Chain Monte Carlo Maximum Likelihood , 1991 .

[37]  J. Shaman,et al.  Forecasting seasonal outbreaks of influenza , 2012, Proceedings of the National Academy of Sciences.

[38]  P. Fearnhead,et al.  Improved particle filter for nonlinear problems , 1999 .

[39]  Christopher Nemeth,et al.  Sequential Monte Carlo Methods for State and Parameter Estimation in Abruptly Changing Environments , 2014, IEEE Transactions on Signal Processing.

[40]  Adam Kucharski,et al.  Temporal Changes in Ebola Transmission in Sierra Leone and Implications for Control Requirements: a Real-time Modelling Study , 2015, PLoS currents.

[41]  Ronald Meester,et al.  Modeling and real-time prediction of classical swine fever epidemics. , 2002, Biometrics.

[42]  James S. Martin.  Some new results in sequential Monte Carlo , 2012 .

[43]  Radford M. Neal.  Sampling from multimodal distributions using tempered transitions , 1996, Stat. Comput..

[44]  Arnaud Doucet,et al.  Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo , 2011 .

[45]  G. Roberts,et al.  A novel approach to real-time risk prediction for emerging infectious diseases: a case study in Avian Influenza H5N1. , 2009, Preventive veterinary medicine.

[46]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[47]  Benjamin J. Cowling,et al.  School Closure and Mitigation of Pandemic (H1N1) 2009, Hong Kong , 2010, Emerging infectious diseases.

[48]  Anthony Lee,et al.  Accelerating Metropolis-Hastings algorithms by Delayed Acceptance , 2015, Foundations of Data Science.

[49]  Joseph Dureau,et al.  Capturing the time-varying drivers of an epidemic using stochastic dynamical systems. , 2012, Biostatistics.

[50]  A. Cook,et al.  Real-Time Epidemic Monitoring and Forecasting of H1N1-2009 Using Influenza-Like Illness from General Practice and Family Doctor Clinics in Singapore , 2010, PloS one.

[51]  Ajay Jasra,et al.  On population-based simulation for static inference , 2007, Stat. Comput..

[52]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .